Nonreciprocal propagation of bending waves in spatiotemporally modulated prestressed beam

Abstract

Breaking time or/and spatial symmetry can lead to unprecedent mechanical responses of a structure, the design of which is usually very intricate. This paper proposes a simple design of a beam structure with spatiotemporal modulation. In fact, a time-varying axial load applied to the ends of an elastic beam will induce space-time dependent axial force propagating in the form of longitudinal wave in the beam, which can modulate spatiotemporally the propagation of transverse bending waves. The governing equation is derived, of which the Floquet solution leads to a quadratic eigenvalue problem that can be solved for the frequency as a function of the wavenumber. Theoretical results show the existence of asymmetric wavenumber bandgaps and the unique dispersion diagram which is not periodic with respect to time or space. The breaking of temporal symmetry enables nonreciprocal propagation of transverse bending waves, which is confirmed by the finite element simulations. This modulation method offers promise for applications in the fields of elastic wave filter, frequency converter and magnitude amplifier.