Analytical and experimental investigation of the free vibrations of clamped plates of regular polygonal shape carrying concentrated masses

Abstract

Traditionally it has been possible to approximate most printed circuit boards as flat rectangular plates with appropriate edge conditions. However, growing use of electronics in unusual new applications is bringing new challenges to packaging design. Since electronic equipment is being packed into every available inch of space in most airplanes, missiles, and even television sets, the shape of the circuit board is often dictated by the geometry of the available space. On the other hand, a proper and rational design requires knowledge of natural frequencies and mode shapes. This paper presents a comparison of frequency results obtained by means of analytical, numerical and experimental methods in the case of the fundamental mode of transverse vibration of a clamped, regular polygonal plate carrying concentrated masses. It is shown that it is also possible to obtain an approximate value of the frequency corresponding to a higher mode by using an analytical approach (with no concentrated mass acting on the plate). © 1977, Academic Press Inc. (London) Limited. All rights reserved.