An analytical approach for the analysis of stress wave transmission and reflection in waveguide systems based on Timoshenko beam theory

The paper presents an analytical continuous solution for the analysis of wave refraction and transmission/reflection caused by arbitrarily complex waveguide subsystems. It allows analyzing the way stress wave components are altered as they go through a substructure. The method is new in that it investigates the wave phenomena which govern the dynamic behavior of a structural system explicitly and studies the effectiveness of different serrated and fractal subsystem designs functioning as wave content filters. Timoshenko beam theory is used to model stress wave propagation in waveguides because of its accuracy and consistency over a wide range of vibration frequencies. The versatility of the method is demonstrated using a number of numerical examples characterizing stress wave refraction in single input/single output and single input/multiple output subsystems to study periodic, fractal, and serrated forms. The low computation cost and stable accuracy of the method over a very wide range of frequencies, make it an effective tool for metaheuristic optimization approaches which require massive calculations over many generations. The method is demonstrated to perform seamlessly in coupling with a genetic algorithm optimization framework to determine the optimal serrated configuration of a wave filter.