Calculation of vibration frequencies by a hybrid element method based on a generalized complementary energy principle

TLDR: In this article, a generalized complementary energy principle is used for the derivation of the element matrices for the calculation of natural frequencies, where degrees-of-freedom are not defined on nodal points but in an abstract way.

Abstract: Based on a generalized complementary energy principle the derivation of the element matrices is presented for calculation of natural frequencies. The degrees-of-freedom are not defined on nodal points but in an abstract way. No restrictions about the number of interpolation functions in the interior and at the boundaries of the element have been introduced. The exact solution of the discretized element equations leads to the dynamic stiffness matrix while the approximate solution results in a linear eigenvalue problem. Plate bending problems are used to study the convergence of frequencies depending on the degrees of interpolation functions within the element and on its boundaries and on the number of elements.