Mechanical Vibrations Paper Sample

Three Concepts of Mechanical Vibration

Mechanical vibration is divided into three concepts namely the damped vibration, un-damped, and free vibration. Damped vibration takes place when the resistance from a medium leads to amplitude from a free vibration. Un-damped vibration takes place when there is constancy despite the amplitude of a motion, while free vibration happens when an object or system moves from an internal force (Rao & Yap, 2011). Damping is the mechanism and process in which a material converts its vibrational energy into sound or heat. Dry friction damping takes place when there is a constant magnitude but in an opposing direction from which the motion of an object derives. On the other hand, viscous damping takes place when the force applied is equal or proportional to the speed of an object when moving in a medium such as air. On the other hand, solid damping is the energy trapped by an object when friction takes place between places.

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Under the undamped translational system, the principle of virtual displacements is applicable. It states that if an object is at its equilibrium state and external forces drove into it with a virtual displacement, then there is no work done. This is because there is no virtual work performed by the internal or external forces (Rao & Yap, 2011). The principle guiding the conservation of energy dictates that a system is considered to conserve energy when there is no significant amount of friction or objects, which can produce the energy. When the external forces do not have any impact on the system, then energy is preserved. In engineering, some of the structural and mechanical systems are considered having a single degree when compared to the freedom in systems. For instance, the stiffness and mass of a system is interpreted as a single degree of freedom.

Coulomb Damping

According to Coulomb's law affiliated with dry fiction, the force required when two bodies are in together to produce a sliding on them is directly proportional to the amount of force on contact. The force of friction is dependent on the direction in which the velocity flows (Rao & Yap, 2011). With Coulomb damping, he viscous damping is linear while the equation from the motion is nonlinear. Therefore, the natural and internal frequency of any system does not chance with the incoming Coulomb damping since the impact reduces based on the addition of viscous damping. This means that whereas motion becomes periodic on Coulomb damping, there is a high probability of it being non-periodic when in an overdamped area. This leads to rest when Coulomb damping takes place and there is an infinite continuity with viscous damping.

In free vibration accompanied by Coulomb damping, the force at the end of each cycle becomes the condition of the superseding cycle which continues until the motions comes to an end since the force impacted in the beginning has reduced significantly. The coefficient of friction from a measured position of mass leads to a consistent frequency and cycle with each of them has a special impact on the amplitude (Rao & Yap, 2011). On the other hand, when a controlled force, like from a pulley is exerted on a Coulomb damping, cycles have to escape before there is a consistent angular motion on the pullet. The force applied on the pulley has a direct impact on the cycles produced before it stops without an internal or external interruption.

References

Rao, S. S., & Yap, F. F. (2011). Mechanical vibrations (Vol. 4). Upper Saddle River: Prentice Hall.