Energy approach to analysis of natural oscillations of plates with cracks or added masses

Abstract

In elastic systems, small changes in stiffness or inertia yield a shift in natural frequencies. The so-called energy approach allows to obtain a linear approximation to estimate this frequency shift using energetic considerations. The goal of this thesis is to test this energy approach for a square plate with a crack or applied mass for different mode shapes. In particular, the behaviour of the frequency shift is to be determined with finite element analyses and checked for convergence with the solution according to the energy approach. First, necessary theoretical aspects from Kirchhoff's plate theory and the linear finite element method are stated. Then, the energy approach is introduced and a mathematical justification is given. Afterwards, the simulation model and the used meshes are presented. Following this, the results of the finite element analyses for the plate with additional mass/crack are discussed. The simulations clearly show that the previously known form of the energy approach fails in the case of repeated natural frequencies, as they occur with square plates. Apart from that, good correspondence can be seen for the considered examples.