Flexural wave propagation and localized vibration in narrow Mindlinʹs plate

In this paper, based on Mindlinʹs theory of thick plates, using Hamiltonian formulism, the elastic wave propagation and localized vibration in narrow plates with free boundary conditions are investigated. The existence of localized vibration mode and propagation mode is analyzed. The dispersion relation of propagation modes in strip plates is deduced from eigenfunction expansion method. And it is compared with the dispersion relation that is gained using Mindlinʹs thick plate theory. Based on the two kinds of theories, dispersion relation curves differ much under short wave. Cutoff frequencies are higher under Hamilton formulism. But dispersion curves are almost same under long wave.