New techniques in dynamıc analysis of structures: Spectral element method, travelling wave method and enenrgy flux

Abstract

The Spectral Element Method (SEM), Travelling Wave Method (TWM), and the Energy Flux are robust techniques to calculate the dynamic response of the structures, which are all based on the exact solution of the governing differential equations. In the formulation of these methods, either elementary or higher order element theories can be adopted. Since they use the exact solution, the inertia terms are implemented prop erly. An element without any discontinuity can be modeled as a single element. Thus, the number of degrees of freedoms (DOFs) decreases considerably, providing significant reduction in the problem size and the computation time. High-frequency wave modes, which are the modes more sensitive to small changes in the dynamic characteristics of the structure, can be captured more accurately with these methods. The matrix equa tions for the dynamic response of two and three-dimensional structures can easily be formed by assembling the element response matrices derived from the SEM, TWM and Energy Flux approach. All the formulations are given in frequency domain. There fore, damping and SSI (Soil-Structure Interaction) effects can be incorporated more accurately, because many element-level damping properties and foundation impedance functions are frequency dependent. The propagation path of the disturbance within the structure, as well as the dissipated and reflected waves and energies can be tracked. This gives more insight into the dynamic behavior and the energy absorption capacity of the structure. Since they are very accurate in high frequencies, these methods also provide more powerful tools for system identification and damage detection. Most of the small and invisible damages in structures are hidden in high frequencies.