Free vibration of thick rectangular orthotropic plates with clamped edges- using asymptotic analysis of infinite systems

Exact solutions for free vibration of thick rectangular orthotropic plates when their all edges are clamped sought through asymptotic analysis infinite systems without resorting to the usual truncation series solution. The use modified trigonometric functions made it possible obtain a general solution problem which has same form four cases symmetry quarter plate. Thus, an system linear algebraic equations is derived unknown coefficients representing each case. This in sharp contrast previous publications based on series-solution does not allow satisfaction quasi-regularity condition corresponding system, and therefore, method used earlier, was amenable system. In this investigation, proved, but importantly, algorithm determining natural frequencies plate theorem existence quasi-regular presented. behaviour non-trivial homogeneous ascertained by generalising law Koialovich essentially led development algorithm. Numerical examples given with significant conclusions drawn.