Flexural wave control via the profile modulation of non-uniform Timoshenko beams

Abstract

A methodology to control the flexural wave propagation via modulating the beam profile is presented in this paper. Firstly, the power series method is utilized to theoretically solve the flexural waves in a non-uniform Timoshenko beam with arbitrarily contoured profiles. It is demonstrated that this method is effective for most of inhomogeneous beams as long as the convergence criterion about the beam thickness is satisfied in advance. After validation by comparing the theoretical results with those from the finite element analysis for different thickness variations, lenses are designed by using the quadratic thickness variation pattern with the aim of focusing the wave emitted from a point source on one or two particular positions. Additionally, according to the generalized Snell's law, the thickness-induced phase modulation of the flexural wave is proved from the views of theoretical analysis and numerical simulations, based on which lenses for focusing a plane flexural wave are also realized. It is illustrated through systematic analysis in the frequency domain that all of the lenses designed can exhibit good performances with the evidently increased energy at actual focal positions and the focusing sizes smaller than one working wavelength, which has great potentials in versatile engineering applications.