Frequency filter for elastic bending waves: Poincaré map method and experiment

Abstract In this work, the Poincaré map numerical method was successfully developed to solve fourth-order differential equation that describes flexural vibrations of a beam, within Timoshenko beam theory. The Euler-Bernoulli continuity conditions were considered, which are valid for frequencies smaller than critical frequency. As an example, used design complex elastic structure, characterized by frequency spectrum with broad band gap. Such structure consists two coupled phononic crystals, designed filling factor values in such way their bending spectra, allowed first part, overlaps gap second one and vice versa. resulting composed system has much wider effective its original components, between 4 10.5 kHz. This works as wave filter. Finally, these three structured systems constructed, acoustic resonance spectroscopy technique. natural well corresponding amplitudes each measured. experimental measurements show excellent agreement simulation.