Sharif Digital Repository

This paper aims at investigating the interaction of two flexible permanent magnet beams facing each other. The governing equations of motion are obtained based on the Euler-Bernoulli beam model along with Hamiltons principle. Assuming that the beams tips are far enough, each magnet beam is considered as a series of dipole segments and the external force and moment distributions over each beam due to the magnetic field of the other one is calculated in the deformed configuration. The transverse deflections of the beams are written as series expansions of the mode shapes of an unloaded cantilever beam and the Galerkin method is applied to determine the stability and resonance frequencies.... 

Meshless methods are a relatively new type of numerical methods that have attracted the attention of many researchers over the past years. So far, a number of meshless methods have been developed and applied to solve problems in various fields of engineering, including solid mechanics and geotechnical problems. The Element-Free Galerkin (EFG) method is adopted in this study for solving the governing partial differential equations of equilibrium and continuity of pore fluid flow for numerical simulation of coupled hydro-mechanical problems. For this purpose, the weak form of the governing equations is derived by applying the weighted residual method and Galerkin technique. The penalty method... 

Nonlinear torsional vibrations of thin-walled beams exhibiting primary and secondary warpings are investigated. The coupled nonlinear torsional-axial equations of motion are considered. Ignoring the axial inertia term leads to a differential equation of motion in terms of angle of twist. Two sets of torsional boundary conditions, that is, clamped-clamped and clamped-free boundary conditions are considered. The governing partial differential equation of motion is discretized and transformed into a set of ordinary differential equations of motion using Galerkin's method. Then, the method of multiple scales is used to solve the time domain equations and derive the equations governing the... 

Application of curved beams in special structures requires a special analysis. In this study, the differential quadrature method (DQM) as a well-known numerical method is utilized in the dynamic analysis of the Euler-Bernoulli curved beam problem with a uniform cross section under a constant moving load. DQ approximation of the required partial derivatives is given by a weighted linear sum of the function values at all grid points. A prismatic semicircular arch with simply supported boundary conditions is assumed. The accuracy of the obtained results is corroborated by employing the Galerkin and finite element methods. Finally, the convergence rate of the DQM and Finite Element Method (FEM)... 

The small-scale effect on the natural frequencies and buckling of pressurized nanotubes is investigated in this study. Based on the firstorder shear deformable shell theory, the nonlocal theory of elasticity is used to account for the small-scale effect and the governing equations of motion are obtained. Applying modal analysis technique and based on Galerkin's method a procedure is proposed to obtain natural frequencies of vibrations. For the case of nanotubes with simply supported boundary conditions, explicit expressions are obtained which establish the dependency of the natural frequencies and buckling loads of the nanotube on the small-scale parameter and natural frequencies obtained by... 

This paper aims the nonlinear aeroelastic analysis of slender wings using a nonlinear structural model coupled with the linear unsteady aerodynamic model. High aspect ratio and flexibility are the specific characteristic of this type of wings. Wing flexibility, coupled with long wingspan can lead to large deflections during normal flight operation of an aircraft; therefore, a wing in vertical/forward-afterward/torsional motion using a third-order form of nonlinear general flexible Euler-Bernoulli beam equations is used for structural modeling. Unsteady linear aerodynamic strip theory based on the Wagner function is used for determination of aerodynamic loading on the wing. Combining these... 

In this paper application of Functionally Graded Materials (FGMs) in suspension bridge structures for the purpose of vertical vibration improvement is investigated. Functionally graded materials are inhomogeneous composites, which are usually made from a mixture of metal and ceramic. Initially the classical equation of motion is modified based on the FGM model and natural frequencies of structure are extracted by Galerkin method. The material properties of structure vary continuously in the longitude direction according to power law form. In this regard, combination of materials is structured in such a way that the desired frequencies of the bridge are achieved by designing the proper power... 

This paper is devoted to investigate the nonlinear behaviors of a V-shaped microcantilever of an atomic force microscope (AFM) operating in its two major modes: amplitude modulation and frequency modulation. The nonlinear behavior of the AFM is due to the nonlinear nature of the AFM tip-sample interaction caused by the Van der Waals attraction/repulsion force. Considering the V-shaped microcantilever as a flexible continuous system, the resonant frequencies, mode shapes, governing nonlinear partial and ordinary differential equations (PDE and ODE) of motion, boundary conditions, frequency and time responses, potential function and phase-plane of the system are obtained analytically. The... 

In this study, the nonlinear vibrations analysis of an inclined pinned-pinned self-weight Timoshenko beam made of linear, homogenous and isotropic material with a constant cross section and finite length subjected to a traveling mass/force with constant velocity is investigated. The nonlinear coupled partial differential equations of motion for the rotation of warped cross section, longitudinal and transverse displacements are derived using the Hamilton's principle. These nonlinear coupled PDEs are solved by applying the Galerkin's method to obtain dynamic responses of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are obtained for various... 

In this paper, size dependent static behavior of micro and nano cantilevers actuated by a static electric field including deflection and pull-in instability, is analyzed implementing nonlocal theory. Euler-bernoulli assumptions are made to model the relation between deflection of the beam and bending moment. Differential form of the constitutive equation of nonlocal theory is used to find the revised equation for bending moment and substituting in the equilibrium equation of electrostatically actuated beams final nonlinear ordinary differential equation is arrived. Also the boundary conditions for solving the equation are revised and to analyze the size effect better governing equation is... 

A finite element analysis was developed to determine thermomechanical behaviours of strip and work-roll during cold rolling process under practical rolling conditions. The velocity field was first obtained using a rigid-plastic finite element formulation and then it was used to assess the strain and stress distributions within the strip and at the same time, a thermal finite element model based on streamline upwind Petrov-Galerkin scheme was employed to predict temperature distribution within the metal being rolled. In the next stage, the predicted temperature and stress fields at the contact region of strip/work-roll were employed as the boundary conditions to evaluate the thermomechanical... 

An investigation of the possible performance improvements of thin walled composite beams through the use of the variable stiffness concept with curvilinear fiber is presented. The beams are constructed from a single-cell closed cross section and a number of non-classical effects such as material anisotropy, transverse shear, warping inhibition and nonuniform torsional model are considered in the beam model. The governing equations were derived by means of the extended Hamilton's principle. Also the extended Galerkin's method is used to solve governing equations. Composite beams subjected to different loading with given geometry and material properties are optimized for maximum failure load.... 

This paper proposes a control strategy for the autonomous (islanded) operation of a four-wire, electronically-coupled distributed generation (DG) unit which can feed a highly unbalanced load, e.g., due to the presence of single-phase loads. In the grid-connected mode, the power-electronic interface of the DG unit enables the exchange of real and reactive power with the distribution network, based on the conventional dq-frame current control strategy. The current control scheme is disabled subsequent to the detection of an islanding event, and the proposed controller is activated. The proposed control strategy utilizes: i) an internal oscillator to maintain the island frequency and ii) a... 

This paper proposes a hybrid possibilistic-probabilistic evaluation tool for analyzing the effect of uncertain power production of distributed generations (DGs) on active losses of distribution networks. The considered DG technologies are gas and wind turbines. This tool is useful for distribution network operators (DNOs) when they are faced with uncertainties which some of them can be modeled probabilistically and some of them are described possibilistically. The generation pattern of DG units changes the flow of lines and this will cause change of active losses which DNO is responsible for compensating it. This pattern is highly dependent on DG technology and also on decisions of DG... 

This paper undertakes to facilitate appraisal of aeroelastic interaction of a locally distributed, flap-type control surface with aircraft wings operating in a subsonic potential flow field. The extended Hamilton's principle serves as a framework to ascertain the Euler-Lagrange equations for coupled bending-torsional-flap vibration. An analytical solution to this boundary-value problem is then accomplished by assumed modes and the extended Galerkin's method. The developed aeroelastic model considers both the inherent flexibility of the control surface displaced on the wing and the inertial coupling between these two flexible bodies. The structural deformations also obey the Euler-Bernoulli... 

Prior to the design and fabrication of MEMS/NEMS devices, analysis of static and dynamic behaviors of these systems is necessary. In the present study, the nonlinear dynamic behavior of micro- and nano-mechanical resonators is investigated and classified based on the resonator’s physical parameters for first time. The Galerkin method is used to convert the distributed-parameter model to a nonlinear ordinary differential equation where mid-plane stretching, axial stress, DC electrostatic and AC harmonic voltages are taken into account. To obtain the analytical frequency response of the micro resonator near its primary resonance, the second order multiple scales method is applied to the... 

Abstract In this paper, the solution of multi-group neutron/adjoint equation using Finite Element Method (FEM) for hexagonal and rectangular reactor cores is reported. The spatial discretization of the neutron diffusion equation is performed based on two different Finite Element Methods (FEMs) using unstructured triangular elements generated by Gambit software. Calculations are performed using Galerkin and Generalized Least Squares FEMs; based on which results are compared. Using the power iteration method for the neutron and adjoint calculations, the neutron and adjoint flux distributions with the corresponding eigenvalues are obtained. The results are then validated against the valid... 

In this paper, a reduced order model for the nonlinear dynamic analysis of the wind turbine blade under operational loading is presented. The accuracy and efficiency of the proposed model are investigated through various static and dynamic analyses. A comprehensive straightforward formulation for the nonlinear beam model is developed based on different large deformation strain theories. Also, the fluid-structure coupling effects due to quasi-steady aerodynamics and gravitational forces are included. The new matrix expressions are introduced for direct conversion of the developed formulation into the reduced order model (ROM). Thereafter, the ROM based on the Galerkin method is developed... 

In this paper, the coupled three-dimensional flexural vibration of micro-rotors is investigated by taking into account the small-scale effects utilizing the strain gradient theory, which is a powerful nonclassical continuum theory in capturing small-scale effects. A micro-rotor consists mainly of a flexible micro-rotating shaft and a disk. With the aid of Hamilton's principle, governing equations of motion are derived and then transformed to the complex form. By implementing the Galerkin's method, a coupled ordinary differential equation is attained for the system. Expressions for the first two natural frequencies of the spinning micro-rotors are obtained with truncated two-term equation.... 

Motivated by specific applications, electrostatically actuated bistable arch shaped micro-nano resonators have attracted growing attention in the research community in recent years. Nevertheless, some issues relating to their nonlinear dynamics, including the possibility of chaos, are still not well known. In this paper, we investigate the chaotic vibrations of a bistable resonator comprised of a double clamped initially curved microbeam under combined harmonic AC and static DC distributed electrostatic actuation. A reduced order equation obtained by the application of the Galerkin method to the nonlinear partial differential equation of motion, given in the framework of Euler-Bernoulli beam...