In the present study, nonlinear free vibration behavior of nanobeam subjected to magnetic field is investigated based on Eringen’s nonlocal elasticity and Euler–Bernoulli beam theory. The Hamilton’s principal is adopted to derive the governing equations together with Euler–Bernoulli beam theory and the von-Kármán’s nonlinear strain–displacement relationships. An approximate analytical solution ...

Complete dynamical PDE systems of one-dimensional nonlinear elasticity satisfying the principle of material frame indifference are derived in Eulerian and Lagrangian formulations. These systems are considered within the framework of equivalent nonlocally related PDE systems. Consequently, a direct relation between the Euler and Lagrange systems is obtained. Moreover, other equivalent PDE system...

Nonlocal gradient operators are basic elements of nonlocal vector calculus that play important roles in nonlocal modeling and analysis. In this work, we extend earlier analysis on nonlocal gradient operators. In particular, we study a nonlocal Dirichlet integral that is given by a quadratic energy functional based on nonlocal gradients. Our main finding, which differs from claims made in previo...

in this paper, a numerical solution procedure is presented for the forced vibration of a piezoelectric nanowire under thermo-electro-mechanical loads based on the nonlocal elasticity theory within the framework of timoshenko beam theory. using hamilton’s principle, the nonlocal governing differential equations are derived. the governing equations and the related boundary conditions are discreti...

In this paper, a continuum model based on the nonlocal elasticity theory is developed for vibration analysis of embedded orthotropic circular and elliptical micro/nano-plates. The nano-plate is bounded by a Pasternak foundation. Governing vibration equation of the nonlocal nano-plate is derived using Nonlocal Classical Plate Theory (NCPT). The weighted residual statement and the Galerkin method...

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 ...

We propose a family of mixed finite elements that are robust for the nearly incompressible strain gradient model, which is fourth-order singular perturbed elliptic system. The element similar to [C. Taylor and P. Hood, Comput. & Fluids, 1(1973), 73–100] in Stokes flow. Using uniform discrete B-B inequality pairs, we show optimal rate convergence limit. By new regularity result both materials pa...