The present work mainly studies the free vibration of circular magneto-electro-elastic (MEE) nano-plates based on the Kirchhoff’s plate theory within the framework of nonlocal elasticity theory to account for the small scale effect. The MEE nano-plate studied here is considered to be fully clamped and subjected to the external magnetic and electric potentials. Using nonlocal constitutive relati...

A macroscopic constitutive equation is developed for a high-density cellulose insulation material with emphasis on the outof-plane stress relaxation behavior. A hypothesis is proposed where the total stress is additively composed by an out-of-plane visco-elastic isotropic contribution and an in-plane elastic orthotropic response. The theory is validated against out-of-plane stress relaxation, c...

The Casimir attraction can significantly interfere the physical response of nanoactuators. The intensity of the Casimir force depends on the geometries of interacting bodies. The present paper is dedicated to model the influence of the Casimir attraction on the electrostatic stability of nanoactuators made of cylindrical conductive nanowire/nanotube. An asymptotic solution, based on path-integr...

In this paper, we will present a unified formulation of discontinuous Galerkin method (DGM) for Maxwell’s equations in linear dispersive and lossy materials of Debye type and in the artificial perfectly matched layer (PML) regions. An auxiliary differential equation (ADE) method is used to handle the frequency-dependent constitutive relations with the help of auxiliary polarization currents in ...

We study a dynamic model for viscoelastic materials based on a constitutive equation of fractional order. This results in an integrodifferential equation with a weakly singular convolution kernel. We discretize in the spatial variable by a standard Galerkin finite element method. We prove stability and regularity estimates which show how the convolution term introduces dissipation into the equa...

In order to develop a constitutive equation for foamed polymer solutions their flow behavior was investigated in a large-scale vertical tube. Starting from theoretical considerations, two new constitutive equations are proposed. A new variable+the specif;c t&me expansion mti+is introduced to characterize the relative gas content of the foam. With the new variable the proposed constitutive equat...

A single correlation for sand erosion of a “family” of polyurethanes is presented. By “family” is meant a group of chemically similar compounds. For the first time, an implication of Truesdell’s [1] observations regarding the number of dimensional parameters in viscoelastic constitutive equations has been used together with the Pi theorem to prepare a single dimensionless correlation for a grou...

The purpose of this paper is to solve the seventh-order functional equation as follows:  --------------------------- Next, we study the stability of this type of functional equation. Clearly, the function ----------  holds in this type functional equation. Also, we prove Hyers-Ulam stability for this type functional equation in the β-Gaussian Banach space.