Sharif Digital Repository

In the current paper, a coupled two degree of freedom model which considers both bending and torsion of the supporting torsion beams is presented for electrostatically actuated torsional nano/micro-actuators under the effect of van der Waals (vdW) force. Newton's second law is utilized for finding the normalized equations governing the static behavior of the actuator. The implict function theorem is then utilized for finding the equations governing the pull-in state of the actuator. The related results show that torsion model considerably overestimates the pull-in parameters of the nano/micro-actuator. The concept of the instability mode is introduced, and it is shown that when the ratio of... 

The objective of this paper is to apply He's homotopy perturbation method (HPM) to analyze nonlinear free vibration of simply supported Timoshenko beams considering the effects of rotary inertia and shear deformation. First, the equation governing the nonlinear free vibration of a Timoshinko beam is nondimensionalized. Galerkin's projection method is utilized to reduce the governing nonlinear partial differential equation to a nonlinear ordinary differential equation. HPM is then used to find analytic expressions for nonlinear natural frequencies of the pre-stretched beam. A parametric study has also been applied in order to investigate the effects of design parameters such as applied axial... 

This paper studies the effect of Casimir force on the pull-in instability of electrostatically actuated torsional nano/micro actuators. Dependence of the actuator's pull-in angle and pull-in voltage on several design parameters are investigated and it is found that Casimir force can considerably reduce the stability limits of the torsional actuators. Nonlinear equilibrium equation is solved numerically and analytically using straight forward perturbation expansion method. It is observed that a fourth-order perturbation approximation can precisely model the behavior of a torsional actuator. The results of this paper can be used for safe and stable design of torsional nano/micro actuators  

In this paper, the nonlinear oscillation of a pendulum wrapping and unwrapping on two cylindrical bases is studied, and an analytical solution is obtained using the multiple scales method. The equation of motion is derived based on an energy conservation technique. By applying the perturbation method to the differential equation, the nonlinear natural frequency of the system is calculated, along with its time response. Analytical results are compared with numerical findings and good agreement is found. The effect of large amplitude and radius of cylinders on system frequency is evaluated. The results indicate that as the radius of the cylinder increases, the system frequency is increased.... 

This paper deals with the problem of static instability of Micro/Nano mirrors under the combined effect of capillary force and Casimir force. At the First the governing equations of the statical behavior of Micro/Nano mirrors under the combined effect of capillary force and casimir force is obtained. The dependency of the critical tilting angle on the physical and geometrical parameters of the nano/micromirror and its supporting torsional beams is investigated. It is found that existence of casimir force can considerably reduce the stability limits of nano/micromirror. It is also found that rotation angle of the mirror due to capillary force highly depends on the casimir force applied to the... 

In the current paper, a general theoretical model for the problem of micromirrors under the effect of capillary forces is presented. The presented model considers the coupling effect between torsion and bending of the torsion beams supporting the micromirror. First, the energy method, the principal of minimum potential energy is utilized for finding the equations governing the micromirror rotation and its deflection. Then using the implicit functions theorem, the equations governing the pull-in angle and pull-in displacement of the micromirror is derived. The results, shows that ignoring the bending effect in micromirrors under the effect of capillary forces, can cause a significant (up to... 

In this paper, the static behavior of micromirrors under the effect of capillary forces is studied. First the equation governing the static behavior of micromirrors is obtained using both Newton method and minimum potential energy principle. Then energy method is employed to investigate the static instability of micromirrors equilibrium points. It is proved that when there exist two equilibrium points, the smaller one is stable and the larger one is unstable. Furthermore a design equation is suggested for the successful fabrication process of micromirrors in the stable operatives range. Then the statical behavior of micromirrors is investigated numerically and analytically using the Homotopy... 

In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational and buckling analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differential equation. Homotopy and modified Lindstedt-Poincare (HPM) are applied to find analytic expressions for nonlinear natural frequencies and critical axial loads of the beams. Effects of design parameters such as axial load and slenderness ratio are investigated. The analytic expressions... 

This paper deals with the problem of static instability of nano switches under the effect of Casimir force and electrostatic actuation. The nonlinear fringing field effect has been accounted for in the model. Using a Galerkin decomposition method and considering only one mode, the nonlinear boundary value problem describing the static behavior of nano-switch, is reduced to a nonlinear boundary value ordinary differential equation which is solved using the homotopy perturbation method (HPM). In order to ensure the precision of the results, the number of included terms in the perturbation expansion has been investigated. Results have been compared with numerical results and also with... 

In this study, static deflection and Instability of double- clamped nanobeams actuated by electrostatic field and intermolecular force, are investigated. The model accounts for the electric force nonlinearity of the excitation and for the fringing field effect. Effects of mid-plane stretching and axial loading are considered. Galerkin's decomposition method is utilized to convert the nonlinear differential equation of motion to a nonlinear algebraic equation which is solved using the homotopy perturbation method. The effect of the design parameters such as axial load and mid-plane stretching on the static responses and pull-in instability is discussed. Results are in good agreement with... 

This paper presents an extended Kantorovich approach to investigate the vibrational behavior of electrically actuated rectangular microplates. The model accounts for the electric force of the excitation and for the applied in plane loads. Starting from a one term Galerkin approximation and following the extended Kantorovich procedure, the partial differential equation governing the microplate vibration, is discretized to two ordinary differential equation with constant coefficients. These equations are then solved analytically and iteratively with a rapid convergence procedure for finding microplate natural frequencies and modeshapes. Results in some specific cases are validated against... 

This paper presents dynamic and vibration analysis of a flight vehicle with consideration of the free fitting between its two sections. Using the Lagrangian approach, a general analytical model is developed for a non-spinning elastic vehicle in planar motion. The model contains rigid body motions and bending deformations of two sections of the flight vehicle and a nonlinear rotational spring that models the freeplay between the two sections. To express bending deformation, the mode summation method is applied. It is shown that freeplay in the joints significantly affects the trajectory of the flight vehicle. Numerical examples reveal the effect of a joint's nonlinearity on the trajectory and... 

This paper applies the homotopy perturbation method to the simulation of the static response of nano-switches to electrostatic actuation and intermolecular surface forces. The model accounts for the electric force nonlinearity of the excitation and for the fringing field effect. Using a mode approximation in the Galerkin projection method, the nonlinear boundary value differential equation describing the statical behavior of nano-switch is reduced to a nonlinear algebraic equation which is solved using the homotopy perturbation method. The number of included terms in the perturbation expansion for achieving a reasonable response has been investigated. Three cases have been specifically... 

The aim of this paper is to present an Extended Kantorovich approach to simulate the static deflection of microplates under electrostatic voltage. The model accounts for the electric force nonlinearity of the excitation. Starting from a one term Galerkin approximation and following the Extended Kantorovich procedure, the equations governing the microplate deflection are obtained. These equations are then solved iteratively with a rapid convergence procedure to yield the desired solution. The results are validated, comparing them with other theoretical results and experimental findings, reported in the literature. It is shown that rapid convergence, high precision and independency of initial... 

This study presents a novel statistical volume element (SVE) for micromechanical modeling of the white matter structures, with histology-informed randomized distribution of axonal tracts within the extracellular matrix. The model was constructed based on the probability distribution functions obtained from the results of diffusion tensor imaging as well as the histological observations of scanning electron micrograph, at two structures of white matter susceptible to traumatic brain injury, i.e. corpus callosum and corona radiata. A simplistic representative volume element (RVE) with symmetrical arrangement of fully alligned axonal fibers was also created as a reference for comparison. A... 

Optimal hyperplastic coeficients of the micromechanical constituents of the human brain stem were investigated. An evolutionary optimization algorithm was combined with a Finite Element (FE) model of a Representative Volume Element (RVE) to nd the optimal material properties of axon and Extra Cellular Matrix (ECM). The tension and compression test results of a previously published experiment were used for optimizing the material coeficients, and the shear experiment was used for the validation of the resulting constitutive model. The optimization algorithm was used to search for optimal shear moduli and ber sti ness of axon and ECM by tting the average stress in the axonal direction with the... 

A diffusion tensor imaging (DTI) -based statistical micromechanical model was developed to study the effect of axonal fiber architecture on the inter- and intra-regional mechanical heterogeneity of the white matter. Three characteristic regions within the white matter, i.e., corpus callosum, brain stem, and corona radiata, were studied considering the previous observations of locations of diffuse axonal injury. The embedded element technique was used to create a fiber-reinforced model, where the fiber was characterized by a Holzapfel hyperelastic material model with variable dispersion of axonal orientations. A relationship between the fractional anisotropy and the dispersion parameter of... 

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... 

A diffusion tensor imaging (DTI) -based statistical micromechanical model was developed to study the effect of axonal fiber architecture on the inter- and intra-regional mechanical heterogeneity of the white matter. Three characteristic regions within the white matter, i.e., corpus callosum, brain stem, and corona radiata, were studied considering the previous observations of locations of diffuse axonal injury. The embedded element technique was used to create a fiber-reinforced model, where the fiber was characterized by a Holzapfel hyperelastic material model with variable dispersion of axonal orientations. A relationship between the fractional anisotropy and the dispersion parameter of...