1、Noise, Vibration and HarshnessPart IIIntroduction Mechanical vibration is the motion of a particle or body which oscillates about a position of equilibrium. Most vibrations in machines and structures are undesirable due to increased stresses and energy losses. Time interval required for a system to
2、complete a full cycle of the motion is the period of the vibration. Number of cycles per unit time defines the frequency of the vibrations. Maximum displacement of the system from the equilibrium position is the amplitude of the vibration. When the motion is maintained by the restoring forces only,
3、the vibration is described as free vibration. When a periodic force is applied to the system, the motion is described as forced vibration. When the frictional dissipation of energy is neglected, the motion is said to be undamped. Actually, all vibrations are damped to some degree.Free Vibrations of
4、Particles. Simple Harmonic Motion If a particle is displaced through a distance xm from its equilibrium position and released with no velocity, the particle will undergo simple harmonic motion, General solution is the sum of two particular solutions, x is a periodic function and wn is the natural ci
5、rcular frequency of the motion. C1 and C2 are determined by the initial conditions:Free Vibrations of Particles. Simple Harmonic Motionperiodnatural frequencyamplitudephase angle Displacement is equivalent to the x component of the sum of two vectorswhich rotate with constant angular velocity Forced
6、 Vibrations19 - 5Forced vibrations - Occur when a system is subjected to a periodic force or a periodic displacement of a support.forced frequencyForced VibrationsAt wf = wn, forcing input is in resonance with the system.Damped Free Vibrations With viscous damping due to fluid friction, Substituting
7、 x = elt and dividing through by elt yields the characteristic equation, Define the critical damping coefficient such that All vibrations are damped to some degree by forces due to dry friction, fluid friction, or internal friction.Damped Free Vibrations Characteristic equation,critical damping coef
8、ficient Heavy damping: c cc- negative roots - nonvibratory motion Critical damping: c = cc- double roots - nonvibratory motion Light damping: c ccdamped frequencyDamped Forced Vibrationsmagnification factorphase difference between forcing and steady state responseReason for vibration analysis Lightl
9、y damped structures can produce high levels of vibration from low level sources if frequency components in the disturbance are close to one of the systems natural frequencies. This means that well designed and manufactured sub- systems, which produce low level disturbing forces, can still create problems when assembled on a vehicle. In order to avoid these problems, at the design stage it is necessary to model the system accurately and analyze its response to anticipated disturbances
