Sharif Digital Repository

In this paper, the strain gradient theory, a non-classical continuum theory capable of capturing the size effect observed in micro-scale structures, is employed in order to investigate the size-dependent mechanical behavior of microbars. For a strain gradient bar, the governing equation of motion and classical and non-classical boundary conditions are derived using Hamilton's principle. Closed form solutions have been analytically obtained for static deformation, natural frequencies and mode shapes of strain gradient bars. The static deformation and natural frequencies of a clamped-clamped microbar subjected to a uniform axial distributed force are derived analytically and the results are... 

The classical continuum theory is neither able to accurately model the mechanical behavior of micro/nano-scale structures nor capable of justifying the size-dependent behavior observed in these structures; so the non-classical continuum theories such as the strain gradient theory have been emerged and developed. In order to enable the finite element method (FEM) to more accurately deal with the problems in micro/nano-scale structures, a size-dependent Euler-Bernoulli beam element is developed based on the strain gradient theory. Compared to the classical Euler-Bernoulli beam element, the nodal displacement vector of the new Euler-Bernoulli beam element has an additional component, i.e. the... 

The dynamic behavior of a functionally graded (FG) simply supported Euler-Bernoulli beam subjected to a moving oscillator has been investigated in this paper. The Young's modulus and the mass density of the FG beam vary continuously in the thickness direction according to the power-law model. The system of equations of motion is derived by using Hamilton's principle. By employing Petrov-Galerkin method, the system of fourth-order partial differential equations of motion has been reduced to a system of second-order ordinary differential equations. The resulting equations are solved using Runge-Kutta numerical scheme. In this study, the effect of the various parameters such as power-law... 

In this paper, a two-link flexible manipulator is considered. For a prescribed motion, Timoshenko and Euler-Bernoulli beam models are considered. Using the Galerkin method, nonlinear equations of motion are solved. The Runge-Kutta method is employed for the time response integration method. A comparative study is made between the Euler-Bernoulli and Timoshenko beam models, with and without foreshortening effects. It is demonstrated that for two-link manipulators, both theories provide good models, and the results for both theories are very similar for all ranges of slenderness ratio. The findings suggest that for two-link manipulators with relatively high slenderness ratios, there is a... 

The effect of elastic foundation on the free vibration characteristics of embedded nanocones is investigated in this paper. The nanocone is modeled as a thin shell and the nonlocal elasticity theory is used to derive the governing equations of motion. Also the elastic medium is simulated using Winkler and Pasternak foundation models. Based on the modal analysis technique and applying the Galerkin method the governing equations are solved to obtain the natural frequencies. The drawn results emphasis the effects of geometry and small-scale parameter on the natural frequencies of nanocone. Also the effect of elastic foundation modulus on the resonance frequencies of the nanocones are studied... 

This paper aims to investigate aeroelastic stability boundary of subsonic wings under the effect of thrust of two engines. The wing structure is modeled as a tapered composite box-beam. Moreover, an indicial function based model is used to calculate the unsteady lift and moment distribution along the wing span in subsonic compressible flow. The two jet engines mounted on the wing are modeled as concentrated masses and the effect of thrust of each engine is applied as a follower force. Using Hamilton's principle along with Galerkin's method, the governing equations of motion are derived, then the obtained equations are solved in frequency domain using the K-method and the aeroelastic... 

A closed-loop control methodology is investigated for stabilization of a vibrating non-classical micro-scale Euler-Bernoulli beam with nonlinear electrostatic actuation. The dimensionless form of governing nonlinear Partial Differential Equation (PDE) of the system is introduced. The Galerkin projection method is used to reduce the PDE of system to a set of nonlinear Ordinary Differential Equations (ODE). In non-classical micro-beams, the constitutive equations are obtained based on the non-classical continuum mechanics. In this work, proper control laws are constructed to stabilize the free vibration of non-classical micro-beams whose governing PDE is derived based on the modified strain... 

Various methods for solving the forward/adjoint equation in hexagonal and rectangular geometries are known in the literatures. In this paper, the solution of multigroup forward/adjoint equation using Finite Element Method (FEM) for hexagonal and rectangular reactor cores is reported. The spatial discretization of equations is based on Galerkin FEM (GFEM) using unstructured triangle elements. Calculations are performed for both linear and quadratic approximations of the shape function; based on which results are compared. Using power iteration method for the forward and adjoint calculations, the forward and adjoint fluxes with the corresponding eigenvalues are obtained. The results are then... 

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... 

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 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... 

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... 

A decentralized servomechanism controller for islanded (autonomous) operation of radial connection of two distributed generation (DG) units is proposed in this paper. Each DG unit utilizes a voltage-sourced converter (VSC) for interface to its dedicated load. The DG units and the loads are to operate in the islanded mode of operation. Each DG unit regulates the voltage of its dedicated load in a decentralized manner. In this paper, it is first shown that the radial connection of two DG units in the islanded mode constitutes an interconnected composite system consisting of two subsystems. Moreover, the paper shows that the overall islanded system can be controlled by the local controllers,... 

In this study vibration amplitude, frequency and damping of a microbeam is controlled using a RLC block containing a capacitor, resistor and inductor in series with the microbeam. Applying this method all of the considerable characteristics of the oscillatory system can be determined and controlled with no change in the geometrical and physical characteristics of the microbeam. Euler-Bernoulli assumptions are made for the microbeam and the electrical current through the microbeam is computed by considering the microbeam deflection and its voltage. Considering the RLC block, the voltage difference between the microbeam and the substrate is calculated. Two coupled nonlinear partial... 

An accurate approximate closed-form solution is presented for bending of thin skew plates with clamped edges subjected to uniform loading using the extended Kantorovich method (EKM). Successive application of EKM together with the idea of weighted residual technique (Galerkin method) converts the governing forth-order partial differential equation (PDE) to two separate ordinary differential equations (ODE) in terms of oblique coordinates system. The obtained ODE systems are then solved iteratively with very fast convergence. In every iteration step, exact closed-form solutions are obtained for two ODE systems. It is shown that some parameters such as angle of skew plate have an important... 

In this paper, the nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions subjected to a traveling mass with variable velocity is investigated. The nonlinear coupled partial differential equations of motion for the bending rotation of cross-section, longitudinal and transverse displacements are derived using Hamilton's principle. These nonlinear coupled PDEs are solved by applying Galerkin's method to obtain dynamic response of the beam under the act of a moving mass. The appropriate parametric studies by taking into account the effects of the magnitude of the traveling mass, the velocity of the traveling mass with a constant acceleration/ deceleration...