3

Dynamics

English

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 cross-section 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 cross-section of a bar of the moments about its centroid of forces acting on that cross-section.
3.2.41 TORSIONAL MOMENT [TWISTING MOMENT, TORQUE]
Component normal to the plane of a cross-section of a bar of the moments about the centroid of the forces acting on the cross-section.
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 NON-CONSERVATIVE 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 non-cyclic 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 PRINCI-PLE 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 linear-elastic 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 RI-GIDITY [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 cross-sections 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, pin-jointed at its ends, which has the same critical load as a given bar of the same material and the same cross-section.
3.5.27 SLENDERNESS RATIO (OF A BAR)
Ratio of the equivalent buckling length of a bar to the radius of gyration of its cross-section 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 cross-section 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 cross-section of a bar in which the shear stresses have a non-zero resultant.
3.5.39 SHEAR [FLEXURAL] CENTRE
Point in the cross-section 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 cross-section of a bar in torsion rotates.
3.5.41 ELASTIC AXIS [LINE]
Locus of the shear centres of the cross-sections of a beam.
3.5.42 NEUTRAL AXIS
Straight line which lies in the plane of the cross-section 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 FRIC-TION
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 PERCU-SSION
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 SIMPLY-SUPPORTED 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 MULTI-LAYERED 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] SU-PPORT
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 axi-symmetric 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 cross-sections 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 NON-HOLONOMIC 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 [DRIVING-POINT] 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
Non-dimensional ratio of the response amplitude of a system in steady-state 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 time-histories such whose statistical properties are invariant with respect to time.
3.7.51 ERGODIC PROCESS
Stationary process involving an ensemble of time-histories where time averages are the same for every time-history.

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 NON-HOLONOMIC SYSTEM
Mechanical system with at least one non-holonomic 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 three-dimensional 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 [MULTI-DEGREE-OF-FREEDOM, LUMPED-PARAMETER] 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 VARIABLE-MASS 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 PEAK-TO-PEAK VALUE
Algebraic difference between the extreme values of an oscillating quantity.
3.9.14 HARMONIC [SINUSOIDAL] VIBRA-TION
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 STEADY-STATE VIBRATION
Continuing periodic vibration.
3.9.17 TRANSIENT VIBRATION
Vibratory motion of a system other than steady-state 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 peak-to-peak 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 [Q-FACTOR]
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.