Sharif Digital Repository

Dynamic response of infinite beams supported by random viscoelastic Pasternak foundation subjected to harmonic moving loads is studied. Vertical stiffness in the support is assumed to follow a stochastic homogeneous field consisting of a small random variation around a deterministic mean value. By employing the first order perturbation theory and calculating appropriate Green's functions, the variance of the deflection and bending moment are obtained analytically in integral forms. To simulate the induced uncertainty, two practical cases of cosine and exponential covariance are utilized. A frequency analysis is performed and influences of the correlation length of the stiffness variation on... 

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... 

In the present work, the thermodynamic of dense fluids, both compressed liquids and dense supercritical fluids, has been modeled, solely, based on the contribution of attraction of effective pair potential. The intermolecular interaction is modeled by the hard-core Yukawa potential (HCY) as an effective pair potential (EPP) with temperature dependent hard-core diameter. Using this EPP in the exact thermodynamic relations, an equation of state (EoS) for the compressibility factor of dense fluid has been derived. This EoS shows that (Z - ZCS) as function of ρ1/3 must be linear for each isotherm of fluid where ZCS is the compressibility factor of the reference fluid (Carnahan-Starling (CS) EoS)... 

The limitations of the microfabrication technology do not allow producing perfectly smooth microchannels. Hence, exploring the influences of roughness on transport phenomena in microtubes is of great importance to the scientific community. In the present work, consideration is given toward the corrugated roughness effects on fully developed electroosmotic flow and heat transfer in circular microtubes. Analytical solutions based on perturbation technique are presented for the problem assuming a low zeta potential under the constant heat flux boundary condition of the first kind. It is revealed that higher values of the corrugation number and relative roughness give rise to smaller Nusselt... 

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... 

In the present work, several new thermodynamic linear isotherm regularities for the dense fluids have been derived for the first time. For this purpose, the thermodynamic perturbation theory (TPT) employing only the attractive effective pair potential (AEPP) as u(r) = - ϵeff (σeff / r)m was used, where σeff which is the effective hard core diameter, is temperature dependent and m > 0. Based on the derived regularities, the isotherm (Z - Z(0))v2 is a linear function of ρ2, ρ and 1/ρ, depends on the values of m = 12, 9 and 6, respectively where Z - Z(0) is the difference between the experimental compressibility factor of the real fluid (Z) and that of the reference fluid (Z(0)). Also, Z - Z(0)... 

Application of piezoelectric materials in vibration energy harvesters is expanding rapidly, especially in MEMS-based devices, due to their uncomplicated fabrication processes and reasonable power generation potential. In addition to standard power extraction methods, nonlinear switched techniques with capability of generated power enhancement, are previously developed and extensively applied in energy harvesting using piezoelectric materials. In this article, vibratory behavior of bimorph resonant harvesters coupled to nonlinear circuits of energy harvesting including standard and switched techniques is investigated. An analytical approach employing some perturbation technique, is utilized... 

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... 

The behavior of non-Newtonian fluids is considered as an important subject in micro scale and microfluidic flow researches. Because of the complexity and cost in the numerical works and the experimental set-ups in some instances, the analytical approach can be taken into account as a robust alternative tool to solve the non-Newtonian microfluidic flows in some special cases benefiting from a few simplified assumptions. In this work, we analyze the flow of two non-Newtonian fluids including the power-law and grade-fluid models in microchannels. For the grade-fluid, the stress tensors are defined considering the Rivlin-Ericksen tensor definitions. To avoid the complexities in the entrance... 

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... 

As sizes decrease, the advantages of application of piezoelectric materials for mechanical to electrical energy conversion become more obvious in comparison with electromagnetic and electrostatic techniques, according to uncomplicated fabrication processes of microscale piezoelectric harvesters together with their considerable amounts of generated power. Cantilevered silicon beams with surface bounded piezoelectric layers form the main structure of these MEMS-based harvesters. Lowering the resonance frequency down to the range of environmental vibration frequencies is one of the most significant challenges in MEMS harvesters which is usually attempted to be achieved by thinning the beam and... 

Application of piezoelectric materials in vibration energy harvesters is expanding rapidly, especially in MEMS-based devices, due to their uncomplicated fabrication processes and reasonable power generation potential. In addition to standard power extraction methods, nonlinear switched techniques with capability of generated power enhancement, are previously developed and extensively applied in energy harvesting using piezoelectric materials. In this article, vibratory behavior of bimorph resonant harvesters coupled to nonlinear circuits of energy harvesting including standard and switched techniques is investigated. An analytical approach employing some perturbation technique, is utilized... 

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... 

The purpose of this paper is to design and analyze a 3-link micro-device proposed as a micro-manipulator. This micro-manipulator includes 3 micro-beams as links connected to one another with no conventional or flexural joints. While the structure of the micro-manipulator is monolithic, end-effector workspace is achieved through deflection of links which is actuated by piezoelectric layers. By combining static analysis of the links through a multilayer piezoelectric beam model and kinematic analysis of the micro-manipulator, inverse kinematic has been solved utilizing the Taylor series expansion technique and the perturbation method. The obtained results through the present model reveal that... 

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... 

Environmental issues and energy crisis have caused the world attention to the renewable energies; especially the wind power, since they have low cost and high reliability. To achieve higher capacity, wind turbines have increased in their size over the years. However, the large size of the modern turbines has exacerbated the problem of vibrations, which results in lower efficiency and power generation. Because of the large deformations, the conventional linear theories cannot model the blades accurately, due to the importance of nonlinear effects in large scale wind turbines. In this research, a nonlinear kinematic model of the wind turbine blade is developed using the Hamilton's principle.... 

The feasibility and performance of standard and boundary layer perturbation techniques in nonlinear analyses of cylindrical shells are investigated. To this end, the nonlinear axisymmetric behavior of short and long functionally graded (FG) cylindrical shells is considered. The nonlinear governing equations of shell theory with first-order approximation and the von Karman nonlinearity are decoupled. This uncoupling makes it possible to present an analytical solution. A new boundary layer perturbation solution is presented by reducing the governing equations to a normalized form of boundary-layer type. Also, the uncoupled governing equations are solved using standard one-, two-, and...