Sharif Digital Repository

Because of technological restrictions, it is actually impossible to fabricate smooth microchannels. Therefore, exploring the roughness effects on the flow characteristics at microscale is of great importance for scientific communities. The present investigation deals with the effects of corrugated roughness on the fully developed slip flow forced convection in micropipes. The governing equations subject to first-order slip boundary conditions are solved by means of the straightforward perturbation method. Closed-form expressions are obtained for the dimensionless velocity and temperature distributions, for the friction coefficient and pressure drop, and finally for the Nusselt number. The... 

This paper addresses the optimality of Network topology for localization purposes when measurements are range-only. Localization procedures based on TOA and TDOA range measurements are considered in this paper. As of now, the optimal placement of fixed terminals to locate mobile terminals has been studied based on Cramer-Rao Lower Bound (CRLB). CRLB is a universal bound on the variance of a general unbiased estimator and therefore is not dependent to the estimator and methods of localization. Here we introduce another algorithm dependent criterion, based on perturbation theory of linear equations. Different optimal topologies are presented using the new criterion. These optimal topologies,... 

This paper uses Hes Homotopy Perturbation Method (HPM) to analyze the nonlinear free vibrational behavior of clamped-clamped and clamped-free microbeams considering the effects of rotary inertia and shear deformation. Galerkins projection method is used to reduce the governing nonlinear partial differential equation. to a nonlinear ordinary differential equation. HPM is used to find analytic expressions for nonlinear natural frequencies of the pre-stretched microbeam. A parametric study investigated the effects of design parameters such as applied axial loads and slenderness ratio. The effect of rotary inertia and shear deformation on the nonlinear natural frequency was investigated. For... 

In this paper, an analytical circuit model is proposed for 2-D arrays of graphene disks. First, we derive an analytical expression for the surface current density on a single graphene disk in the subwavelength regime, induced by a normally incident plane wave. The solution is then extended to 2-D arrays of graphene disks using perturbation theory. Finally, by applying appropriate boundary conditions, an R - L - C equivalent circuit of the structure is obtained. It is shown that both a single graphene disk and periodic array of graphene disks have dual capacitive-inductive nature. The results of the proposed model are in excellent agreement with those obtained by full-wave simulations  

Based on the first-order nonlinear von Karman theory, the post-buckling analysis of FG circular plates under asymmetric transverse and in-plane loadings are presented. The nonlinear governing equations are reformulated using a stress function and a boundary layer function, and solved by employing a multi-parameter perturbation technique and Fourier series method. The material properties are assumed to vary through the plate thickness according to a power-law distribution of the volume fractions of the constituents. The results are verified with the known results in the literature. The effects of loading, material properties, and boundary conditions on different response quantities are... 

Limit cycle walkers are known as a class of walking robots capable of presenting periodic repetitive gaits without having local controllability at all times during motion. A well-known subclass of these robots is McGeer’s passive dynamic walkers solely activated by the gravity field. The mathematics governing this style of walking is hybrid and described by a set of nonlinear differential equations along with impulses. In this paper, by applying perturbation method to a simple model of these machines, we analytically prove that for this type of nonlinear impulsive system, there exist different switching surfaces, leading to the same equilibrium points (periodic solutions) with different... 

The dynamics of multi-tethered satellite formations consisting of three masses are studied in this paper. The triple-mass triple-tethered satellite system is modeled under the low Earth orbit perturbations of drag and Earth's oblateness and its equilibrium conditions are derived. It is modeled as three equal end-masses connected by a uniform-mass straight tether. The lengths of tethers are supposed to be constant and in this manner the angles of the plane consisting the masses are taken as the state variables of the system. The governing equations of motion are derived using Lagrangian approach. The aerodynamic drag perturbation is expressed as an external nonconservative force and the Earth... 

Neutron noise induced by propagating thermal-hydraulic disturbances (propagation noise for short) in pressurized water reactors is investigated in this paper. A closed-loop neutron-kinetic/thermal-hydraulic noise simulator (named NOISIM) has been developed, with the capability of modeling the propagation noise in both Western-type and VVER-type pressurized water reactors. The neutron-kinetic/thermal-hydraulic noise equations are on the basis of the first-order perturbation theory. The spatial discretization among the neutron-kinetic noise equations is based on the box-scheme finite difference method (BSFDM) for rectangular-z, triangular-z and hexagonal-z geometries. Furthermore, the finite... 

Peripheral milling is extensively used in manufacturing processes, especially in aerospace industry where end mills are used for milling of wing parts and engine components. Knowledge of the cutting forces is the first necessary stage in analysis of the milling process. In this paper, cutting forces are presented for both two and three dimensional models. Instead of the common linear dependency of cutting forces to the cut chip thickness, two nonlinear models are presented. In the first model, cutting forces are considered as a function of chip thickness with a complete third order polynomial. In the second one, the quadratic and constant terms of the third order polynomial are set to zero.... 

This paper presents a nonlinear size-dependent Timoshenko beam model based on the modified couple stress theory, a non-classical continuum theory capable of capturing the size effects. The nonlinear behavior of the new model is due to the present of induced mid-plane stretching, a prevalent phenomenon in beams with two immovable supports. The Hamilton principle is employed to determine the governing partial differential equations as well as the boundary conditions. A hinged-hinged beam is chosen as an example to delineate the nonlinear size-dependent static and free-vibration behaviors of the derived formulation. The solution for the static bending is obtained numerically. The solution for... 

Nonlinear vibration of a microbeam actuated by a suddenly applied voltage with considering the effect of voltage distribution on the beam due to electrical resistivity of beam is investigated. Homotopy perturbation method is implemented to solve the coupled nonlinear partial differential equations of motion. The vibration frequency variation and damping at various resistivities is studied. Considering resistivity, effect of applied voltage and beam length on the frequency shift and damping ratio is analyzed. Findings indicate there exists a jump in frequency shift and damping ratio at a critical resistivity. Variation of critical resistivity with respect to modulus of elasticity and beam... 

The development of damage detection techniques for offshore jacket structures is vital for preventing catastrophic events. This paper applies a frequency response based method for the purpose of structural health monitoring. In this approach, the concept of a minimum rank perturbation theory is used. The feasibility of using a finite number of sensors and its effect on damage detection capabilities is investigated. In addition, the performance of the proposed method is evaluated in the case of multiple damages. The aforementioned points are illustrated using the numerical study of a two dimensional jacket platform  

The free longitudinal vibration of tapered nanowires is investigated in the context of nonlocal continuum theory. The problem is studied for the nanowires with linearly varied radii under fixedfixed and fixedfree boundary conditions. In order to assess the problem in a more general form, a perturbation technique is proposed based on the Fredholm alternative theorem. The natural frequencies, corresponding mode shapes, and phase velocities of the tapered nanowires are derived analytically up to the second-order perturbation for different boundary conditions. The predicted results by the perturbation technique are successfully verified with those of the exact solution. The obtained results... 

In this paper, primary resonance of a double-clamped microbeam has been investigated. The Microbeam is predeformed by a DC electrostatic force and then driven to vibrate by an AC harmonic electrostatic force. Effects of midplane stretching, axial loads and damping are considered in modeling. Galerkin's approximation is utilized to convert the nonlinear partial differential equation of motion to a nonlinear ordinary differential equation. Afterward, a combination of homotopy perturbation method and the method of multiple scales are utilized to find analytic solutions to the steady-state motion of the microbeam, far from pull-in. The effects of different design parameters on dynamic behavior... 

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  

In this study, static pull-in instability of electrostatically-actuated microbridges and microcantilevers is investigated considering different nonlinear effects. Galerkin's decomposition method is utilized to convert the nonlinear differential equations of motion to nonlinear integro-algebraic equations. Afterward, analytic solutions to static deflections of the microbeams are obtained using the homotopy perturbation method. Results are in excellent agreement with those presented in the literature  

The iterated perturbation theory (IPT) equations of the dynamical mean field theory (DMFT) for the half-filled Hubbard model are solved on nearly real frequencies at various values of the Hubbard parameters, U, to investigate the nature of metal-insulator transition (MIT) at finite temperatures. This method avoids the instabilities associated with the infamous Padé analytic continuation and reveals fine structures across the MIT at finite temperatures, which cannot be captured by conventional methods for solving DMFT-IPT equations on Matsubara frequencies. Our method suggests that at finite temperatures, there is a crossover from a bad metal to a bad insulator in which the height of the... 

Topological color codes are among the stabilizer codes with remarkable properties from the quantum information perspective. In this paper, we construct a lattice, the so-called ruby lattice, with coordination number 4 governed by a two-body Hamiltonian. In a particular regime of coupling constants, in a strong coupling limit, degenerate perturbation theory implies that the low-energy spectrum of the model can be described by a many-body effective Hamiltonian, which encodes the color code as its ground state subspace. Ground state subspace corresponds to a vortex-free sector. The gauge symmetry Z2 ×Z2 of the color code could already be realized by identifying three distinct plaquette... 

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...