Nonlinear tension effects on an infinite elastic plate loaded with a linear shear current

This work examines the dynamics of a fluid-loaded thin elastic plate, with a particular focus on the effects of nonlinear tension. While previous studies have concentrated on finite or infinite plates with periodically arranged hinges subjected to uniform mean flows – resulting in a fixed wavelength – our research broadens this framework to consider general periodic waves propagating along an infinite plate influenced by a linear shear current. Moreover, we present new rigorous formulations to address the structural nonlinearities of the plate. Given that the tension coefficient (denoted as N ) can be significant in practical applications, we explore the system’s modulational behavior across three distinct tension coefficient regimes. In the case of small N , an additional integral term emerges in the nonlinear Schrodinger equation; however, it does not influence the modulational instability. For intermediate values of N , the energy exchange during three-wave resonance is slowed down. In scenarios with large N , we identify a nonlinear dispersion relation along with an amplitude-dependent speed for wavepacket propagation. To analyze the full Euler equations, we utilize the conformal mapping method in conjunction with an iterative scheme
for numerical computations. The results of direct numerical simulations align well with our theoretical analyses.