Sharif Digital Repository

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... 

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... 

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 the present study, a theoretical model of a reaction–diffusion within an entrapped-cell photobioreactor packed with gel-granules containing immobilized photosynthetic bacterial cells is presented. The model is based on a system of two coupled nonlinear reaction–diffusion equations under steady-state condition for biochemical reactions occurring in the photobioreactor that describes the substrate and product concentration within the gel-granule. Simple analytical expressions for the concentration of substrate and product have been derived for all values of reaction–diffusion parameters, demonstrating competition between the diffusion and reaction in the gel-granule, using the homotopy... 

Piezoelectric materials are extensively applied for vibrational energy harvesting especially in micro-scale devices where other energy conversion mechanisms such as electromagnetic and electrostatic methods encounter fabrication limitations. A cantilevered piezoelectric bimorph beam with an attached proof (tip) mass for the sake of resonance frequency reduction is the most common structure in vibrational harvesters. According to the amplitude and frequency of applied excitations and physical parameters of the harvester, the system may be pushed into a nonlinear regime which arises from material or geometric nonlinearities. In this study nonlinear dynamics of a piezoelectric bimorph harvester... 

Characterization of droplet-hydrogel interfaces is of crucial importance to engineer droplet-hydrogel composites for a variety of applications. In order to develop electrokinetic diagnostic tools for probing droplet-hydrogel interfaces, the displacement of a charged droplet embedded in a polyelectrolyte hydrogel exposed to an oscillating electric field is determined theoretically. The polyelectrolyte hydrogel is modeled as an incompressible, charged, porous, and elastic solid saturated with a salted Newtonian fluid. The droplet is considered an incompressible Newtonian fluid with no charges within the droplet. The droplet-hydrogel interface is modeled as a surface with the thickness of zero... 

The phase diagram of the quantum compass ladder model is investigated through numerical density matrix renormalization group based on infinite matrix product state algorithm and analytic effective perturbation theory. For this model we obtain two symmetry-protected topological phases, protected by a Z2 × Z2 symmetry, and a topologically-trivial Z2-symmetry-breaking phase. The symmetry-protected topological phases - labeled by symmetry fractionalization - belong to different topological classes, where the complexconjugate symmetry uniquely distinguishes them. An important result of this classification is that, as revealed by the nature of the Z2-symmetry-breaking phase, the associated quantum... 

In this work, PC-SAFT, an equation of state based on perturbation theory, is applied to predict the reservoir fluids phase behavior. PC-SAFT parameters for pure components have previously been assessed, but they cannot be determined for petroleum fractions with unspecified components and composition. In order to remove this difficulty and making use of PC-SAFT model in the reservoir fluids simulations, a new approach is studied which leads to appearing generalized correlations for the estimation of PC-SAFT parameters for petroleum cuts and plus fractions using only their molecular weight and specific gravity, without the essential need for the characterization of petroleum fractions in... 

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... 

Piezoelectric materials are extensively applied for vibrational energy harvesting especially in micro-scale devices where other energy conversion mechanisms such as electromagnetic and electrostatic methods encounter fabrication limitations. A cantilevered piezoelectric bimorph beam with an attached proof (tip) mass for the sake of resonance frequency reduction is the most common structure in vibrational harvesters. According to the amplitude and frequency of applied excitations and physical parameters of the harvester, the system may be pushed into a nonlinear regime which arises from material or geometric nonlinearities. In this study nonlinear dynamics of a piezoelectric bimorph harvester... 

Conceptual discussion on highly nonlinear duffing type equation of surge motion of TLP gives a deep view on structural response under environmental loads with some simplifications. Such analytical response is a simple form that clarifies important points in behavior of the structure. This paper presents the dynamic motion responses of a TLP in regular sea waves obtained by applying three methods in time domain using MATLAB software. Surge motion equation of TLP is highly nonlinear because of large displacement and it should be solved with large perturbation parameter in time domain. In this paper, homotopy perturbation method (HPM) is used to solve highly nonlinear differential equation of... 

Micro-scale piezoelectric unimorph beams with attached proof masses are the most prevalent structures in MEMS-based energy harvesters considering micro fabrication and natural frequency limitations. In doubly clamped beams a nonlinear stiffness is observed as a result of midplane stretching effect which leads to amplitude-stiffened Duffing resonance. In this study, a nonlinear model of a doubly clamped piezoelectric micro power generator, taking into account geometric nonlinearities including stretching and large curvatures, is investigated. The governing nonlinear coupled electromechanical partial differential equations of motion are determined by exploiting Hamilton's principle. A... 

Conceptual discussion on highly nonlinear Duffing type equation of surge motion of TLP gives a deep view on structural response under environmental loads with some simplifications. Such analytical response is a simple form that clarifies important points in behavior of the structure. This paper presents the dynamic motion responses of a TLP in regular sea waves obtained by applying three methods in time domain using MATLAB software. Surge motion equation of TLP is highly nonlinear because of large displacement and it should be solved with large perturbation parameter in time domain. In this paper, homotopy perturbation method (HPM) is used to solve highly nonlinear differential equation of...