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For linear systems, the frequency of the steady-state vibration response resulting from the application of a periodic, harmonic input is equal to the frequency of the applied force or motion, with the response magnitude being dependent on the actual mechanical system.ĭamped vibration: When the energy of a vibrating system is gradually dissipated by friction and other resistances, the vibrations are said to be damped. Examples of these types of vibration include a washing machine shaking due to an imbalance, transportation vibration caused by an engine or uneven road, or the vibration of a building during an earthquake. The periodic input can be a harmonic or a non-harmonic disturbance. The disturbance can be a periodic and steady-state input, a transient input, or a random input. The mechanical system vibrates at one or more of its natural frequencies and damps down to motionlessness.įorced vibration is when a time-varying disturbance (load, displacement, velocity, or acceleration) is applied to a mechanical system. Examples of this type of vibration are pulling a child back on a swing and letting it go, or hitting a tuning fork and letting it ring.

4.3 Multiple DOF problem converted to a single DOF problemįree vibration occurs when a mechanical system is set in motion with an initial input and allowed to vibrate freely.

4.2 Illustration of a multiple DOF problem.

4 Multiple degrees of freedom systems and mode shapes.

3.3.2 Applying "complex" forces to the mass–spring–damper model.

3.2.1 Damped and undamped natural frequencies.

3.1.1 What causes the system to vibrate: from conservation of energy point of view.

Hence, attempts to reduce noise are often related to issues of vibration. vocal cords) these pressure waves can also induce the vibration of structures (e.g. Sound, or pressure waves, are generated by vibrating structures (e.g. The studies of sound and vibration are closely related. Careful designs usually minimize unwanted vibrations. Such vibrations could be caused by imbalances in the rotating parts, uneven friction, or the meshing of gear teeth. For example, the vibrational motions of engines, electric motors, or any mechanical device in operation are typically unwanted.

In many cases, however, vibration is undesirable, wasting energy and creating unwanted sound. Vibration can be desirable: for example, the motion of a tuning fork, the reed in a woodwind instrument or harmonica, a mobile phone, or the cone of a loudspeaker. The oscillations may be periodic, such as the motion of a pendulum-or random, such as the movement of a tire on a gravel road.

The word comes from Latin vibrationem ("shaking, brandishing"). Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. For other uses, see Vibration (disambiguation) and Vibrate (disambiguation).