Vibration analysis of triangular plates using the ray-tracing technique

Abstract

A new ray-tracing technique is proposed for the dynamic analysis of thin plates in flexure. This approach is based on the fundamental solution to the plate biharmonic equation and suitably placed image sources which simulate waves reflected from the plate edges. In this paper, this method is applied specifically to a class of triangular plates with certain aspect ratios. Since exact eigensolutions for some plates with simply supported boundary conditions are known, these cases are analyzed first. The method of images is also being extended or arbitrary polygonal plates where all the image sources may not be seen by all points inside the plate unlike the previous cases. Consequently, the image sources have to be selectively chosen depending on the excitation and observation points. Preliminary results, when compared with exact solutions and finite-element calculations, indicate that this method is capable of accurately predicting harmonic response. Another advantage of this technique is that the solution can be obtained within a spectral bandwidth. Convergence studies show that the error norms rapidly decrease with an increase in frequency and damping. Hence, this method is computationally efficient in the high-frequency regime. [Work supported by the Army Research Office.]