Wave Dispersion in Multilayered Reinforced Nonlocal Plates under Nonlinearly Varying Initial Stress

Abstract

This paper deals with the effects of initial stress on wave propagations in small-scale plates with shape memory alloy (SMA) nanoscale wires. The initial stress is exerted on the small-scale plate along both in-plane directions. A scale-dependent model of plates is developed for taking into consideration size influences on the wave propagation. In addition, in order to take into account the effects of SMA nanoscale wires, the one-dimensional Brinson’s model is applied. A set of coupled differential equations is obtained for the non-uniformly prestressed small-scale plate with SMA nanoscale wires. An exact solution is obtained for the phase and group velocities of the prestressed small-scale system. The influences of non-uniformly distributed initial stresses as well as scale and SMA effects on the phase and group velocities are explored and discussed. It is found that initial stresses as well as the orientation and volume fraction of SMA nanoscale wires can be used as a controlling factor for the wave propagation characteristics of small-scale plates.