The Driving-Point Impedance of an Infinite Solid Plate

Abstract

In the design of mechanical filters whose function is, to prevent the transmission of vibration from one structure to another, it is necessary to know the impedances of the structures between which the filter is to be connected. In many of the cases which arise in practice, the impedance may be estimated from a knowledge of the driving-point impedance of an infinite plate. An expression is obtained for the impedance of an infinite plate of constant thickness when connection is made to the plate at a single point. The impedance may be written in the form 8ρh2v, where ρ is the density, h the thickness of the plate, and v a velocity approximately equal to the velocity of shear waves in the material. It is shown that the driving-point impedance is equal, except for a constant factor, to the impedance of a mass equal to the mass of a disk cut from the plate whose radius is the mean proportional of the thickness and the wave-length which corresponds to v. The results are exemplified by applying them to the case of a steel plate.