Vibration

Vibration (from Latin vibrāre 'to shake') is a mechanical phenomenon whereby oscillations occur about an equilibrium point.

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.

For example, the vibrational motions of engines, electric motors, or any mechanical device in operation are typically unwanted.

Such vibrations could be caused by imbalances in the rotating parts, uneven friction, or the meshing of gear teeth.

Forced vibration is when a time-varying disturbance (load, displacement, velocity, or acceleration) is applied to a mechanical system.

The vibrations gradually reduce or change in frequency or intensity or cease and the system rests in its equilibrium position.

The measured response may be ability to function in the vibration environment, fatigue life, resonant frequencies or squeak and rattle sound output (NVH).

Squeak and rattle testing is performed with a special type of quiet shaker that produces very low sound levels while under operation.

A random (all frequencies at once) test is generally considered to more closely replicate a real world environment, such as road inputs to a moving automobile.

It is difficult to design a vibration test fixture which duplicates the dynamic response (mechanical impedance)[5] of the actual in-use mounting.

[7][8] VA is a key component of a condition monitoring (CM) program, and is often referred to as predictive maintenance (PdM).

Note: This article does not include the step-by-step mathematical derivations, but focuses on major vibration analysis equations and concepts.

To start the investigation of the mass–spring–damper assume the damping is negligible and that there is no external force applied to the mass (i.e. free vibration).

For example, the above formula explains why, when a car or truck is fully loaded, the suspension feels "softer" than unloaded—the mass has increased, reducing the natural frequency of the system.

The mass then begins to decelerate because it is now compressing the spring and in the process transferring the kinetic energy back to its potential.

In this simple model the mass continues to oscillate forever at the same magnitude—but in a real system, damping always dissipates the energy, eventually bringing the spring to rest.

) of the mass-spring-damper model is: For example, metal structures (e.g., airplane fuselages, engine crankshafts) have damping factors less than 0.05, while automotive suspensions are in the range of 0.2–0.3.

The plot of these functions, called "the frequency response of the system", presents one of the most important features in forced vibration.

As discussed earlier, when the mass and spring have no external force acting on them they transfer energy back and forth at a rate equal to the natural frequency.

As in the case of the swing, the force applied need not be high to get large motions, but must just add energy to the system.

At this point, the system has reached its maximum amplitude and will continue to vibrate at this level as long as the force applied stays the same.

In a previous section only a simple harmonic force was applied to the model, but this can be extended considerably using two powerful mathematical tools.

The second mathematical tool, the superposition principle, allows the summation of the solutions from multiple forces if the system is linear.

Applying the 1 Hz square wave from earlier allows the calculation of the predicted vibration of the mass.

The frequency response function (FRF) does not necessarily have to be calculated from the knowledge of the mass, damping, and stiffness of the system—but can be measured experimentally.

When there are many degrees of freedom, one method of visualizing the mode shapes is by animating them using structural analysis software such as Femap, ANSYS or VA One by ESI Group.

An example of animating mode shapes is shown in the figure below for a cantilevered Ɪ-beam as demonstrated using modal analysis on ANSYS.

In this case, the finite element method was used to generate an approximation of the mass and stiffness matrices by meshing the object of interest in order to solve a discrete eigenvalue problem.

Note that, in this case, the finite element method provides an approximation of the meshed surface (for which there exists an infinite number of vibration modes and frequencies).

^ Note that when performing a numerical approximation of any mathematical model, convergence of the parameters of interest must be ascertained.