جستجوی مقالات مرتبط با کلیدواژه "galerkin" در نشریات گروه "مکانیک"

The present paper is aimed to analyze static deformation, natural frequency and subharmonic resonance of a bilayer cantilever microbeam, the second layer of which has a variable width and is located on a point along the microbeam's length. Electrostatic actuation is induced by applying the voltage between the microbeam and its opposite electrode. The importance of such configuration is revealed particularly in mass and pollutants micro-sensors. First, the nonlinear equation of motion, which has been extracted in previous studies using Hamilton's principle and considering the bending neutral axis shortening assumption, was rewritten for a microbeam with variable-width second layer. Then differential equations governing the static deflection and free vibration equation around the stability point are solved using Galerkin method. Three mode shapes of a doubled stepped-microbeam are employed as the comparison function. The shapes such as triangular, parabolic, symmetric parabolic and hyperbolic are considered for the second layer. In order to find the optimal length and thickness for the selected form, the relevant diagrams were plotted for static deformation and natural frequency at constant volume and different lengths and thicknesses, and then were analyzed and investigated. The discretized equations are solved by the perturbation theory. The excitation frequency is tuned near twice the fundamental natural frequencies (subharmonic excitation). The results show that system behavior depends on the size, position and width of the coated layer. The results of this paper can be used for optimum design of microsystems such as microswitches and mass and pollutant microsensors.

In this study, static deflection, natural frequency and nonlinear vibration in bi-layer clamped-clamped microbeam are investigated. In this configuration, the second layer is the viscoelastic layer which covers a part of the microbeam length. This model is the main element of many chemical microsensors. The governing equations of motion for the system are obtained by Lagrange method and discretized using the assumed mode method. The non-uniform micro-beam modes shape are used as the comparison function in the assumed mode method. Initially, considering the DC voltage, system static response and natural frequency around the static position are obtained. Then, considering the AC voltage, the dynamic response around the dynamic position is calculated by both analytical (perturbation method) and numerical methods (Rung-kutta) and compared for validation purposes. The effect of different geometrical parameters of the viscoelastic layer on the static and dynamic behaviors of the system is also analyzed. The results indicate that the dimensions and location of the viscoelastic layer significantly affect the static and dynamic behavior of the system. Therefore, by using this property and considering the application of microsensors, their behaviors can be made efficient. For sensors operating based on resonance frequency shift, the optimum shift of frequency state can be obtained by varying the dimensions and position of the viscoelastic layer. Moreover, time of response can be optimized when the system is operating based on changes in the capacity of a capacitor. The results also represent that convergence in the assumed mode method used in this paper is feasible even using a single mode, whereas in previous works and using the Galerkin method, convergence was fulfilled in the presence of 3 modes.

In this paper, pull-in behavior of cantilever micro/nano beams made of bi directional functionally graded materials (BDFGM) with small scale effects under electrostatic force is investigated. Couple stress theory is employed to study the influence of small-scale on pull-in behavior. The material properties except Poisson’s ratio obey the arbitrary function in the thickness and length direction. The approximate analytical solutions for the pull-in voltage and pull-in displacement of the microbeams are derived using the Galerkin method. Comparison between the results of present work with other article for pull-in behavior of a microbeams made of isotropic material reveals the accuracy of this study. Numerical results explored the effects of material length scale parameter, inhomogeneity constant, gap distance and dimensionless thickness.

In this paper, the vibration behavior of the sandwich beams with functionally graded face-sheets is investigated based on the high order sandwich beam theory.The properties of the FGM are varied gradually across the thickness of the structures in accordant with the power-law rule. First-order shear deformation theory and polynomial patterns are used to model the displacements of the face-sheets and the core, respectively. The governing equations of the motion are obtained based on Hamilton’s energy principle and solved by a Galerkin method. An algebraic method is used to reduce the number of equations. Boundary conditions are considered as simply supported and clamped.The effect of the power-law index and geometrical variations are surveyed on the fundamental frequency parameter for different sandwich beams in some numerical examples. In order to verify the results of the present study, they are compared with special cases of the literature.

This article provides a fully analytical approach for nonlinear equilibrium path of rectangular sandwich plates. The core of structure is made of symmetric cross-ply laminated composite and the outer surfaces are piezoelectric actuators which perfectly bonded to inner core. The structure is subjected to electro-thermo-mechanical loads simultaneously. One side of plate is rested on Pasternak type elastic foundation. The equilibrium equations of plate are derived based on the higher-order shear deformation theory of Reddy taking into account initial geometrical imperfection, nonlinear strain-displacement relations of von-Karman, temperature dependent properties, and different types of boundary conditions. Some numerical examples are presented to verify the accuracy of the proposed formulation. The effects of various parameters such as voltage on actuators, elastic foundation, imperfection, and pre-load condition on the buckling and postbuckling behaviors are studied. As an important finding of current research, there may be exists bifurcation point for imperfect plates by applying voltage on actuators.