Flexural waves at the edge of nonlocal elastic plate associated with the Pasternak foundation

Abstract

In this article, an elastic foundation is used to study the characteristics of flexural edge waves propagating on a piezoelectric structure. The nonlocal elasticity theory is introduced to investigate the microscale effect on edge wave propagation. The traditional Kirchhoff plate hypothesis is used to determine the kinematics of the piezoelectric plate. By considering the sinusoidal waveform, a closed-form dispersion relation can be obtained. In the context of a flexural edge wave on a piezoelectric plate, an analytical and graphical comparison between the two boundary conditions (i.e. short circuit and open circuit) is discussed. In the presence of nonlocal elasticity, the dispersion relation is implied as an implicit function of frequency and wave number. A significant difference occurred between the dispersion curves for piezoelectric plates with different foundations and nonlocal parameters. Due to the Pasternak elastic foundation, an increasing rate of the fundamental mode of frequency is observed at the traction-free edge of a thin, semi-infinite piezoelectric plate. In contrast, the nonlocal elasticity tends to decrease this fundamental frequency mode for a particular wave number value. The corresponding phase velocity decreases rapidly within a short range of wave numbers.

Bending edge wave on a functionally graded fluid‐saturated porous magneto‐electro‐elastic plate

“…The existence of this type of surface wave on an anisotropic plate has been proved by Fu [17]. The propagating characteristic of bending edge wave on the piezoelectric plate is examined by Nie et al [18], Althobaiti and Hawwa [19], Piliposian and Ghazaryan [20], and Manna and Som [21]. Nobili et al [22] investigate the generation of edge waves due to the propagating crack and load motion, then analyze the dynamic stress intensity factor to extract the resonance behavior of the model.…”

“…The propagating characteristic of bending edge wave on the piezoelectric plate is examined by Nie et al. [18], Althobaiti and Hawwa [19], Piliposian and Ghazaryan [20], and Manna and Som [21]. Nobili et al.…”