ABSTRACT
Continuous systems like beams, plates, and shells are the most commonly used elements in the construction of any structure or machine. Flexural vibration in these elements, also known as bending vibration, is the vibration perpendicular to the beam axis or plate surface, and is the most commonly encountered wave type. In addition, flexural vibration very easily couples with the surrounding air and is thus the most dominant source of airborne noise from machines. The general differential equation for flexural vibration of beams is derived first. Then equations for natural frequencies and their corresponding mode shapes are derived. These are used to derive the general equations for resonant frequencies and mode shapes of cantilever and simple supported beams. Orthogonality conditions are derived and used to obtain uncoupled equations in terms of generalized coordinates, generalized masses, and forces to obtain the response.
