Vibration Basics for Plates
This chapter addresses basic equations, theories, stress-strain relations related to the vibration basics for plates. Study of vibration of plates is an extremely important area owing to its wide variety of engineering applications such as in aeronautical, civil, and mechanical engineering. Since the members, viz., beams, plates, and shells, form integral parts of structures, it is essential for a design engineer to have a prior knowledge of the first few modes of vibration characteristics before finalizing the design of a given structure. Different theories have been introduced to handle the vibration of plate problems. The transverse shear effects as well as the rotatory inertia effect are important when the plate is relatively thick or when higher-mode vibration characteristics are needed. The theorem of minimum potential energy is defined as the following: Of all the displacements satisfying compatibility and the prescribed boundary conditions, those that satisfy equilibrium equations make the potential energy a minimum.