The article is concerned with a new nonlocal model based on Eringen’s nonlocal elasticity and generalized thermoelasticity. A study is made of the magneto-thermoelastic waves in an isotropic conducting thermoelastic finite rod subjected to moving heat sources permeated by a primary uniform magnetic field and rotating with a uniform angular velocity. The Laplace transform technique with respect ...

In this study, the second type of Green and Naghdi's thermoelasticity theory is applied to present the vibration of a nanobeam subjected to rectified sine wave heating based upon the nonlocal thermoelasticity theory. Both Young's modulus and thermal conductivity are considered to be linear functions of the temperature. The Laplace transform domain is adopted to solve the governing partial diffe...

Nonlocal problems is a major research area in many branches of modern physics, biotechnology, chemistry and engineering, which arises when it is impossible to determine the boundary values of unknown function and its derivatives. Increasingly often, there arise problems with nonlocal integral boundary conditions, especially in particle diffusion [1] and heat conduction [2, 3]. Partial different...

In the present manuscript, we investigated a two dimensional axisymmetric problem of nonlocal microstretch thermoelastic circular plate subjected to thermomechanical sources. An eigenvalue approach is proposed to analyze the problem. Laplace and Hankel transforms are used to obtain the transformed solutions for the displacements, microrotation, microstretch, temperature distribution and stresse...

For 1-D parabolic PDEs with disturbances at both boundaries and distributed disturbances we provide ISS estimates in various norms. Due to the lack of an ISS Lyapunov functional for boundary disturbances, the proof methodology uses (i) an eigenfunction expansion of the solution, and (ii) a finite-difference scheme. The ISS estimate for the sup-norm leads to a refinement of the well-known maximu...

It is shown that the canonical balance of momentum of continuum mechanics can be formulated in a general way, but not independently of the usual balance of linear momentum, even in the absence of specified constitutive equations. A parallel construct can be made for the accompanying time-like canonical energy equation. On specifying the energy, previous particular cases can be deduced including...

In this article, the thermoelastic interactions in an isotropic and homogeneous semi-infinite medium with variable thermal conductivity caused by an ultra-short pulsed laser heating based on the linear nonlocal theory of elasticity has been considered. We consider that the thermal conductivity of the material is dependent on the temperature. The surface of the surrounding plane of the medium is...

A nonlocal theory for thermoelastic materials with voids based on Mindlin’s strain gradient was derived in this paper some qualitative properties. We have also established the size effect of heat conduction aids extended irreversible thermodynamics and generalized free energy. The obtained system equations is a coupling three higher gradients terms due to length scale parameters ϖ l . This pose...