Mode-Series Expansion of Solutions of Elasticity Problems for a Strip
Oscillations of a strip are considered as a plane problem of elasticity theory. Description of oscillation modes is provided. Properties of eigenvalues and eigenfunctions are studied for a boundary value problem for their amplitudes. Greens function is constructed as a kernel of the inverse operator. Completeness and expansion theorems are proved which allow one to solve problems for finite and infinite membranes under arbitrary boundary conditions.