3 


3.1 
General 

3.1.1 
DYNAMICS Branch of theoretical mechanics dealing with the motion and equilibrium of bodies and mechanical systems under the action of forces. Note: Sometimes the terms KINETICS and KINETOSTATICS are applied to the same field or some aspects of it. 

3.1.2 
STATICS Branch of theoretical mechanics dealing with the equilibrium of bodies under the action of forces. 

3.1.3 
ENGINE [PRIME MOVER] Machine designed to transform any other form of energy into mechanical energy. 

3.2 
Force and moment 

3.2.1 
FORCE Action of its surroundings on a body tending to change its state of rest or motion. 

3.2.2 
LINE OF ACTION OF A FORCE Straight line along which the vector representing a given force lies. 

3.2.3 
MAGNITUDE OF A FORCE Number of units of force obtained by comparing a given force with a standard, taken as unit force. 

3.2.4 
ACTIVE [APPLIED] FORCE Force capable of producing motion. 

3.2.5 
REACTION Force arising in a constraint and acting upon a constrained body due to the action of an active force upon that body. 

3.2.6 
NORMAL REACTION Component of reaction perpendicular to the surface of a body. 

3.2.7 
TANGENTIAL REACTION Component of reaction tangential to the surface of a body. 

3.2.8 
CENTRIPETAL FORCE Force causing the centripetal acceleration of a particle. 

3.2.9 
INERTIA FORCE Product of the mass of a particle and the negative of its acceleration. Following D'Alembert, the inertia force can be regarded as being in equilibrium with the resultant of the all the forces acting on the particle. 

3.2.10 
CENTRIFUGAL FORCE Inertia force of a particle moving uniformly along a circular path.. 

3.2.11 
CORIOLIS FORCE Inertia force equal to the product of the mass of a particle and the negative of its Coriolis component of acceleration. 

3.2.12 
RELATIVE FORCE Inertia force equal to the product of the mass of a particle and the negative of its acceleration relative to a moving frame of reference. 

3.2.13 
TRANSPORTATION FORCE Inertia force equal to the product of the mass of a particle and the negative of its transportation acceleration. 

3.2.14 
CENTRAL FORCE Force whose line of action at all times and at every point in space passes through one fixed point (the centre). 

3.2.15 
EXTERNAL FORCE Force due to the action of another body or system on the body or system under consideration. 

3.2.16 
INTERNAL FORCE Force acting upon a particle or set of particles of a given system, originating from another particle or set of particles in the same system. 

3.2.17 
ELASTIC FORCE Internal force arising in an elastically strained body. 

3.2.18 
CONCENTRATED FORCE Force whose action may be regarded as being applied at a point. 

3.2.19 
DISTRIBUTED [CONTINUOUS] FORCE Force that is spread along a line or over a surface. 

3.2.20 
BODY FORCE Force which acts on the elements of the volume of a body. 

3.2.21 
SURFACE FORCE Force whose action is distributed over the surface or part of the surface of a body. 

3.2.22 
COMPRESSIVE FORCE Normal component of a force that acts on the surface of a body and which is directed into the body. 

3.2.23 
TENSILE FORCE Normal component of a force that acts on the surface of a body and which is directed out from the body. 

3.2.24 
AXIAL [LONGITUDINAL] FORCE Force that acts normal to a given crosssection of bar and through its centroid. 

3.2.25 
SHEAR [SHEARING, TRANSVERSE] FORCE Force that acts normal to the central axis of a bar. 

3.2.26 
CRITICAL FORCE (FOR A BAR IN COMPRESSION) Maximum compressive force that can be sustained by a bar in stable equilibrium. 

3.2.27 
EQUIVALENT [REDUCED] FORCE Force applied at an arbitrary point in a mechanism such that its power equals the power of the given set of forces. 

3.2.28 
BEARING FORCE Action of one link of a mechanism upon another at a bearing. 

3.2.29 
SHAKING FORCE {MOMENT} Resultant of all inertia forces {moments of inertia forces} of the moving links of a mechanism. 

3.2.30 
IMPULSIVE FORCE Force existing during an interval of time that is short compared to the time constant of the system to which it is applied. 

3.2.31 
IMPULSE Integral with respect to time of a force over the interval during which it acts. 

3.2.32 
DETERMINISTIC FORCE Force that is fully determined at any instant of time. 

3.2.33 
STOCHASTIC FORCE Force the magnitude and/or direction of which varies in a stationary random manner but is not completely random. 

3.2.34 
MOMENT OF A FORCE ABOUT AN AXIS Component along a given axis of the moment of a force about any point on the axis. 

3.2.35 
MOMENT OF A FORCE ABOUT A POINT Vector product of a radius vector from the point to the line of action of the force and the force itself. 

3.2.36 
MOMENT ARM Shortest distance to the line of action of a force from a given point. 

3.2.37 
COUPLE 1. Pair of parallel forces that are equal in magnitude, but opposite in sense. 2. Vector moment of two parallel forces that are equal in magnitude but opposite in sense. 

3.2.38 
MOMENT OF A COUPLE Vector sum of the moments about any point in space of the forces that form a given couple. 

3.2.39 
RESULTANT MOMENT Moment equal to the vector sum of the moments of all the forces of a system about a chosen point. 

3.2.40 
BENDING MOMENT Component in the plane of a crosssection of a bar of the moments about its centroid of forces acting on that crosssection. 

3.2.41 
TORSIONAL MOMENT [TWISTING MOMENT, TORQUE] Component normal to the plane of a crosssection of a bar of the moments about the centroid of the forces acting on the crosssection. 

3.2.42 
INPUT TORQUE Torque applied to driving (or input) link of a mechanism. 

3.2.43 
OUTPUT TORQUE Torque supplied by the output link of a mechanism. 

3.2.44 
EQUIVALENT [REDUCED] MOMENT Couple whose power, when applied to a chosen link of a mechanism, equals the power of the actual forces and couples that act on the mechanism. 

3.2.45 
INERTIA [D'ALEMBERT] COUPLE Moment equal to the product of the moment of inertia of a body and the negative of its angular acceleration. 

3.2.46 
EQUIVALENT FORCE SYSTEM Set of forces whose resultant force and moment with respect to a chosen point equal those of the original set of forces. 

3.2.47 
RESULTANT FORCE Vector sum of a set of forces. 

3.2.48 
PARALLEL FORCE SYSTEM Set of forces whose lines of action are parallel. 

3.2.49 
COPLANAR FORCE SYSTEM Set of forces whose lines of action lie in one plane. 

3.2.50 
CONCURRENT FORCE SYSTEM Set of forces whose lines of action intersect each other at one point. 

3.2.51 
SPATIAL FORCE SYSTEM Set of forces whose lines of action do not lie in one plane. 

3.2.52 
WRENCH Set of forces that can be reduced to a resultant force and a couple whose vector is parallel to the force. 

3.2.53 
EQUILIBRIUM State of a system of forces and couples when the resultant force and the resultant couple of the system are simultaneously zero. 

3.2.54 
BALANCING Act of distributing the masses of the links of a mechanism so that the resultant inertia force and couple exerted on the frame are zero. 

3.2.55 
STATIC BALANCE (OF A ROTATING BODY) State in which the mass of a rotor is distributed so that its centre of mass lies on its axis of rotation. 

3.2.56 
DYNAMIC BALANCE (OF A ROTATING BODY) State in which the mass of a rotor is distributed so that the axis of rotation coincides with one of the principal axes of inertia. 

3.2.57 
BALANCED MECHANISM Mechanism whose inertia forces are in equilibrium. 

3.2.58 
LOAD Set of active forces acting upon a body or system. 

3.2.59 
CONTINUOUS [DISTRIBUTED] LOAD Load whose points of application continuously fill a given segment or surface. 

3.2.60 
UNIFORM [UNIFORMLY DISTRIBUTED] LOAD Distributed load whose magnitude per unit area or length is constant. 

3.2.61 
DEAD [FIXED, PERMANENT] LOAD Load consisting of forces whose values, directions and points of application to a given body are invariant. 

3.2.62 
LIVE LOAD Load that varies in its point of application and/or with time. 

3.2.63 
DYNAMIC LOAD Load changing so fast that inertia forces are not negligible. 

3.2.64 
ALTERNATING LOAD Load varying periodically between limits that are equal in absolute value, but opposite in sign. 

3.2.65 
PULSATING LOAD Load varying periodically between limits of the same sign. 

3.2.66 
ROLLING LOAD Load consisting of a set of forces which are constant in value and direction, but whose points of application change their position in relation to the given body. 

3.2.67 
FOLLOWER LOAD Load whose direction relative to the structure on which it acts remains constant as the structure deflects. 

3.2.68 
CRITICAL LOAD Least load to cause the loss of stability of a structure. 

3.2.69 
FIELD OF FORCE Region of space in which force is a function of position. 

3.2.70 
FORCE FUNCTION The function whose partial derivatives give the components of force in the direction of differentiation. 

3.2.71 
CONSERVATIVE FIELD OF FORCE Field of force possessing potential. 

3.2.72 
CONSERVATIVE FORCE Force of a potential field of forces. 

3.2.73 
NONCONSERVATIVE FORCE Force having a component dissipating energy from, or imparting energy to, a system. 

3.2.74 
DISSIPATIVE FORCE Force which, during the motion of a system, causes a loss in the total mechanical energy of the system, due to its transformation into other forms of energy. 

3.2.75 
GENERALIZED FORCE Quantity which, when multiplied by a virtual increment of one generalized coordinate, meanwhile the other generalized coordinates remain unchanged, gives the virtual work of all the forces of the system. 

3.2.76 
(RAYLEIGH) DISSIPATION FUNCTION Function of generalized coordinates and generalized velocities of a system such that its partial derivatives with respect to the generalized velocities and reversed in sign equal the corresponding generalized dissipative forces. 

3.3 
Momentum, energy, work and power 

3.3.1 
MOMENTUM [LINEAR MOMENTUM] Vector sum of the products of the velocities and masses of the individual particles of a system of one or more particles. 

3.3.2 
GENERALIZED MOMENTUM Partial derivative of the kinetic energy of a system with respect to a generalized velocity. 

3.3.3 
MOMENT OF MOMENTUM Vector product between a radius vector drawn from the point about which moments are being taken to a momentum vector, and the momentum vector itself. 

3.3.4 
ANGULAR MOMENTUM (OF A BODY) Vector equal to the product of the moment of inertia of a body about a given principal axis and its angular velocity about the same axis. 

3.3.5 
CANONICAL [HAMILTONIAN] VARIABLE Generalized coordinate or generalized momentum. 

3.3.6 
CYCLIC [CYCLIC IGNORABLE] COORDINATE Generalized coordinate that does not appear explicitly in the function for the kinetic potential, but in the form of its derivative with respect to time. 

3.3.7 
APPARENT MOTION Motion in which the noncyclic coordinates change. 

3.3.8 
CONCEALED MOTION Motion in which only the cyclic coordinates change. 

3.3.9 
PERTURBATION Deviation of system variables from a reference state. 

3.3.10 
INITIAL CONDITION Value of a dependent variable such as displacement, velocity, etc. of a system at the instant of time taken as the origin. 

3.3.11 
HAMILTONIAN FUNCTION Total (mechanical) energy of a system expressed through canonical variables. 

3.3.12 
LAGRANGIAN FUNCTION [KINETIC POTENTIAL] Difference between the kinetic energy and the potential energy of a system. 

3.3.13 
POTENTIAL ENERGY (OF A PARTICLE) Scalar quantity equal to the work done in a conservative force field in moving a particle from a given position to a reference position where the potential energy is conventionally taken to be zero. 

3.3.14 
POTENTIAL ENERGY (OF A SYSTEM) Sum of potential energies of all particles of a system. 

3.3.15 
STRAIN ENERGY Work done by the internal forces of an elastic body in restoring it from a deformed state to its undeformed state. 

3.3.16 
KINETIC ENERGY (OF A PARTICLE) Energy of motion. It equals ½ m v2 for a particle of mass m and velocity v. 

3.3.17 
KINETIC ENERGY (OF A SYSTEM) Sum of kinetic energies of all particles of the system. 

3.3.18 
MECHANICAL ENERGY Sum of kinetic and potential energies . 

3.3.19 
WORK Integral of elementary work for a finite displacement. 

3.3.20 
ELEMENTARY WORK Scalar product of a force and elementary displacement at its point of application. 

3.3.21 
VIRTUAL WORK The work done by a force in a virtual displacement of the point at which it acts. 

3.3.22 
WORK OF DEFORMATION Work done by external forces during the deformation of a body. 

3.3.23 
POWER Rate of work with respect to time. 

3.3.24 
POWER OF A FORCE Scalar product of a force and the velocity of its point of action. 

3.3.25 
EFFECTIVE [USEFUL] POWER Mean output power of a machine at its steady state. 

3.3.26 
MECHANICAL EFFICIENCY Ratio of the effective power of a machine to the power that is necessary to drive it. 

3.3.27 
CYCLIC EFFICIENCY (OF A MACHINE) Ratio of the net work output of a machine to the work that is required to drive it during a complete period of its steady motion. 

3.4 
Principles 

3.4.1 
PRINCIPLE OF WORK AND ENERGY Principle according to which the change in the sum of kinetic and potential energies of a system is equal to the work done by all the forces acting upon the system during an interval of its motion. 

3.4.2 
PRINCIPLE OF CONSERVATION OF (MECHANICAL) ENERGY Principle according to which the mechanical energy of a system moving in a conservative field of forces remains constant. 

3.4.3 
PRINCIPLE OF MOMENTUM Principle according to which the change in momentum of a system in a given interval of time is equal to the total impulse acting on the system in the same interval of time. 

3.4.4 
PRINCIPLE OF CONSERVATION OF MOMENTUM Principle according to which the momentum of a system remains constant if the resultant force of the external forces acting on the system is zero during some interval of time. 

3.4.5 
PRINCIPLE OF MOMENT OF MOMENTUM Principle according to which the derivative with respect to time of the moment of momentum of a system about a fixed point or axis is equal to the sum of the moments of all the forces acting upon the system about this point or axis. 

3.4.6 
PRINCIPLE OF CONSERVATION OF MOMENT OF MOMENTUM [ANGULAR MOMENTUM] Principle according to which the moment of momentum of a system about a fixed point is constant when the resultant moment of the external forces is zero. 

3.4.7 
PRINCIPLE OF MOTION OF CENTRE OF MASS Principle according to which the centre of mass of a system moves as if it were a particle with mass equal to the total mass of the system and as if the resultant external force were acting on it. 

3.4.8 
SUPERPOSITION PRINCIPLE Principle according to which the responses of a linear system to independent excitations are additive. 

3.4.9 
PRINCIPLE OF VIRTUAL WORK Principle according to which the necessary and sufficient condition of equilibrium of a system is that the virtual work done by forces acting upon the system in an arbitrary virtual displacement is zero. 

3.4.10 
D’ALAMBERT’S PRINCIPLE Principle according to which the external forces that act on a body can be viewed as being in equilibrium with its inertia force. Similarly external moments can be viewed as being in equilibrium with the body’s inertial couple. 

3.4.11 
HAMILTON'S PRINCIPLE Principle according to which the integral of the Lagrangian function with respect to time for actual motion attains a value which is extreme, when compared with all other conceivable motions of a given system. 

3.4.12 
GALILEO'S LAW OF RELATIVITY Law stating that every system of reference moving with respect to a given inertial system with uniform rectilinear translation is also an inertial system. 

3.4.13 
LAW OF (UNIVERSAL) GRAVITATION Law stating that every particle attracts every other particle with a force that is proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. 

3.4.14 
NEWTON'S FIRST LAW (OF MOTION) [FIRST PRINCIPLE OF DYNAMICS] Law according to which a particle subject only to forces in equilibrium continues in its state of rest or uniform rectilinear motion. 

3.4.15 
NEWTON'S SECOND LAW (OF MOTION) [SECOND PRINCIPLE OF DYNAMICS] Law stating that the product of the mass of a particle and its acceleration is at any given instant equal to the resultant force acting on the particle. 

3.4.16 
NEWTON'S THIRD LAW (OF MOTION) [THIRD PRINCIPLE OF DYNAMICS] Law stating that the forces of action and reaction between bodies in contact have the same magnitude, same line of action, but opposite sense. 

3.5 
Structural behaviour and characteristics 

3.5.1 
DENSITY 1. Mass of a homogeneous body divided by its volume. 2. Derivative of mass with respect to volume. 

3.5.2 
ELASTICITY Property of a body to recover its original shape and size immediately after removal of the external forces which cause it to deform. 

3.5.3 
ELASTIC HYSTERESIS Incomplete reversibility of the work of deformation occurring in solid bodies. 

3.5.4 
YOUNG'S MODULUS OF ELASTICITY Ratio of the change in stress to the change in strain for a material that obeys Hooke’s law. 

3.5.5 
HOOKE'S LAW Law of proportionality between stress and strain for linearelastic materials. 

3.5.6 
PLASTICITY Property of a body whereby some deformation persists after the forces that originally caused it have been removed. 

3.5.7 
STIFFNESS Measure of the ability of a body or structure to, resist deformation due to the action of external forces. 

3.5.8 
COMPLIANCE [FLEXIBILITY] Measure of the ability of a body or structure to exhibit a deformation due to the action of external forces (reciprocal of stiffness). 

3.5.9 
STIFFNESS (COEFFICIENT) Change of force (or torque) divided by the corresponding translational (or rotational) displacement of an elastic element. 

3.5.10 
ANISOTROPY Variation of the physical properties in a body with direction. 

3.5.11 
ISOTROPY Independence of direction of the physical properties of a body. 

3.5.12 
LONGITUDINAL RIGIDITY Ratio of the magnitude of an axial force on a bar to the change in length that it causes. 

3.5.13 
TORSIONAL RIGIDITY Ratio of the magnitude of an axial torque on a bar to the angle of twist that it causes. 

3.5.14 
BENDING STIFFNESS [FLEXURAL RIGIDITY] Ratio of the magnitude of a bending moment on a bar to the change in curvature that it causes. 

3.5.15 
MODULUS OF RIGIDITY [SHEAR MODULUS] Ratio shear stress to the shear strain that it causes. 

3.5.16 
STRAIN Change in the dimensions or shape of a body due to stress. 

3.5.17 
ELASTIC STRAIN [DEFORMATION] Strain that disappears after removal of the static system of forces causing it. 

3.5.18 
PLASTIC STRAIN [PLASTIC DEFORMATION, PERMANENT SET] Strain that does not disappear after removal of the static system of external forces causing it. 

3.5.19 
TORSION [TWIST] Rotational deformation of a shaft or bar about its axis as a result of torque applied about that axis. 

3.5.20 
DIRECT [LONGITUDINAL] STRAIN Fractional change in length. 

3.5.21 
ANGLE OF TWIST [TORSION] Angle of relative rotation of two crosssections of a bar or shaft about its longitudinal axis. 

3.5.22 
SHEAR STRAIN [ANGLE OF DEFORMATION] Change in the angle (in radians) between two straight lines that are drawn perpendicular to each other in a body when the body is undeformed. 

3.5.23 
DEFLECTION (OF A BEAM) Displacement of a point on the longitudinal axis of a beam in bending, in a direction normal to this axis. 

3.5.24 
DEFLECTION (OF A PLATE) Displacement of a point in the middle surface of a plate in the direction normal to this surface. 

3.5.25 
BUCKLING (OF A BAR OR PLATE) Bending of a member that is initially straight or flat due to instability when a compressive stress induced in it exceeds a critical value. 

3.5.26 
EQUIVALENT BUCKLING LENGTH (OF A BAR) Length of the bar, pinjointed at its ends, which has the same critical load as a given bar of the same material and the same crosssection. 

3.5.27 
SLENDERNESS RATIO (OF A BAR) Ratio of the equivalent buckling length of a bar to the radius of gyration of its crosssection with respect to the axis about which bending takes place during buckling. 

3.5.28 
LATERAL BUCKLING (OF A BEAM) Loss of stability of a beam bent about one transverse, as a result of which bending occurs about another transverse axis. 

3.5.29 
VIRTUAL DEFORMATION Arbitrary deformation of a body or a structure during which the magnitudes and directions of the forces and the stresses are considered to remain constant. 

3.5.30 
STRESS Limit of the ratio of force to the area it acts, as the area tends to zero. 

3.5.31 
NORMAL STRESS Component of stress in the direction normal to the element of surface on which the stress acts. 

3.5.32 
SHEAR STRESS Component of stress lying in the plane of the surface on which it acts. 

3.5.33 
TENSION State in which forces on the ends of a bar tend to extend it. 

3.5.34 
AXIAL TENSION Tension in which the resultant force acts through the centroid of the crosssection of a bar. 

3.5.35 
COMPRESSION State in which forces on the ends of a bar tend to reduce its length. 

3.5.36 
ULTIMATE STRENGTH Limit of resistance of the internal forces in a solid body to external forces acting upon it. 

3.5.37 
BENDING State of stress tending to change the curvature of the longitudinal axis of a bar or central plane of a plate. 

3.5.38 
SHEARING State of stress on a crosssection of a bar in which the shear stresses have a nonzero resultant. 

3.5.39 
SHEAR [FLEXURAL] CENTRE Point in the crosssection of a beam in bending through which the resultant of the shear stresses must act for the angle of twist to be zero. 

3.5.40 
CENTRE OF TWIST Point about which the crosssection of a bar in torsion rotates. 

3.5.41 
ELASTIC AXIS [LINE] Locus of the shear centres of the crosssections of a beam. 

3.5.42 
NEUTRAL AXIS Straight line which lies in the plane of the crosssection of a beam in bending and along which the normal stresses are zero. 

3.5.43 
FRICTION Complex of phenomena arising in the contact area between two bodies and which resists any relative motion between them. 

3.5.44 
SLIDING [KINETIC] FRICTION Friction occurring when sliding takes place between the surfaces of two bodies in contact. 

3.5.45 
ROLLING FRICTION Resistance to motion that occurs when one deformable body rolls on another. 

3.5.46 
PIVOTING [SPIN] FRICTION Friction due to relative rotation of two bodies about the common normal at their point of contact. 

3.5.47 
STATIC FRICTION Friction between two bodies that are at rest relative to each other. 

3.5.48 
LIMITING FRICTION Static friction when slip is impending. 

3.5.49 
FRICTIONAL FORCE Tangential reaction resisting the relative movement of two bodies whose surfaces are in contact. 

3.5.50 
COEFFICIENT OF (STATIC) FRICTION Ratio of the magnitude of the limiting frictional force to the magnitude of the normal component of the reaction. 

3.5.51 
ANGLE OF FRICTION Greatest possible angle between the reactions of two bodies in contact and the common normal to their surfaces at the point of contact. 

3.5.52 
CONE OF FRICTION Conical surface within which the reactions between two bodies in contact must lie. 

3.5.53 
MECHANICAL SHOCK Excitation in the form of a sudden change in force, position , velocity or acceleration, accompanied by a rapid transient transmission of mechanical energy. 

3.5.54 
IMPACT Sudden contact of short duration between two bodies. 

3.5.55 
IMPACT FORCE Force between contacting bodies during impact. 

3.5.56 
CENTRAL IMPACT Impact in which the impact forces pass through the centres of mass of the colliding bodies. 

3.5.57 
ECCENTRIC IMPACT Impact in which the impact forces on two colliding bodies do not pass through at least one of the centres of mass. 

3.5.58 
DIRECT IMPACT Impact in which the relative velocities of the centres of mass of two colliding bodies are in the direction of the common normal to their surfaces at the point of contact. 

3.5.59 
OBLIQUE IMPACT Impact in which the relative velocities of the centres of mass of the bodies are not in the direction of the common normal to their surfaces at the point of contact. 

3.5.60 
LONGITUDINAL IMPACT Impact wherein the impact force is along the centre line of a bar. 

3.5.61 
TRANSVERSE IMPACT Impact wherein the impact force is perpendicular to the centre line of a bar. 

3.5.62 
ELASTIC IMPACT Impact in which only elastic deformation occurs in the region of contact between two colliding bodies. 

3.5.63 
INELASTIC IMPACT Impact in which only plastic deformation occurs in the region of contact between two colliding bodies. 

3.5.64 
COMPRESSION PERIOD Interval of time during which impact forces are increasing. 

3.5.65 
RESTITUTION PERIOD Interval of time during which impact forces decrease to zero. 

3.5.66 
COEFFICIENT OF RESTITUTION Ratio of the magnitude of the impulse of an impact force in the restitution period to the magnitude of the impulse of impact force in the compression period. 

3.5.67 
CENTRE OF PERCUSSION Point in a body which is free to rotate about a fixed axis, through which the line of action of an applied impulse must pass if there is to be no impulsive reaction at the fixed axis. 

3.5.68 
FORCE OF GRAVITY Force of attraction arising from the law of gravitation. 

3.5.69 
WEIGHT Magnitude of the force of gravity on a body. 

3.5.70 
GRAVITATIONAL FIELD Field of force in which the force acting upon a particle is gravitational. 

3.5.71 
ACCELERATION DUE TO GRAVITY Acceleration produced by the force of gravity. (Note: By international agreement, the value g = 9.806 m/s2 has been chosen as the standard acceleration due to gravity) . 

3.5.72 
GYROSCOPIC [GYRO] EFFECT [GYROSTATIC ACTION] Effect of inertia of a rotating rigid bodymanifesting by its precession after a forced angular change of the spin axis of the body. 

3.6 
Structural concepts 

3.6.1 
RIGID BODY Theoretical model of a solid body in which the distances between particles are considered to be constant, regardless of any forces acting upon the body. 

3.6.2 
ELASTIC BODY Body that can deform elastically. 

3.6.3 
HOMOGENEOUS BODY Body whose physical properties are the same at all points. 

3.6.4 
ISOTROPIC BODY Body within which physical properties are independent of direction. 

3.6.5 
HETEROGENEOUS BODY Body whose physical properties are not the same at all points. 

3.6.6 
BAR [ROD] Body whose transverse dimensions are small in comparison with its length. 

3.6.7 
STRING Member infinitely flexible and capable of carrying only a tensile force. 

3.6.8 
STRUT [COLUMN] Straight bar subjected to compression. 

3.6.9 
CURVED BAR Bar whose centre line in its unloaded state is curved. 

3.6.10 
ARCH Curved bar that acts primarily in compression. 

3.6.11 
SPRING Elastic body shaped so that it can suffer substantial elastic deformation. 

3.6.12 
TRUSS [FRAMEWORK] System of bars connected at their ends to form a rigid structure. 

3.6.13 
BEAM Bar loaded with forces perpendicular to its longitudinal axis. 

3.6.14 
SIMPLYSUPPORTED BEAM Beam on two supports which prevent transverse movement only. 

3.6.15 
CONTINUOUS BEAM Beam resting on three or more supports. 

3.6.16 
CANTILEVER BEAM Beam having one end fully restrained and the other end free. 

3.6.17 
SPAN (OF A BEAM) Distance between the two adjacent points of support of a beam. 

3.6.18 
GRID [GRILLAGE] Two or more sets of parallel beams with all the beams in one plane and the axes of the sets intersecting. 

3.6.19 
THICK PLATE Plate whose thickness is of the same order as other dimensions. 

3.6.20 
THIN PLATE Plate whose thickness is small compared with all other dimensions. 

3.6.21 
MEMBRANE Thin plate or shell with negligible flexural rigidity. 

3.6.22 
MIDDLE SURFACE (OF A PLATE) Surface that bisects the thickness of a plate. 

3.6.23 
DISK Plate whose middle surface is circular in shape. 

3.6.24 
CYLINDRICAL SHELL Shell whose middle surface is cylindrical. 

3.6.25 
SANDWICH STRUCTURE Beam, plate or shell constructed in three layers, the properties of the middle layer being different from those of the outer layers. 

3.6.26 
MULTILAYERED STRUCTURE Beam, plate or shell which has two or more layers with differing physical properties. 

3.6.27 
SMOOTH SUPPORT Support that offers no frictional restraint. 

3.6.28 
SIMPLE [FREE] SUPPORT Support that allows only a rotation about a particular axis. 

3.6.29 
ELASTIC SUPPORT Support that deflects elastically under the load of the body supported. 

3.6.30 
ROLLER SUPPORT Support that allows a rotation about an axis and a translation in a direction perpendicular to that axis. 

3.6.31 
FOUNDATION Supporting structure 

3.6.32 
ELASTIC FOUNDATION Elastic body constituting a continuous support for a beam or plate. 

3.7 
Dynamical concepts 

3.7.1 
PARTICLE [POINT MASS] Geometrical point to which a finite mass is assigned. 

3.7.2 
MASS (OF A PARTICLE) Amount of matter in a particle as measured by the force necessary to cause unit acceleration of the particle. 

3.7.3 
MASS (OF A BODY) Sum of the masses of the particles that make up a body. 

3.7.4 
CENTRE OF MASS Point in a body or system of particles such that the sum (integral) taken over all the particles, of the vector drawn from the point in question to each particle and multipled by the mass of the particle is zero. 

3.7.5 
CENTRE OF GRAVITY Point in a body at which the resultant of the gravitational forces on its component particles acts. 

3.7.6 
EQUIVALENT [REDUCED] MASS OF A MECHANISM Mass to be attached to a particular point in a mechanism so that its kinetic energy is equal to the sum of the kinetic energy of all links in the mechanism. 

3.7.7 
MOMENT OF INERTIA Sum (integral) of the products of the masses of the individual particles (elements of mass) of a solid body and the squares of their distances from a given axis. 

3.7.8 
POLAR MOMENT OF INERTIA OF A LAMINA Sum (integral) of the products of the masses of the individual particles (elements of mass) of a lamina and the squares of their distances from its centroid. 

3.7.9 
POLAR MOMENT OF INERTIA OF A BODY Moment of inertia of an axisymmetric body about its axis of symmetry. 

3.7.10 
PRODUCT OF INERTIA Sum (integral) of the products of the masses of individual particles (elements of mass) of a solid body and their distances from two mutually perpendicular planes. 

3.7.11 
PRINCIPAL AXIS (OF INERTIA) One of three mutually perpendicular axes intersecting each other at a given point with respect to which the products of inertia of a solid body are zero. 

3.7.12 
PRINCIPAL MOMENT OF INERTIA Moment of inertia about a principal axis of inertia. 

3.7.13 
INERTIA TENSOR Symmetrical tensor whose components for a rigid body are three moments of inertia and the negatives of three products of inertia about the axes of a system of coordinates fixed in the body. 

3.7.14 
EQUIVALENT [REDUCED] MOMENT OF INERTIA (OF A MECHANISM) Moment of inertia about its fixed axis of rotation that is assigned to a member of a mechanism so that the kinetic energy of that link is equal to the total kinetic energy of the actual mechanism. 

3.7.15 
RADIUS OF GYRATION Distance from an axis of a point at which the total mass of a body may be concentrated so as to have the same moment of inertia about that axis as the original body. 

3.7.16 
ELLIPSOID OF INERTIA [MOMENTAL ELLIPSOID, POINSOT ELLIPSOID OF INERTIA] Locus of the ends of vectors measured from a given point and along every axis through this point, the lengths of the vectors being inversely proportional to the radii of gyration. 

3.7.17 
CENTRAL ELLIPSOID OF INERTIA Ellipsoid of inertia for the centre of mass. 

3.7.18 
CENTROID Point whose cartesian coordinates are the mean values of the coordinates of all the points that constitute a given line, surface or solid. 

3.7.19 
CENTRAL AXIS Locus of the centroids of the crosssections of a bar. 

3.7.20 
CONSTRAINT Restriction imposed on the positions and velocities of a system that must be fulfilled at any instant. 

3.7.21 
UNILATERAL CONSTRAINT Requirement that a particular variable should not be less than a given datum value, or alternatively that it should not be greater than a given datum value. 

3.7.22 
BILATERAL CONSTRAINT Constraint expressed by equations linking the coordinates of the particles of a system (and possibly their derivatives with respect to time) and time. 

3.7.23 
GEOMETRIC CONSTRAINT Constraint whose equations depend only on the coordinates of the points of a system and, possibly, on time. 

3.7.24 
DIFFERENTIAL CONSTRAINT Constraint whose equations depend not only on coordinates of the points of a system but also on their first derivatives with respect to time and, possibly, on time. 

3.7.25 
RHEONOMIC CONSTRAINT Constraint that is dependent on time. 

3.7.26 
SCELERONOMIC CONSTRAINT Constraint that is independent of time. 

3.7.27 
HOLONOMIC CONSTRAINT Geometric constraint or a differential constraint whose equations are integrable. 

3.7.28 
NONHOLONOMIC CONSTRAINT Differential constraint whose equations are not integrable. 

3.7.29 
DEGREE OF FREEDOM (OF A MECHANICAL SYSTEM) Number of independent generalized coordinates required to define completely the configuration of a system at any instant of time. 

3.7.30 
MECHANICAL MOBILITY Complex velocity response at a point in a linear system to a unit force excitation applied at the same point or another point in the system (inverse of mechanical impedance). 

3.7.31 
DIRECT [DRIVINGPOINT] MOBILITY Complex velocity response at a point in a linear system to a unit force excitation applied at the same point or another point in the system and in the same direction as the force (inverse of direct [driving  point] impedance). 

3.7.32 
DIRECT RECEPTANCE Amplitude of the displacement in a linear system that is at the same point and in the same direction as the simple harmonic force excitation of unit amplitude that causes it. 

3.7.33 
CROSS RECEPTANCE Amplitude of the displacement at a point in a linear system due to a simple harmonic force excitation of unit amplitude applied at another point. 

3.7.34 
EQUILIBRIUM CONFIGURATION Geometrical form of a system in which the forces acting upon it it are in equilibrium. 

3.7.35 
STABLE EQUILIBRIUM State in which a system stays close to its equilibrium configuration for all time after a vanishingly small disturbance has been applied. 

3.7.36 
UNSTABLE EQUILIBRIUM State in which a system tends to move away from its equilibrium configuration indefinitely after a vanishingly small disturbance has been applied. 

3.7.37 
NEUTRAL EQUILIBRIUM State in which the equilibrium configuration of a system is to some extent indefinite. 

3.7.38 
EQUATIONS OF EQUILIBRIUM Mathematical expression of the conditions of equilibrium. 

3.7.39 
VIRTUAL DISPLACEMENT Arbitrary displacement of a particle or a system from a given state during which all forces are considered to remain constant in magnitude and direction. 

3.7.40 
EXCITATION [STIMULUS] Time dependent external force (or other input) whereby energy is imparted to a system. 

3.7.41 
COMPLEX EXCITATION Harmonic excitation represented as a complex number. 

3.7.42 
COMPLEX RESPONSE 1. Response represented as a complex number. 2. Response of a damped linear system to a harmonic excitation. 

3.7.43 
SUBHARMONIC RESPONSE Response of a system exhibiting some of the characteristics of resonance at a frequency that is an integer part of the frequency of the excitation. 

3.7.44 
TRANSFER FUNCTION [TRANSMITTANCE] Ratio of the Laplace transform of the output of a system to that of the input. 

3.7.45 
TRANSMISSIBILITY Nondimensional ratio of the response amplitude of a system in steadystate forced vibration to the excitation amplitude. The ratio may be one of forces, displacements, velocities, or accelerations. 

3.7.46 
DYNAMIC STIFFNESS [SPRING CONSTANT] Ratio of the amplitude of an exciting force to the amplitude of displacement during harmonic forced vibration of a linear system. 

3.7.47 
IMPEDANCE Ratio of harmonic input of a linear system to its output expressed in complex form. 

3.7.48 
PROCESS See 6.25. 

3.7.49 
RANDOM [STOCHASTIC] PROCESS Set (ensemble) of time functions that can be characterized through statistical properties. 

3.7.50 
STATIONARY PROCESS Ensemble of timehistories such whose statistical properties are invariant with respect to time. 

3.7.51 
ERGODIC PROCESS Stationary process involving an ensemble of timehistories where time averages are the same for every timehistory. 

3.8 
Dynamical systems and characteristics 

3.8.1 
SYSTEM See 6.21. 

3.8.2 
MECHANICAL SYSTEM System in which the main properties are mass, stiffness and damping. 

3.8.3 
SIMPLE PENDULUM Particle suspended from a fixed point under gravity by inextensible, massless thread and able to move in a given vertical plane through the support. 

3.8.4 
SPHERICAL PENDULUM Particle suspended from a fixed point under gravity by an inextensible, massless thread. 

3.8.5 
COMPOUND PENDULUM Rigid body suspended under gravity so that it is free to rotate about a fixed horizontal axis other than one through its centre of gravity. 

3.8.6 
DOUBLE PENDULUM Two pendulums hinged together so that one provides a moving support for the other. 

3.8.7 
GYROSCOPE Cylindrical rigid body rotating about a fixed point, having an angular velocity about its spin axis much larger than remaining components of its angular velocity. 

3.8.8 
HOLONOMIC SYSTEM Constrained system for which all the constraints are holonomic. 

3.8.9 
NONHOLONOMIC SYSTEM Mechanical system with at least one nonholonomic constraint. 

3.8.10 
RHEONOMIC SYSTEM Constrained system in which at least one constraint depends on time. 

3.8.11 
SCELERONOMIC SYSTEM Constrained system in which all the constraints are independent of time. 

3.8.12 
INVARIANT SYSTEM System in which the distances between individual particles are invariant. 

3.8.13 
PLANAR [COPLANAR] SYSTEM System capable of being loaded and/or moving in one plane only. 

3.8.14 
SPATIAL SYSTEM System capable of being loaded by a spatial force system and/or moving in threedimensional space. 

3.8.15 
STATICALLY DETERMINATE SYSTEM System for which the distribution of internal forces is determined by the principles of statics alone. 

3.8.16 
STATICALLY INDETERMINATE [HYPERSTATIC] SYSTEM System in which the distribution of internal forces depends on the material properties of the members of the system. 

3.8.17 
LINEAR SYSTEM System in which the magnitude of the response is proportional to the magnitude of the excitation. 

3.8.18 
DISCRETE [MULTIDEGREEOFFREEDOM, LUMPEDPARAMETER] SYSTEM System which requires only a finite number of coordinates to specify its configuration. 

3.8.19 
CONTINUOUS SYSTEM [CONTINUUM] System in which physical properties are continuously distributed. 

3.8.20 
VARIABLEMASS SYSTEM System whose total mass may change in time due to the addition or subtraction of mass. 

3.8.21 
INERTIAL SYSTEM System of reference coordinates [frame of reference] in which the basic principles of classical mechanics hold. 

3.9 
Vibrations 

3.9.1 
VIBRATION Mechanical oscillation. 

3.9.2 
PERIOD Interval at which a set sequence of events is repeated. 

3.9.3 
FREQUENCY Number of periods occurring in unit time. 

3.9.4 
FUNDAMENTAL FREQUENCY (OF A PERIODIC QUANTITY) Lowest of the set of frequencies associated with the harmonic components of a periodic quantity. 

3.9.5 
CYCLE Whole sequence of the periodic quantity during one period. 

3.9.6 
OSCILLATION Variation, usually with time, of the magnitude of a quantity about its mean value. 

3.9.7 
AMPLITUDE 1. Greatest deviation of the instantaneous value of a periodic quantity from its mean. 2. Maximum value of a simple harmonic quantity. 

3.9.8 
SIMPLE HARMONIC QUANTITY Periodic quantity that is a sinusoidal function of an independent variable. 

3.9.9 
HARMONIC [FOURIER COMPONENT] Sinusoid whose frequency is an integral multiple of the fundamental frequency of a periodic quantity. 

3.9.10 
SUBHARMONIC Sinusoidal quantity, the period of which is an integer multiple of the fundamental period of the system. 

3.9.11 
SUPERHARMONIC Sinusoidal quantity, the frequency of which is an integer multiple of the fundamental frequency of the system. 

3.9.12 
SPECTRUM Set of quantities characterizing harmonic components expressed as a function of frequency and wavelength. 

3.9.13 
PEAKTOPEAK VALUE Algebraic difference between the extreme values of an oscillating quantity. 

3.9.14 
HARMONIC [SINUSOIDAL] VIBRATION Vibration in which the motion is a sinusoidal function of time. 

3.9.15 
FUNDAMENTAL VIBRATION Harmonic component of a vibration with the lowest frequency. 

3.9.16 
STEADYSTATE VIBRATION Continuing periodic vibration. 

3.9.17 
TRANSIENT VIBRATION Vibratory motion of a system other than steadystate motion. 

3.9.18 
RANDOM VIBRATION Vibration whose magnitude cannot be precisely predicted for any given instant of time. 

3.9.19 
FREE VIBRATION Vibration over an interval of time during which the system is free from excitation. 

3.9.20 
NORMAL VIBRATION Free vibration in a normal mode. 

3.9.21 
FORCED VIBRATION Vibration of a system caused by a sustained excitation. 

3.9.22 
SYNCHRONOUS VIBRATION Vibration at the same frequency as another periodic quantity. 

3.9.23 
BEAT Periodic variation of the amplitude of vibration with time, arising from the superposition of two sinusoidal vibrations with slightly different frequencies. 

3.9.24 
LONGITUDINAL VIBRATION Vibration parallel to the longitudinal axis of a member. 

3.9.25 
TRANSVERSE VIBRATION Vibration in a direction perpendicular to the longitudinal axis or central plane of a member. 

3.9.26 
TORSIONAL VIBRATION Vibration that involves torsion of a member. 

3.9.27 
MODE OF VIBRATION Configuration of the displacements of characteristic points of a system from their mean positions when the system is undergoing simple harmonic vibration at any time other than when all the deflections are zero. 

3.9.28 
NORMAL [NATURAL, CHARACTERISTIC, EIGEN, PRINCIPAL] MODE (OF VIBRATION); MODAL [PROPER, LATENT] VECTOR Mode of free harmonic vibration of an undamped linear system vibrating at one of its natural frequencies. 

3.9.29 
FUNDAMENTAL MODE Normal mode of vibration associated with the lowest natural frequency of a vibrating system. 

3.9.30 
COUPLED MODES Modes of vibration that are not independent but which influence one another because of energy transfer from one mode to another. 

3.9.31 
UNCOUPLED MODES Modes of vibration that can exist in a system concurrently with, and independently of, other modes, no energy being transferred from one mode to another. 

3.9.32 
NODE Stationary point of a mode of periodic vibration or a standing wave. (Note: An entirety of such points form nodal lines or nodal surfaces). 

3.9.33 
ANTINODE Point of a mode of periodic vibration or a standing wave for which the peaktopeak value is a maximum relative to neighbouring points. Note: An entirety of such points forms antinodal lines or surfaces. 

3.9.34 
RESONANCE Large amplitude response to a simple harmonic excitation at or near to a natural frequency of a system. 

3.9.35 
RESONANCE FREQUENCY Frequency of forced vibration at which resonance occurs. 

3.9.36 
CRITICAL SPEED Characteristic speed, such that resonance of a system occurs. 

3.9.37 
QUALITY FACTOR [QFACTOR] Quality which is a measure of the sharpness of resonance, or frequency selectivity of a resonant oscillatory system (mechanical or electrical) having a single degree of freedom. 

3.9.38 
LOGARITHMIC DECREMENT Natural logarithm of the ratio of any two successive maxima of like sign, in the decay of a single frequency oscillation. 

3.9.39 
NATURAL FREQUENCY Frequency of free simple harmonic vibration of an undamped linear system. 

3.9.40 
DAMPING Any influence which tends to dissipate the energy of a system. 

3.9.41 
VISCOUS DAMPING Dissipation of energy that occurs when the relative motion of two elements of a vibration system is resisted by a force whose magnitude is proportional to the relative velocity. 

3.9.42 
EQUIVALENT VISCOUS DAMPING Linear viscous damping assumed for the purpose of analysing a vibratory motion such that the dissipation of energy per cycle is the same as it is for the actual damping. 

3.9.43 
DAMPING COEFFICIENT Coefficient of proportionality between the damping force and relative velocity. 

3.9.44 
DAMPING RATIO Ratio of actual to critical damping coefficient. 

3.9.45 
CRITICAL DAMPING Minimum level of viscous damping that will allow a displaced system to return to its equilibrium position without oscillation. 

3.9.46 
WAVE Change in physical state which is propagated through a medium. 

3.9.47 
TRANSVERSE WAVE Wave in which the direction of disturbance to the medium is perpendicular to the direction of propagation. 

3.9.48 
LONGITUDINAL WAVE Wave in which the direction of disturbance to the medium is parallel to the direction of propagation. 

3.9.49 
SHEAR WAVE Wave which is propagated as a result of shear stresses. 

3.9.50 
SHOCK WAVE Shock motion (displacement, pressure, or other variable) associated with the propagation of the shock through a medium or structure and characterized by a wave front at which a finite change of strain occurs over an infinitesimal distance. 

3.9.51 
COMPRESSION WAVE Wave which is propagated as a result of compressive or tensile stresses in an elastic medium. 

3.9.52 
STANDING WAVE Periodic wave having a fixed amplitude distribution in space. 

3.9.53 
WAVE FRONT Locus of points of a progressive wave having the same phase at a given instant. (Note: A wave front for a surface wave is a continuous line, for a space wave a continuous surface). 

3.9.54 
WAVELENGTH Distance between corresponding points of two successive periods of a wave. 