Dispersion of an inhomogeneous sandwich plate having imperfect interfaces and supported by the Pasternak foundation

Abstract

The purpose of this investigation is to see the dispersion of an inhomogeneous sandwich plate with imperfect interfaces between the layers and supported by the two parameters Pasternak foundation under long-wave low-frequency conditions. The governing equation of motion has been considered from the perspective of an anti-plane shear propagation to achieve simplicity. The overall cut-off frequency and the exact dispersion relation are computed. In the context of the structure under investigation, one material contrast setup has been considered. The shortened polynomial dispersion relation$(SPDR)$, which corresponds to the exact dispersion relation $(EDR)$ under material contrast setup, has been reported and investigated further. Additionally, the variational effects of the Pasternak foundation parameters as well as the interface imperfect parameter on the lowest dispersion curve subject to the long-wave low-frequency domain have been investigated using numerical simulations and graphical representations based on physical data. This study is noteworthy because it sheds light on the behaviour of elastic waves in multilayered structures and may be utilized to enhance the layout of three-layered structures used in a variety of industrial fields. Furthermore, we have provided the optimum values of the involved parameters to control and confine the sandwich plate's vibration within the long-wave low-frequency regime.

Closed-form asymptotic solution for the transport of chlorine concentration in composite pipes

“…where the first condition represents perfect chlorine concentration on the interface; while the second condition states that the chlorine consumption on the interface is equal (just recall the situation of no chlorine consumption in a single-layered pipe, where v r ¶ ¶ = 0 at a given radial point); η 3 is the dimensionless quantity of the respective material constants in the layers. Besides, such types of perfect interfacial conditions, as appeared in the latter equation, are typical to elasticity and thermodynamic problems in composite and multilayered structures, read [8,9,29] for more on perfect interfacial conditions in multilayered bodies, while [30][31][32] give more on the analogous imperfect or sliding interfacial conditions. Certainly, in sliding interfacial conditions, the respective fields (such as concentration or velocities in case of fluid flow, displacements for wave propagation, and even temperature fields in heat transfer) are expected to be equal on the interface(s); while their corresponding derivatives (such as the rate of consumption in chlorine flow, stresses in wave propagation, and heat fluxes in heat transfer).…”