Abstract. In this paper we consider the transmission problem of a material composed of three components; one of them is a Kelvin–Voigt viscoelastic material, the second is an elastic material (no dissipation), and the third is an elastic material inserted with a frictional damping mechanism. The main result of this paper is that the rate of decay will depend on the position of each component. W...

Even when the muscles surrounding a joint are inactive, they still exert a damping effect on joint mobility, because of the passive elastic tension exerted by the stretched muscle fibres and their connective tissue (Clemmesen, 1951). For example, if the forearm muscles are allowed to relax and the forearm is then shaken violently, the hand will swing loosely at the wrist; however, if the experi...

In this article thermoelastic damping in nano-beam resonators is investigated based on nonlocal theory of elasticity and the Euler-Bernoulli beam assumptions. The governing equation of deflection of the beam is obtained from shear and moment resultants and stress–strain relationship of the nonlocal elasticity model and also the governing equations of thermoelastic damping are established by usi...

In this paper we consider a plate equation with internal feedback and viscoelastic damping localized on a part of the boundary. Without imposing restrictive assumptions on the time-dependent frictional damping, we establish an explicit and general decay rate result that allows a wider class of relaxation functions and generalizes previous results existing in the literature.

In this paper, we study the elastic membrane equation with dynamic boundary conditions, source term and a nonlinear weak damping localized on part of past history. Under some appropriate assumptions relaxation function general decay for energy have been established using perturbed Lyapunov functionals properties convex functions.

The response of a bridge tower-pier system resting on elastic soil, with a sliding foundation obeying Coulomb's friction law, is studied. The stiffness and damping of the supporting soil is fully taken into account. The action of the suspension bridge cables is equivalent to a horizontal elastic restraint at the top of the tower. The differential equations of motion of the pier are formulated f...

Abstract The elastic wave propagation in inelastic media gives rise to non-linear equation. We study such a nonlinear two dimensions using Murnaghan model. Lie symmetries, invariant exact solutions and conservation laws the Noether theorem have been found. equation with damping term has dealt partial approach.

The aim of this short note is twofold. First, we give a sketch of the proof of a recent result proved by the authors in the paper [7] concerning existence and uniqueness of renormalized solutions of continuity equations with unbounded damping coe cient. Second, we show how the ideas in [7] can be used to provide an alternative proof of the result in [6, 9, 12], where the usual requirement of bo...

Railway structures are one of the most important structures in transportation. So the lack of precise study of their dynamic behavior leads to irreparable damages. The significant factors contributing to the accurate analysis of the dynamic behavior of railways are the type of load and foundation used in it. In this study, an Euler-Bernoulli beam subjected to a moving load on a finite depth fou...

A new result enables direct calculation of thermoelastic damping in vibrating elastic solids. The mechanism for energy loss is thermal diffusion caused by inhomogeneous deformation, flexure in thin plates. The general result is combined with the Kirchhoff assumption to obtain a new equation for the flexural vibration of thin plates incorporating thermoelastic loss as a damping term. The thermal...