Sharif Digital Repository

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... 

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... 

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... 

In this paper, dynamic modeling and control problem for transfer of a sloshing liquid container suspended through rigid massless links from a team of quadrotors are investigated. By the proposed solution, pose of the slung container and fluid sloshing modes are stabilized appropriately. Dynamics of the container-liquid-quadrotors system is modeled by Euler-Lagrange method. Fluid slosh dynamics is included using multi-mass-spring model. According to derived model, a proper control law is designed for a system with three or more quadrotors. Implementing the proposed control law, quadrotors can control pose of the container, directions of the links and liquid sloshing modes simultaneously.... 

In this paper, nonlinear instability of an elliptical jet is investigated by considering the impacts of orifice geometry variations using regular perturbation method. In the breakup mechanisms, created disturbances on the jet interfaces will grow owing to the nonlinear dynamics of fluid. In this study, a scrutiny of nonlinear cylindrical jet breakup is done initially. Next, Cosserat equations as a low order form of Navies-Stokes equations are solved on the nonlinear form to exert the impacts of orifice deformation on various aspect ratios. These nonlinear equations, Cosserat equations, are linearly solved in the past papers. As a result, the dispersion equation is derived to find the most... 

Marton’s inner bound is the best known achievable rate region for a general two-receiver discrete memoryless broadcast channel. In this paper, we establish improved bounds on the cardinalities of the auxiliary random variables appearing in this inner bound to the true rate region. We combine a perturbation technique, along with a representation using concave envelopes of information-theoretic functions that involve the use of auxiliary random variables, to achieve this improvement. The new cardinality bounds lead to a proof that a randomized time-division strategy achieves every rate triple in Marton’s region for binary input broadcast channels. This extends the result by Hajek and Pursley... 

In this paper, some commonly used model reduction methods for integer-order systems are employed to approximate commensurate fractional-order linear systems. In comparison with the original system, the approximating model possesses a smaller inner dimension, while its fractional order is the same as that of the original system. The applied methods fall into the global reduction category, such as direct truncation and singular perturbation methods, and into the local reduction category, such as Pade approximation, partial realization, shifted Pade approximation, and rational interpolation methods. The applicability of these methods is illustrated by approximating a sample high-dimensional,... 

In the binary alloy with composition AxB1-x of two atoms with ionic energy scales ±Δ, an apparent Anderson insulator (AI) is obtained as a result of randomness in the position of atoms. Using our recently developed technique that combines the local self-energy from strong-coupling perturbation theory with the transfer matrix method, we are able to address the problem of adding a Hubbard U to the binary-alloy problem for millions of lattice sites on the honeycomb lattice. By adding the Hubbard interaction U, the resulting AI phase will become metallic, which in our formulation can be manifestly attributed to the screening of disorder by Hubbard U. Upon further increase in U, again the AI... 

The radiation loss in the whispering gallery resonators causes the eigenvalues of the Maxwell equations with the corresponding boundary conditions complex. The corresponding operators are nonhermitian and for these operators the standard perturbation techniques have some difficulties. In this paper by employing the Floquet theorem a new technique for the φ periodic perturbations is developed. The method is applied to obtain the change of resonance frequencies and losses of φ -perturbed microresonators with cylindrical symmetry. The results are compatible with that are obtained by the Volume Current Method  

In this study, we applied the homotopy perturbation (HP) method for solving linear and nonlinear fourth-order boundary value problems. The analytical results of the boundary value problems have been obtained in terms of a convergent series with easily computable components. Comparisons between the results of the HP method and the analytical solution showed that this method gives very precise results with a few terms. In the implied HP method, some unknown parameters in the initial guess are introduced, which are identified after applying boundary conditions. This improvement results in higher accuracy. © 2008 The Royal Swedish Academy of Sciences  

A two-dimensional depth-integrated numerical model is developed using a fourth-order Boussinesq approximation for an arbitrary time-variable bottom boundary and is applied for submarine-landslide-generated waves. The mathematical formulation of model is an extension of (4,4) Padé approximant for moving bottom boundary. The mathematical formulations are derived based on a higher-order perturbation analysis using the expanded form of velocity components. A sixth-order multi-step finite difference method is applied for spatial discretization and a sixth-order Runge-Kutta method is applied for temporal discretization of the higher-order depth-integrated governing equations and boundary... 

The dynamic response of the leg (tether) of a Tension Leg Platform (TLP), subjected to axial load at the top of the leg, is presented. The structural model is very simple, but several complicated factors, such as foundation effect, buoyancy and simulated ocean wave load, are considered. As an application, the effect of added mass fluctuation on the dynamic response of the leg subjected to such a load is presented. This effect is important in the fatigue life study of tethers. A first order perturbation method is used, in order to formulate and solve the problem. The differential equation is solved by means of non-harmonic Fourier expansion, in terms of eigenfunctions obtained from a... 

Total motion in waves can be considered as a superposition of the motion of the body in still water and the forces on the restrained body. In this study the effect of added mass fluctuation on vertical vibration of tension leg platforms (TLP) in the case of vibration in still water for both free and forced vibration subjected to axial load at the top of the leg is presented. This effect is more important when the amplitude of vibration is large. Also this is important in fatigue life study of tethers. The structural model used here is very simple. Perturbation method is used to formulate and solve the problem. First- and second-order perturbations are used to solve the free and forced... 

The vibration response of a Timoshenko beam supported by a viscoelastic foundation with randomly distributed parameters along the beam length and jected to a harmonic moving load, is studied. By means of the first-order two-dimensional regular perturbation method and employing appropriate Green's functions, the dynamic response of the beam consisting of the mean and variance of the deflection and of the bending moment are obtained analytically in integral forms. Results of a field measurement for a test track are utilized to model the uncertainty of the foundation parameters. A frequency analysis is carried out and the effect of the load speed on the response is studied. It is found that the... 

In this article, the effects of the changes in the mass of the floating wind turbine (as a multi-body system) on its nonlinear vertical vibrations are investigated. The fluctuations of the hydrodynamic added mass of the floating platform and the mass of the vibration absorbers, which added to the structure to mitigate the lateral vibrations, change the mass and consequently the dynamics of the vertical vibrations. In this regard, first, the governing equations of the vertical vibrations of the floating wind turbine are derived. The FAST code is used to validate the proposed model of the dynamics of the vertical vibrations through numerical simulations. Then, derived equations are solved... 

This is the first research on the nonlinear frequency analysis of a multi-scale hybrid nanocomposite (MHC) disk (MHCD) resting on an elastic foundation subjected to nonlinear temperature gradient and mechanical loading is investigated. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macroscale, respectively. We present a modified Halpin–Tsai model to predict the effective properties of the MHCD. The displacement–strain of nonlinear vibration of multi-scale laminated disk via third-order shear deformation theory (TSDT) and using Von Karman nonlinear shell theory is obtained. Hamilton’s principle is employed to establish the governing... 

In this study, the dynamics of the accelerated and steady-state motion of a single bubble in a quiescent highly viscous Newtonian liquid was investigated theoretically and experimentally. The presented mathematical model was based on Newton's second law of motion and a balance of buoyancy, drag, history, and added-mass forces. Due to the presence of non-linear terms in the equation of motion, homotopy perturbation method was used as a powerful analytical method to calculate the velocity analytically. To obtain accurate results in the experiments, a high-speed camera was used to record the bubble motion from the moment of detachment to the time at which the terminal velocity is reached.... 

One of the main challenges in diffusion-based molecular communication is dealing with the non-linearity of reaction-diffusion chemical equations. While numerical methods can be used to solve these equations, a change in the input signals or the parameters of the medium requires one to redo the simulations. This makes it difficult to design modulation schemes and practically impossible to prove the optimality of a given transmission strategy. In this paper, we provide an analytical technique for modeling the non-linearity of chemical reaction equations based on the perturbation method. The perturbation method expresses the solution in terms of an infinite power series. An approximate solution...