Theoretical Study of Resonant Stiffening Devices

摘要

The vibration properties of a plate or a rod with attached mechanical structures, called resonators, are studied by transfer matrix and Green's function techniques. The plate may be in a vacuum, or acoustically coupled to water on one side. The effects of an added resonator at a given frequency depend only on its response strength in each of its modes of vibration. Expressions are derived for the strengths of several useful resonator types. Boundary conditions for the plate, such as clamping or simple support, are satisfied by the mathematical device of attaching resonators of infinite strength. A piston cut out of the plate material is handled similarly. Formulas for the interactions 'influence coefficients' between the modes of different resonators are given. Expansions are developed for the transcendental integrals that arise in the problems treated. (Author)