Sharif Digital Repository

The current paper deals with the problem of static instability of Micro/Nano mirrors under the combined effect of capillary force and van der Waals force. First the governing equations of the statical behavior of Micro/Nano mirrors under the combined effect of capillary force and casimir force is obtained using the newtons first law of motion. The dependence 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 vdW torque can considerably reduce the stability limits of the nano/micromirror. It is also found that rotation angle of the mirror due to capillary force... 

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, a constitutive model with a temperature and strain rate dependent flow stress (Bergstrom hardening rule) and modified Armstrong-Frederick kinematic evolution equation for elastoplastic hardening materials is introduced. Based on the multiplicative decomposition of the deformation gradient,new kinematic relations for the elastic and plastic left stretch tensors as well as the plastic deformation-dependent spin tensor are proposed. Also, a closed-form solution has been obtained for the elastic and plastic left stretch tensors for the simple shear problem.To evaluate model validity, results are compared with known experimental data for SUS 304 stainless steel, which shows a good... 

In this paper, free vibration analysis of thin symmetrically laminated skew plates with fully clamped edges is investigated. The governing differential equation for skew plate which is a fourth order partial differential equation (PDE) is obtained by transforming the differential equation in Cartesian coordinates into skew coordinates. Based on the multi-term extended Kantorovich method (MTEKM) an efficient and accurate approximate closed-form solution is presented for the governing PDE. Application of the MTEKM reduces the governing PDE to a dual set of ordinary differential equations. These sets of equations are then solved with infinite power series solution, in an iterative manner until... 

In this paper, simple analytical expression is presented for large amplitude thermomechanical free vibration analysis of asymmetrically laminated composite beams. Euler-Bernoulli assumptions together with Von Karman's strain-displacement relation are employed to derive the nonlinear governing partial differential equation (PDE) of motion. He's variational method is employed to obtain a simple and efficient approximate closed form solution of the nonlinear governing equation. Comparison between results of the present work and those available in literature shows the accuracy of presented technique. Some new results for the nonlinear natural frequencies of the laminated beams such as the effect... 

Prior to the design and fabrication of MEMS/NEMS devices, analysis of static and dynamic behaviors of these systems is necessary. In the present study, the nonlinear dynamic behavior of micro- and nano-mechanical resonators is investigated and classified based on the resonator’s physical parameters for first time. The Galerkin method is used to convert the distributed-parameter model to a nonlinear ordinary differential equation where mid-plane stretching, axial stress, DC electrostatic and AC harmonic voltages are taken into account. To obtain the analytical frequency response of the micro resonator near its primary resonance, the second order multiple scales method is applied to the... 

This paper presents buckling analysis of a two-dimensional functionally graded cylindrical shell reinforced by axial stiffeners (stringer) under combined compressive axial and transverse uniform distributive load. The shell material properties are graded in the direction of thickness and length according to a simple power law distribution in terms of the volume fractions of the constituents. Primarily, the third order shear deformation theory (TSDT) is used to derive the equilibrium and stability equations. Since there is no closed form solution, the numerical differential quadrature method, (DQM), is applied for solving the stability equations. Initially, the obtained results for an... 

Consideration is given to shear-rate-dependent rheology effects on mass transport in a heterogeneous microreactor of rectangular cross section, utilizing both numerical and analytical approaches. The carrier liquid obeys the power-law viscosity model and is actuated primarily by an electrokinetic pumping mechanism. It is discovered that, considering the shear-thinning biofluids to be Newtonian fluids gives rise to an overestimation of the saturation time. The degree of overestimation is higher in the presence of large Damkohler numbers and electric double layer thicknesses. It is also increased by the application of a favorable pressure gradient, whereas the opposite is true when an opposed... 

Waveform design for target identification and classification in MIMO radar systems has been studied in several recent works. While the previous works assumed that the noise was independent of the transmission signals, here we extend the results to the signal dependent noise (clutter). We consider two scenarios. In the first scenario it is assumed that different transmit antennas see uncorrelated aspects of the target. In the second scenario, we consider the correlated target. As clutter is dependent to signal, target estimation error cannot vanish only by increasing the transmission power. It can be shown that in the second scenario, MIMO radar receiver can nullify the clutter subspace.... 

In this paper, the static stability of the variable cross section columns, subjected to distributed axial force, is considered. The presented solution is based on the singular perturbation method of Wentzel-Kramers-Brillouin and the column is modeled using Euler-Bernoulli beam theory. Closed-form solutions are obtained for calculation of buckling loads and the corresponding mode shapes. The obtained results are compared with the results in the literature to verify the present approach. Using numerous examples, it is shown that the represented solution has a very good convergence and accuracy for determination of the instability condition  

Consider an arbitrarily oriented ellipsoidal domain near the interface of an isotropic bimaterial space. It is assumed that a general class of piecewise nonuniform dilatational eigenstrain field is distributed within the ellipsoidal domain. Two theorems relevant to prediction of the nature of the induced displacement field for the interior and exterior points of the ellipsoidal domain are stated and proved. As a resultant the exact analytical expression of the elastic fields are obtained rigorously. In this work a new Eshelby-like tensor, A is introduced. In particular, the closed-form expressions for A associated with the interior points of spherical and cylindrical inclusion are derived.... 

Prior to the design and fabrication of MEMS/NEMS devices, analysis of static and dynamic behaviors of these systems is necessary. In the present study, the nonlinear dynamic behavior of micro- and nano-mechanical resonators is investigated and classified based on the resonator’s physical parameters for first time. The Galerkin method is used to convert the distributed-parameter model to a nonlinear ordinary differential equation where mid-plane stretching, axial stress, DC electrostatic and AC harmonic voltages are taken into account. To obtain the analytical frequency response of the micro resonator near its primary resonance, the second order multiple scales method is applied to the... 

In this paper, we propose a new 4-legged 6-DOF redundantly actuated UPS parallel mechanism. Kinematics, singularity and dynamics analyses of the proposed mechanism are addressed. Inverse kinematics has a closed-form solution, whereas the forward kinematics has a semi-closed form solution. Also, the Jacobian matrix has been determined using the concept of reciprocal screws. Using the principle of virtual work and minimum norm method, a general formulation for the inverse dynamics of redundantly actuated parallel manipulator is presented. Moreover, the proposed redundant mechanism has been compared with a similar but nonredundant mechanism in three aspects: reachable points, and actuation... 

Calculation of camera projection matrix, also called camera calibration, is an essential task in many computer vision and 3D data processing applications. Calculation of projection matrix using vanishing points and vanishing lines is well suited in the literature; where the intersection of parallel lines (in 3D Euclidean space) when projected on the camera image plane (by a perspective transformation) is called vanishing point and the intersection of two vanishing points (in the image plane) is called vanishing line. The aim of this paper is to propose a new formulation for easily computing the projection matrix based on three orthogonal vanishing points. It can also be used to calculate the... 

An algebraic closed-form solution for locating a moving target using a distributed multiple-input multiple-output radar system is proposed. The position and velocity of the target are estimated by presenting a two-stage weighted least squares algorithm. In contrast to existing research, the proposed estimator is shown analytically to be approximately unbiased and its variance is equal to the Cramer-Rao lower bound. Numerical simulations corroborate the theoretical studies and demonstrate the superiority of this algorithm over the existing methods. © 1997-2012 IEEE  

In this paper, we present a novel power allocation scheme for amplify and forward incremental relaying (IR) systems with the aim to minimize the overall outage probability at the destination. In our problem formulation, we take into account the outage-dependent activation of the relay when writing the power constraint. We provide a simple closed-form solution to the IR power allocation problem that is based on high signal-to-noise (SNR) approximation of the outage probability assuming maximum ratio combining (MRC) at the destination. We investigate the effectiveness of the proposed solution by comparing the achieved outage probabilities with those obtained through global numerical search. We... 

The nonlinear governing equations of three shell theories (Donnell, Love, and Sanders) with first-order approximation and von Kármán’s geometric nonlinearity for laminated sandwich cylindrical shells with isotropic, functionally graded (FG) or isogrid lattice layers are decoupled. This uncoupling makes it possible to present a semi-analytical solution for the nonlinear bending and post-buckling behavior of short and long doubly simply supported, doubly clamped, and cantilever laminated sandwich cylindrical shells subjected to various types of thermo-mechanical loadings. The results for deflection, stress, critical axial traction, and mode shapes in FG shells are verified with those obtained... 

The nonlinear governing equations of three shell theories (Donnell, Love, and Sanders) with first-order approximation and von Kármán’s geometric nonlinearity for laminated sandwich cylindrical shells with isotropic, functionally graded (FG) or isogrid lattice layers are decoupled. This uncoupling makes it possible to present a semi-analytical solution for the nonlinear bending and post-buckling behavior of short and long doubly simply supported, doubly clamped, and cantilever laminated sandwich cylindrical shells subjected to various types of thermo-mechanical loadings. The results for deflection, stress, critical axial traction, and mode shapes in FG shells are verified with those obtained... 

The scaled boundary finite element method (SBFEM) is known for its inherent ability to simulate unbounded domains and singular fields, and its flexibility in the meshing procedure. Keeping the analytical form of the field variables along one coordinate intact, it transforms the governing partial differential equations of the problem into a system of one-dimensional (initial–)boundary value problems. However, closed-form solution of the said system is not available for most cases (e.g. transient heat transfer, acoustics, ultrasonics, etc.) since the system cannot be diagonalized in general. This paper aims to establish a numerical tool within the context of the shooting technique to evaluate... 

In this article, an algebraic solution for localizing a moving target using a nonstationary multistatic radar system is proposed. By utilizing the quadruple hybrid measurement set, which consists of time delay, Doppler shift, angle of arrival, and angle rate measurements, the proposed method can estimate the target position and velocity vectors via a simple one-stage weighted least squares estimator without the need for introduction of the nuisance parameters, which enables us to locate the target with the minimum number of antennas. The proposed estimator takes the uncertainty concerned with the position and velocity of the antennas in its design. The proposed estimator is shown to be...