ABSTRACT

This chapter addresses the vibration equation of simple continuous systems, viz., string, rod, beam, and membrane. Vibration is the mechanical oscillation of a particle, member, or a body from its position of equilibrium. It is the study that relates the motion of physical bodies to the forces acting on them. Vibration is also used in pile-driving, vibratory testing of materials, and electronic units to filter out unwanted frequencies. One of the important purposes of vibration study is to reduce vibration through proper and comparatively accurate design of machines and structures. Mainly free vibration will be taken into consideration, i.e., the vibration that takes place in the absence of external excitations, which is the foundation of other complex vibration studies. Equation of motion of vibrating systems can sometimes be advantageously obtained by using the law of conservation of energy provided that damping is negligible.