Exact Natural Frequencies and Modal Functions for a Thick Off-Axis Lamina

Abstract

The three-dimensional elastic field equations that describe the vibration of a class of thick, orthotropic, laminae are solved exactly. The class is characterized by an arbitrary, in-plane, angle of inclination of the principal orthotropic axes to the plate axes. The frequency spectra and modal func tions are presented for two types of materials and five inclination angles. Comparison of these results to classical thin plate theory shows that clas sical flexural plate theory is adequate for vibration with wave lengths greater than 20 times the thickness. Thin extensional plate theory is ade quate also, but shows larger errors in some of the test cases than flexural theory. In other cases, extensional theory is astoundingly accurate