Vibration Totally Explained

Everything about Vibrations totally explained

Vibration refers to mechanical oscillations about an equilibrium point . 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. Vibration is occasionally "desirable". For example the motion of a tuning fork, the reed in a woodwind instrument or harmonica, or the cone of a loudspeaker is desirable vibration, necessary for the correct functioning of the various devices.
More often, vibration is undesirable, wasting energy and creating unwanted sound -- noise. For example, the vibrational motions of engines, electric motors, or any mechanical device in operation are typically unwanted. Such vibrations can be caused by imbalances in the rotating parts, uneven friction, the meshing of gear teeth, etc. Careful designs usually minimize unwanted vibrations.
The study of sound and vibration are closely related. Sound, or "pressure waves", are generated by vibrating structures (for example vocal cords); these pressure waves can also induce the vibration of structures (for example ear drum). Hence, when trying to reduce noise it's often a problem in trying to reduce vibration. ).]]

Types of vibration

Free vibration occurs when a mechanical system is set off with an initial input and then allowed to vibrate freely. Examples of this type of vibration are pulling a child back on a swing and then letting go or hitting a tuning fork and letting it ring. The mechanical system will then vibrate at one or more of its "natural frequencies" and damp down to zero. Forced vibration is when an alternating force or motion is applied to a mechanical system. Examples of this type of vibration include a shaking washing machining due to an imbalance, transportation vibration (caused by truck engine, springs, road, etc), or the vibration of a building during an earthquake. In forced vibration the frequency of the vibration is the frequency of the force or motion applied, with order of magnitude being dependent on the actual mechanical system.

Vibration testing

Vibration testing is accomplished by introducing a forcing function into a structure, usually with some type of shaker. Generally, one or more points on the structure are kept at a specified vibration level. Two typical types of vibration tests performed are random- and sine test. Sine tests are performed to survey the structural response of the device under test (DUT). A random test is generally conducted to replicate a real world environment.

Vibration analysis

The fundamentals of vibration analysis can be understood by studying the simple mass-spring-damper model. Indeed, even a complex structure such as an automobile body can be modeled as a "summation" of simple mass-spring-damper models. The mass-spring-damper model is an example of a simple harmonic oscillator. The mathematics used to describe its behavior is identical to other simple harmonic oscillators such as the RLC circuit.
Note: In this article the step by step mathematical derivations won't be included, but will focus on the major equations and concepts in vibration analysis. Please refer to the references at the end of the article for detailed derivations.

Free vibration without damping

To start the investigation of the mass-spring-damper we'll assume the damping is negligible and that there's no external force applied to the mass (for example free vibration).
The force applied to the mass by the spring is proportional to the amount the spring is stretched "x" (we will assume the spring is already compressed due to the weight of the mass). The proportionality constant, k, is the stiffness of the spring and has units of force/distance (for example lbf/in or N/m) ť

F_s=- k x !

The force generated by the mass is proportional to the acceleration of the mass as given by Newton’s second law of motion. ť

Sigma F = ma  =   m ddot.

For example, let us calculate the FRF for a mass-spring-damper system with a mass of 1 kg, spring stiffness of 1.93 N/mm and a damping ratio of 0.1. The values of the spring and mass give a natural frequency of 7 Hz for this specific system. If we apply the 1 Hz square wave from earlier we can calculate the predicted vibration of the mass. The figure illustrates the resulting vibration. It happens in this example that the fourth harmonic of the square wave falls at 7 Hz. The frequency response of the mass-spring-damper therefore outputs a high 7 Hz vibration even though the input force had a relatively low 7 Hz harmonic. This example highlights that the resulting vibration is dependent on both the forcing function and the system that the force is applied. The figure also shows the time domain representation of the resulting vibration. This is done by performing an inverse Fourier Transform that converts frequency domain data to time domain. In practice, this is rarely done because the frequency spectrum provides all the necessary information.
The frequency response function (FRF) doesn't necessarily have to be calculated from the knowledge of the mass, damping, and stiffness of the system, but can be measured experimentally. For example, if you apply a known force and sweep the frequency and then measure the resulting vibration you can calculate the frequency response function and then characterize the system. This technique is used in the field of experimental modal analysis to determine the vibration characteristics of a structure.

Further Information

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