Sharif Digital Repository

In this paper, a new procedure is developed for the solution of a general two-dimensional uncoupled symmetric double contact problem with smooth contact zones in which the indenter geometry is described by a piecewise biquadratic function. This procedure gives an approximate closed-form solution for any smooth indenter profile. In order to evaluate the accuracy of this approach, it is applied to the symmetric indentation of a flat surface by two rigidly interconnected parabolic indenters and results are compared with the exact unclosed-form solution. Moreover, this procedure is applied to the symmetric indentation of a flat surface by two rigidly interconnected cylinders to compare the... 

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... 

In this paper, we will address the issue of power distribution and decoding order in the uplink side of a multirate code division multiple access (CDMA) system based on linear successive interference cancellation (SIC). First, the closed form expressions for the required received powers at the base station, in order to achieve the users bit rate and Quality of Service (QoS) requirements, will be derived. Then, we will investigate the problem of optimal decoding order of the users under imperfect interference cancellation condition and will show that optimum decoding order of users, unlike the case of perfect SIC, is a function of their requested SINR values in addition to their path gains.... 

In this paper, the dynamic characteristics of skewed bridges are explored analytically. Closed form solutions for translational and torsional periods of free vibration and mode shapes are given for slab-girder skewed bridges. Moreover, the seismic displacement of the deck of skewed bridges is calculated using the response spectrum method and its skew term is compared with the requirement of AASHTO. The effects of seismic force resisting elements, such as elastomeric bearings and end diaphragms are included. It is shown that the skew term in AASHTO's equation can underestimate the seat width requirement for some bridges. A new skew term for the bridge seat width requirement is suggested  

Non-linear bending analysis of tapered functionally graded (FG) beam subjected to thermal and mechanical load with general boundary condition is studied. The governing equations are derived and a discussion is made about the possibility of obtaining analytical solution. In the case of no axial force along the beam, a closed form solution is presented for the problem. For the general case with axial force, the Galerkin technique is employed to overcome the shortcoming of the analytical solution. Moreover, the Generalized Differential Quadrature (GDQ) method is also implemented to discretize and solve the governing equations in the general form and validate the results obtained from two other... 

MIMO radar is the next generation radar which transmits arbitrary waveforms at each one of its apertures. It has been shown that the design of waveforms for MIMO radars in order to synthesize a desired spatial beampattern is mapped into a waveform correlation matrix R design in the narrowband case. As of now, given a desired beampattern or estimated locations information of targets, calculating R has been modeled as an optimization problem like semi-definite programming. Also, in some special cases like rectangular beampattern, closed-form solutions for R has been proposed. In this paper, we introduce a fast algorithm which is capable of designing R in order to achieve more arbitrary... 

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... 

By reformulating the governing equations of the first-order theory into those describing the interior and edge-zone problems of the plate, closed-form solutions are presented for analysis of functionally graded circular sector plates with vertex angle (Formula presented.) whose radial edges are simply supported and subjected to transverse loading and heat conduction through the plate thickness. Various types of clamped, simply supported, and free-edge boundary supports are considered on the circular edge of the plate. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The effects of material... 

This paper deals with learning an overcomplete set of atoms that have low mutual coherence. To this aim, we propose a new dictionary learning (DL) problem that enables a control on the amounts of the decomposition error and the mutual coherence of the atoms of the dictionary. Unlike existing methods, our new problem directly incorporates the mutual coherence term into the usual DL problem as a regularizer. We also propose an efficient algorithm to solve the new problem. Our new algorithm uses block coordinate descent, and updates the dictionary atom-by-atom, leading to closed-form solutions. We demonstrate the superiority of our new method over existing approaches in learning low-coherence... 

In this paper, an approach is proposed to estimate the location of leakages in liquid transmission lines with a high accuracy. First, the mathematical model is analyzed and a closedform solution is provided for the partial differential equations of the pipeline. Next, the leakage location is calculated using the closed-form solution. The calculations are applied to various leakages and are extended to a case in which the pressure and flowrate do not converge to constant values. Considering a singleleakage pipeline system, a linear observer is utilized to estimate the leakage location with reduced errors. The simulation results are presented and the proposed method is verified by changing the... 

A sheet of graphene under magnetic bias attains anisotropic surface conductivity, opening the door for realizing compact devices such as Faraday rotators, isolators and circulators. In this paper, an accurate and analytical method is proposed for a periodic array of graphene ribbons under magnetic bias. The method is based on integral equations governing the induced surface currents on the coplanar array of graphene ribbons. For subwavelength size ribbons subjected to an incident plane wave, the current distribution is derived leading to analytical expressions for the reflection/transmission coefficients. The results obtained are in excellent agreement with full-wave simulations and predict... 

In this paper, we show how time-sharing method may reduce transmission delay in the dynamic index coding scenario. We propose a novel time-shared dynamic index coding transmission scheme that achieves the maximum index coding gain for a complete bi-directional side information graph and formulate a constrained optimization problem to tune the transmission scheme for the minimum transmission delay. A closed-form solution is presented for the special case of two-user. We also use analytical and simulation results to provide graphical intuition for the obtained results  

In this paper, the two-point boundary value problem (BVP) of the nano-cantilever deflection subjected to Casimir and electrostatic forces is investigated using analytical and numerical methods to obtain the instability point of the nano-beam. In the analytical treatment of the BVP, the nonlinear differential equation of the model is transformed into the integral form by using the Green's function of the cantilever beam. Then, closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. The pull-in parameters of the beam are computed under the combined effects of electrostatic and Casimir forces. Electrostatic microactuators... 

In this paper, a novel hybrid control approach is proposed to control the LLC resonant converter. Since the converter consists of both continuous variables and logical variables, it is intrinsically hybrid. Apart from that, because of fast dynamics of the converter and the fact that there is no closed form solution for discontinuous conduction modes (DCM), modeling and control of the LLC resonant converter is still a challenge. In the authors' previous work, a systematic model was proposed for the converter, the direct piecewise affine model. In this paper, an appropriate controller based on the proposed model is represented and the design procedure is discussed in details; the block diagram... 

In this article, an analytical method for calculating pull-in voltage is proposed. This method can accurately predict pull-in voltage of clamped-free, clamped-clamped and curved micro- and nano-beams. In this study, mid-plane stretching, axial stress, initial deformation and the effect of size are taken into account. To achieve this goal, governing equation of beam based on modified couple stress theory was first derived and then transformed to a single degree of freedom (D.O.F) model by Galerkin method. In this model, electrostatic force appears in integral form which is approximated to non-integral form employing Genetic Algorithm. This single degree of freedom model provides means for... 

This article intends to examine thermoelastic damping (TED) in circular cylindrical nanoshells by considering small-scale effect on both structural and thermal areas. To fulfill this aim, governing equations are extracted with the aid of nonlocal elasticity theory and dual-phase-lag (DPL) heat conduction model. Circular cylindrical shell is also modeled on the basis of Donnell–Mushtari–Vlasov (DMV) equations for thin shells. By inserting asymmetric simple harmonic oscillations of nanoshell into motion, compatibility and heat conduction equations, the size-dependent thermoelastic frequency equation is obtained. By solving this equation and deriving the frequency of nanoshell affected by... 

The present article intends to provide a size-dependent generalized thermoelasticity model and closed-form solution for thermoelastic damping (TED) in cylindrical nanoshells. With the aim of incorporating size effect within constitutive relations and heat conduction equation, nonlocal elasticity theory and Guyer–Krumhansl (GK) heat conduction model are exploited. Donnell–Mushtari–Vlasov (DMV) equations are also employed to model the cylindrical nanoshell. By adopting asymmetric simple harmonic form for oscillations of nanoshell and merging the motion, compatibility and heat conduction equations, the nonclassical frequency equation is extracted. By solving this eigenvalue problem and... 

A closed form solution is presented in this paper to study the dynamics of a composite beam with a single delamination under the action of a moving constant force. The delaminated beam is divided into four interconnected beams using the delamination limits as their boundaries. Governing motion equations are derived in which the differential stretching and the bending-extension coupling are considered. The method of modal analysis is adopted to derive analytically the dynamic response of each beam. The obtained results for the free vibrations of delaminated beam are verified against reported similar results in the literature. Moreover, the maximum dynamic response of such a beam is compared... 

The current paper uses the Extended Kantorovich Method (EKM) to analytically solve the problem of squeezed film damping in micromirrors. First a one term Galerkin approximation is used and following the extended Kantorovich procedure, the solution of the Reynolds equation which governs the squeezed film damping in micromirrors is reduced to solution of two uncoupled ordinary differential equation which can be solved iteratively with a rapid convergence for finding the pressure distribution underneath the micromirror. It is shown that the EKM results are independent of the initial guess function. It is also shown that EKM is highly convergent and practically one iterate is sufficient for...