in this paper, free vibration of functionally graded rectangular simply supported thick plates based on two variable refined plate theory is presented. according to a power-law distribution, the mass density and elasticity modulus of the plate are considered to vary while poisson’s ratio is constant. in order to extract the five constitutive equations of motion, hamilton principle is employed. ...

The discontinuous solutions represent a new direction for the indirect Boundary Element Method (BEM) in formulation. Discontinuous those functions, which when crossing certain lines, transverse deflection, slope angle, bending moment and generalized shear force may have jumps. These can be used to solve important problems existing methods do not or satisfactory accuracy, such as: plates of arbi...

Fastening failures have frequently been found on China high-speed railway curved tracks in recent years. Thus the influence of fastening train-track interaction track needs to be analyzed. A train-curved slab model is built, which real shape rail considered and modeled with reduced beam (RBM) theory, slabs are four-nodes Kirchhoff-Love plate elements. The present validated at first different tr...

In this paper we obtain the constitutive equation for the second Piola-Kirchhoff stress tensor according to the linearized finite theory of elasticity for hyperelastic constrained materials. We show that in such a theory the three stress tensors (Cauchy stress tensor, first and second Piola-Kirchhoff stress tensor) differ by terms that are first order in the strain, while in classical linear th...

We study vibrations of singleand multi-layered rectangular graphene nanoribbons (GNRs) using molecular mechanics (MM) simulations by employing the MM3 potential. Two sets of boundary conditions are considered, namely, clamping atoms on either all four edges (CCCC) or on the two small edges (CFCF). Furthermore, we consider two scenarios for a single-layered GNR – one in which an interior atom is...

Although mathematical study on the synchronization of wave equations at finite horizon has been well developed, there have few results for long-time horizon. The aim paper is to investigate uniform infinite one abstract linear second order evolution system in a Hilbert space. First, using classical compact perturbation theory stability semigroups contractions, we will establish lower bound numb...

The major theme of the thesis is the development of goal-oriented model adaptive continuous-discontinuous Galerkin (c/dG) finite element methods (FEM), for the numerical solution of the Kirchhoff and Mindlin-Reissner (MR) plate models. Hierarchical modeling for linear elasticity on thin domains (beam-like) in two spatial dimensions is also considered, as a natural extension of the Bernoulli and...

Although many improvements in the manufacturing of guitars have been made recently, one aspect that has often been overlooked is that of the acoustical consistency of the final manufactured product. The aim of this paper is to create a better understanding of the effect of a brace on the frequencies of vibration of the brace-soundboard system. This paper seeks to shed light on why a luthier 'tu...