Antisymmetric waves in a thin plate with geometric and material nonlinearities according to a higher order theory

This work investigates nonlinear antisymmetric waves in a plate. Both geometric and constitutive nonlinearities are accounted for in deriving the governing equations. The displacements are expanded in Legendre polynomials of the thickness coordinate instead of the thickness coordinate itself. The method of multiple scales has been employed to solve the nonlinear equations of motion. Evolution equations are derived and solved for small amplitude traveling antisymmetric elastic waves. Waveform distortion, amplitude amplification and harmonic amplification and harmonic generation are computed numerically.