Solving direct and inverse problems of plate vibration by using the Trefftz functions

The paper presents an approximate method of solving direct and inverse problems which are described by a non-homogenous plate vibration equation. The key idea of the presented approach is to use solving polynomials that satisfy the considered homogenous differential equation identically. Inhomogeneity is expanded into the Taylor series and then, for each monomial, the inverse operator is calculated. In the paper, the properties of solving functions are investigated – a theorem concerning their linear independence is formulated and proved. The method of identification of the load (source) is described. It belongs to the group of inverse problems. The paper includes examples which illustrate the usefulness of the method.