Sharif Digital Repository

This paper aims to present an explicit relation for thermoelastic damping in nanobeams capturing the small-scale effects on both the continuum mechanics and heat conduction domains. To incorporate small-scale effects, the coupled equations of motion and heat conduction are obtained by employing the nonlocal elasticity theory and the dual-phase-lag heat conduction model. Adopting simple harmonic forms for transverse deflection and temperature increment and solving the governing equations, real and imaginary parts of the frequency are extracted. According to the complex frequency approach, a closed-form size-dependent expression for evaluating thermoelastic damping in nanobeams is derived. To... 

Design and development of FGMs as the heat treatable materials for high-temperature environments with thermal protection require understanding of exact temperature and thermal stress distribution in the transient state. This information is primary tool in the design and optimization of the devices for failure prevention. Frequently FGMs are used in many applications that presumably produce thermal energy transport via wave propagation. In this study, transient non-Fourier temperature and associated thermal stresses in a functionally graded slab symmetrically heated on both sides are determined. Hyperbolic heat conduction equation in terms of heat flux is used for obtaining temperature... 

In this study, the buckling and postbuckling analysis of FG micro-plates under different kinds of traction on the edges is investigated based on the modified couple stress theory. The static equilibrium equations of an FG rectangular micro-plate as well as the boundary conditions are derived using the principle of minimum total potential energy. The analytical solutions are developed for three case studies including: simply supported micro-plates subjected to uniform transverse load and biaxial tractions, clamped-simply supported micro-plates under uniform transverse load and axial traction, and simply supported micro-plates subjected to shear traction. All plate properties except the length... 

This study provides an exact solution for the size dependent buckling and post-buckling behavior of functionally graded (FG) micro-beams with arbitrary boundary conditions which are subjected to combined thermo-mechanical loading. To this end, a theoretical formulation including the effects of size dependency, elastic foundation and uniform temperature distribution is first derived using the modified couple stress theory and through the principle of minimum total potential energy. Next, the nonlinear equations governing bending and stretching behavior of FG micro-beams are uncoupled to a fourth-order ordinary differential equation. Finally, the differential operator method is utilized to... 

Based on the nonlocal Euler–Bernoulli beam theory, a theoretical approach is developed to investigate the effects of small scale and intermolecular force on the dynamic pull-in behavior of electrostatically actuated nanoresonators. To this purpose, nanoresonators are modeled as multilayer beams with rectangular cross-sections and fixed-fixed and fixed-free end conditions which are embedded in an elastic medium containing Winkler and Pasternak elastic foundations. Also, the effects of nonlocal parameter, fringing field due to the finite width of beams, Casimir or van der Waals intermolecular forces, nonlinear term induced by mid-plane stretching and Winkler and Pasternak elastic foundations... 

In this paper, the static pull-in behavior of electrostatically actuated functionally graded (FG) micro-beams resting on an elastic medium is studied using the modified strain gradient (MSG) theory. To this end, the equilibrium equation along with classical and non-classical boundary conditions is obtained by considering the fringing field and elastic foundations effects within the principle of minimum total potential energy. Also, the elastic medium is composed of a shear layer (Pasternak foundation) and a linear normal layer (Winkler foundation). The governing differential equation is solved for cantilever and doubly fixed FG beams using an iterative numerical method. This method is a... 

Based on the Euler–Bernoulli beam model and the modified strain gradient theory, the size-dependent forced vibration of sandwich microbeams with a functionally graded (FG) core is presented. The equation of motion and the corresponding classical and nonclassical boundary conditions are derived using the Hamilton’s principle. An exact solution of the governing equation is developed for sandwich beams with various boundary conditions and subjected to an arbitrarily distributed harmonic transverse load. Finally, parametric studies are presented to investigate the effects of geometric ratios, length scale parameters, power index, boundary conditions, layup, and thickness of the FG layer on the... 

Optimal design of micron-scale beams as a general case is an important problem for development of micro-electromechanical devices. For various applications, the mechanical parameters such as mass, maximum deflection and stress, natural frequency and buckling load are considered in strategies of micro-manufacturing technologies. However, all parameters are not of equal importance in each operating condition but multi-objective optimization is able to select optimal states of micro-beams which have desirable performances in various micro-electromechanical devices. This paper provides optimal states of design variables including thickness, distribution parameter of functionally graded... 

We prove that to any partial function φ{symbol} defined on a finite set, there corresponds an infinite class of graphs that could be generated by a graph grammar such that each graph in the class represents the function in the sense that evaluation of the function at any point x of its domain can be simulated by finding the unique extension of a partial vertex colouring of the graph specified by x. We show that in the proposed setup, generating such simulator graphs as well as finding the colouring extensions can be computed effectively in polynomial time. We also discuss some applications of this scenario in producing instances of the graph colouring problem near its phase transition that... 

Let G be a finite simple x-chromatic graph and L = {Lu} u∈V(G) be a list assignment to its vertices with Lu {1.....X}- A list colouring problem (G, L) with a unique solution for which the sum Σu∈V(G) |Lu| is maximized, is called a maximum X-list assignment of G. In this paper, we prove a Circuit Simulation Lemma that, strictly speaking, makes it possible to simulate any Boolean function by effective 3-colourings of a graph that is polynomial-time constructable from the Boolean function itself. We use the lemma to simply prove some old results as corollaries, and also we prove that the following decision problem, related to the computation of the fixing number of a graph [Daneshgar 1997,... 

In this work an analytical solution is presented for a viscoelastic micro-beam based on the modified couple stress theory which is a non-classical theory in continuum mechanics. The modified couple stress theory has the ability to consider small size effects in micro-structures. It is strongly emphasized that without considering these effects in such structures the solution will be wrong and not suitable for designing systems in micro-scales. In this study correspondence principle is used for deriving constitutive equations for viscoelastic material based on the modified couple stress theory. Governing equilibrium equations are obtained by considering an element of micro-beam. Closedform... 

Based on the classical Donnell's and Love's shell theories, free vibration behavior of variable-thickness thin cylindrical shells rotating with a constant angular velocity is analyzed. The equations of motion and corresponding boundary conditions of rotating homogenous cylindrical shells with axisymmetric variation of thickness are derived using Hamilton's principle. This formulation includes effects of initial hoop tension due to the centrifugal force as well as Coriolis and centrifugal accelerations. Considering the variation of stiffness coefficients in axial direction, the classical Love's theory results in a coupled system of two second-order and one fourth-order partial differential... 

A nonlinear fluid–structure interaction (FSI) model is presented for nonlinear vibration analysis of sandwich cylindrical shells subjected to an external compressible flow by considering the curvature nonlinearity in impermeability condition and bending. The sandwich shells are made of two face sheets and a central core of advanced materials including functionally graded (FG), metal foam, and anisogrid lattice composite. Based on the Kirchhoff–love hypotheses with the geometric nonlinearities in the normal strain and curvature of mid-surface, one decoupled nonlinear integral–differential equation is obtained for axisymmetric bending vibration of sandwich cylindrical shells. For the first... 

Based on the linear fluid-solid interaction (FSI) model and classical shell theories, vibration behavior of sandwich cylindrical shells subjected to external incompressible or compressible fluid flow is investigated. The sandwich shell includes the same outer and inner face sheets made of carbon nanotube (CNT) reinforced composites and a metal foam core. The effective mechanical properties of CNT reinforced composites are obtained using the extended rule of mixture. Also, the porosity distribution through the foam thickness is assumed to be in the form of a trigonometric function. Equations of motion and corresponding boundary conditions are derived according to the Donnell's, Love's and... 

The governing equations of coupled thermoelasticity of Timoshenko micro-beams are developed based on the generalized thermoelastic theory and non-Fourier heat conduction model. Such problems may arise in MEMS such as micro-pumps as well as micro-sensors. The present model is on the basis of non-classical continuum theory and non-Fourier heat conduction model which has capability of capturing the size-effect in micro-scaled structures. Governing equations and both classical and non-classical boundary conditions of motion are obtained using the variational approach. As the case study, the present model is utilized for the simply supported micro-beams subjected to a constant impulsive force per... 

A size-dependent, explicit formulation for coupled thermoelasticity addressing a Timoshenko microbeam is derived in this study. This novel model combines modified couple stresses and non-Fourier heat conduction to capture size effects in the microscale. To this purpose, a length-scale parameter as square root of the ratio of curvature modulus to shear modulus and a thermal relaxation time as the phase lag of heat flux vector are considered for predicting the thermomechanical behavior in a microscale device accurately. Governing equations and boundary conditions of motion are obtained simultaneously through variational formulation based on Hamilton's principle. As for case study, the model is... 

Based on the first-order shear deformation (FSD) model and nonlocal elasticity theory, the simultaneous effects of shear and small scale on the nonlinear vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams are investigated for the first time. To this end, the governing equations of bending and stretching with von Kármán geometric nonlinearity are decoupled into one fourth-order partial differential equation in terms of transverse deflection. A closed-form solution of the nonlinear natural frequency, which can be used in conceptual design and optimization algorithms of FG- CNTRC beams with different boundary conditions, is developed using a hybrid... 

Based on the first-order shear deformation (FSD) model and nonlocal elasticity theory, the simultaneous effects of shear and small scale on the nonlinear vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams are investigated for the first time. To this end, the governing equations of bending and stretching with von Kármán geometric nonlinearity are decoupled into one fourth-order partial differential equation in terms of transverse deflection. A closed-form solution of the nonlinear natural frequency, which can be used in conceptual design and optimization algorithms of FG- CNTRC beams with different boundary conditions, is developed using a hybrid...