Journal of Solid Mechanics
Volume:4 Issue: 1, Winter 2012

In this study, electro-thermo-mechanical nonlinear vibration and instability of embedded piezoelectric micro-tube is carried out based on nonlocal theory and nonlinear Donnell''s shell model. The smart micro-tube made of Poly-vinylidene fluoride (PVDF) is conveying an isentropic, incompressible fluid. The detailed parametric study is conducted, focusing on the remarkable effects of mean flow velocity, fluid viscosity, elastic medium modulus, temperature change, imposed electric potential, small scale and aspect ratio on the vibration behavior of the micro-tube. It has been found that stability of the system is strongly dependent on the imposed electric potential. Results of this investigation could be applied for optimum design of sensors and actuators in the sensitive applications.

In this paper, the nonlinear dynamic buckling of double-walled boron-nitride nanotube (DWBNNT) conveying viscous fluid is investigated based on Eringen''s theory. BNNT is modeled as an Euler-Bernoulli beam and is subjected to combine mechanical, electrical and thermal loading. The effect of viscosity on fluid-BNNT interaction is considered based on Navier-Stokes relation. The van der Waals (vdW) interaction between the inner and outer nanotubes is taken into account and the surrounding elastic medium is simulated as Winkler and Pasternak foundation. Considering the charge equation for coupling of mechanical and electrical fields, Hamilton''s principle is utilized to derive the motion equations based on the von Kármán theory. Dynamic buckling load is evaluated using differential quadrature method (DQM). Results show that dynamic buckling load depends on small scale factor, viscosity, elastic medium parameters and temperature changes. Also, dynamic instability region is discussed for various conditions.

In this paper, the classic coupled Magneto-thermo-elasticity model of hollow and solid cylinders under radial-symmetric loading condition (r, t) is considered. A full analytical and the direct method based on Fourier Hankel series and Laplace transform is used, and an exact unique solution of the classic coupled equations is presented. The thermal and mechanical boundary conditions, the body force, the heat source and magnetic field vector are considered in the most general forms, where no limiting assumption is used. This generality allows to simulate a variety of applicable problems. The results are presented for thermal and mechanical shock, separately, and compare the effect of magnetic field on temperature and displacement.

The paper deals with the mechanical behavior of a micro-beam bonded with two piezoelectric layers. The micro-beam is suspended over a fixed substrate and undergoes the both piezoelectric and electrostatic actuation. The piezoelectric layers are poled through the thickness and equipped with surface electrodes. The equation governing the micro-beam deflection under electrostatic pressure is derived according to Euler-Bernoulli beam theory and considering the voltage applied to the piezoelectric layers and Maxwell’s equations for the two dimensional electric potential distribution. The obtained nonlinear equation solved by step by step linearization method and Galerkin weighted residual method. The effects of the electric potential distribution and the ratio of the piezoelectric layer thickness respect to the elastic layer thickness on the mechanical behavior of the micro-beam are investigated. The obtained results are compared with the results of a model in which electric potential distribution is not considered.

In this research work، first، based on the three-dimensional elasticity theory and by means of the Generalized Differential Quadrature Method (GDQM)، free vibration characteristics of functionally graded (FG) rectangular plates resting on Pasternak foundation are focused. The two-constituent functionally graded plate consists of ceramic and metal grading through the thickness. A three-parameter power-law distribution is considered for the ceramic volume fraction. The benefit of using a three-parameter power-law distribution is to illustrate and present useful results arising from symmetric، asymmetric and classic profiles. A detailed parametric study is carried out to highlight the influences of different profiles of fiber volume fraction، three parameters of power-law distribution and two-parameter elastic foundation modulus on the vibration characteristics of the FG plates. The main goal of the structural optimization is to minimize the weight of structures while satisfying all design requirements imposed. Thus، for the second aim of this paper، volume fraction optimization of FG plates with objective of minimizing the density to achieve a specified fundamental frequency is presented. The primary optimization variables are the three parameters of the volume fraction of ceramic. Since the optimization processes is complicated and too much time consuming، a novel meta–heuristic called Imperialist Competitive Algorithm (ICA) which is a socio-politically motivated global search strategy and Artificial Neural Networks (ANNs) are applied to obtain the best material profile through the thickness. The performance of ICA is evaluated in comparison with other nature inspired technique Genetic Algorithm (GA). Comparison shows the success of combination of ANN and ICA for design of material profile of FG plates. Finally the optimized material profile for the considered optimization problem is presented.

Free vibration characteristics of continuous grading fiber orientation (CGFO) beams resting on variable Winkler and two-parameter elastic foundations have been studied. The beam is under different boundary conditions and assumed to have arbitrary variations of fiber orientation in the thickness direction. The governing differential equations for beam vibration are being solved using Generalized Differential Quadrature (GDQ) method. Numerical results are presented for a beam with arbitrary variation of fiber orientation in the beam thickness and compared with similar discrete laminate beam. The main contribution of this work is to present useful results for continuous grading of fiber orientation through thickness of a beam on variable elastic foundation and its comparison with similar discrete laminate composite beam. The results show the type of elastic foundation plays very important role on the natural frequency parameter of a CGFO beam. According to the numerical results, frequency characteristics of the CGFO beam resting on a constant Winkler elastic foundation is almost the same as of a composite beam with different fiber orientations for large values of Winkler elastic modulus, and fiber orientations has less effect on the natural frequency parameter. The interesting results show that normalized natural frequency of the CGFO beam is smaller than that of a similar discrete laminate beam and tends to the discrete laminated beam with increasing layers. It is believed that new results are presented for vibrational behavior of CGFO beams are of interest to the scientific and engineering community in the area of engineering design.

Free bending vibration analysis of the functionally graded viscoelastic circular sandwich plates is accomplished in the present paper, for the first time. Furthermore, local shear corrections factors are presented that may consider simultaneous effects of the gradual variations of the material properties and the viscoelastic behaviors of the materials, for the first time. Moreover, in contrast to the available works, a global-local zigzag theory rather than an equivalent single-layer theory is employed in the analysis. Another novelty is solving the resulted governing equations by a power series that may cover several boundary conditions. To extract more general conclusions, sandwich plates with both symmetric and asymmetric (with a bending-extension coupling) layups are considered. Results are validated by comparing some of them with results of the three-dimensional theory of elasticity, even for the thick plates. Influences of various geometric and material properties parameters on free vibration of the circular sandwich plates are evaluated in detail in the results section.

The examination of variation of elastic modules in single wall carbon nanotubes (SWCNTs) is the aim of this paper. Full nonlinear spring-like elements are employed to simulate specific atomic structures in the commercial code ABAQUS. Carbon atoms are attached to each node as a mass point using atomic mass of carbon atoms. The influence of dimensions such as variation of length, diameter, aspect ratio and chirality is explored separately on the variations of young''s and shear modules. It is observed that the effect of dimensions after a critical aspect ratio in nanotubes is negligible. Also, the influence of chirality on the elastic modules for same dimensions is observable. The results are compared with experimental results and theoretical data.