Solution of the Membrane Eigenvalue Problem by FEM with Smooth Piecewise Polynomial Approximation
Georgij Kostin
Abstract: The presentation is devoted to development of the FEM with the shape functions, which guarantees the continuity of the function and its first derivatives. The mass and stiffness matrices were analytically derived for membrane model. In order to find the eigenvalues and eigenfunctions the finite element approximations (Argyres triangle element) and Ritz polynomial interpolations are used. The accuracy of the solutions for homogeneous triangular membranes are analyzed and the dependency of lower eigenvalues with respect to the membrane geometry are considered.