Sharif Digital Repository

A single-walled nanotube structure embedded in an elastic matrix is simulated by the nonlocal EulerBernoulli, Timoshenko, and higher order beams. The beams are assumed to be elastically supported and attached to continuous lateral and rotational springs to take into account the effects of the surrounding matrix. The discrete equations of motion associated with free transverse vibration of each model are established in the context of the nonlocal continuum mechanics of Eringen using Hamilton's principle and an efficient meshless method. The effects of slenderness ratio of the nanotube, small scale effect parameter, initial axial force and the stiffness of the surrounding matrix on the natural... 

In this work we present an ellipsoid cavity regime for the production of a bunch of quasi-monoenergetic electrons. The electron output beam is more effective than the periodic plasma wave method or the plasma-channel-guided method. A hyperbola, parabola or ellipsoid path is described for the electron trajectory motion in this model. A dense bunch of relativistic electrons with a quasi-monoenergetic spectrum is self-generated here. The obtained results show a smaller width for the electron energy spectrum in comparison with the previous results. We found that there are optimum conditions to form the ellipsoid cavity. Laser beam properties (such as the spot size, power and pulse duration) and... 

Dynamic response of multispan viscoelastic thin beams subjected to a moving mass is studied by an efficient numerical method in some detail. To this end, the unknown parameters of the problem are discretized in spatial domain using generalized moving least square method (GMLSM) and then, discrete equations of motion based on Lagrange's equation are obtained. Maximum deflection and bending moments are considered as the important design parameters. The design parameter spectra in terms of mass weight and velocity of the moving mass are presented for multispan viscoelastic beams as well as various values of relaxation rate and beam span number. A reasonable good agreement is achieved between... 

In this paper, the effect of basic parameters of laser and plasma on controlling self-focusing is investigated, and based on the introduced effective parameter for self-focusing (EPSF), the effects of laser wavelength, the initial spot size of laser beam, the initial intensity of laser, and the plasma electron density on self-focusing are discussed. It is found that the relativistic self-focusing strongly depend on the laser wavelength and the beam intensity. The nonlinear effect of beam intensity on the introduced parameter EPSF indicates that after an increasing region for focusing, the self-focusing effect decreases at ultrarelativistic intensities. The effect of the initial beam spot... 

This paper presents the dynamic response of a delaminated composite beam under the action of a moving oscillating mass. In this analysis the Poisson's effect is considered for the first time. Moreover, the effects of rotary inertia and shear deformation are incorporated. In our modeling linear springs are used between delaminated surfaces to simulate the dynamic interaction between sub-beams. To solve the governing differential equations of motion using modal expansion series, eigen-solution technique is used to obtain the natural frequencies and their corresponding mode shapes necessary for forced vibration analysis. The obtained results for the free and forced vibrations of beams are... 

The dynamic response of a delaminated composite beam under the motion of an oscillatory mass moving with a constant velocity has been studied. The delaminated composite beam is modeled as four interconnected sub-beams using the delamination limits as their boundaries. The constrained model is used to model the delamination region. The continuity and equilibrium conditions are forced to be satisfied between the adjoining beams. A set of derived governing differential equations along with those obtained by imposing boundary conditions are simultaneously solved in a closed form manner. The results for the response of the delaminated beam were compared with those of the intact beam. Furthermore,... 

Predominance of nano-scale effects observed in material behavior at small scales requires implementation of new simulation methods which are not merely based on classical continuum mechanic. On the other hand, although the atomistic modeling methods are capable of modeling nano-scale effects, due to the computational cost, they are not suitable for dynamic analysis of nano-structures. In this research, we aim to develop a continuum-based model for nano-beam vibrations which is capable of predicting the results of molecular dynamics (MD) simulations with considerably lower computational effort. In this classical-based modeling, the surface and core regions are taken to have different... 

The resonant second harmonic generation in the presence of a wiggler magnetic field by twisted laser plasma interaction is surveyed. The wiggler magnetic field provides additional momentum required for the phase matching. The Laguerre-Gaussian modes can be used to control the self-focusing and improve the second harmonic generation in laser plasma interaction. The wave equations for the fundamental and the second harmonic fields have been solved in the paraxial approximation. The generation of the second harmonic considering self-focusing is investigated. Also, the dependence of the second harmonic power on the propagation distance for different values of initial fundamental beam intensity,... 

Propagation of Gaussian X-ray laser beam is presented in collisional quantum plasma and the beam width oscillation is studied along the propagation direction. It is noticed that due to energy absorption in collisional plasma, the laser energy drops to an amount less than the critical value of the self-focusing effect and consequently, the laser beam defocuses. It is found that the oscillation amplitude of the laser spot size enhances while passing through collisional plasma. For the greater values of collision frequency, the beam width oscillates with higher amplitude and defocuses in a shallower plasma depth. Also, it is realized that in a dense plasma environment, the laser self-focusing... 

This paper investigates the free vibration analysis of a doubly tapered magnetorheological rotating sandwich beam based on the Euler-Bernoulli theory. The beam is made of a magnetorheological elastomer core sandwiched between two elastic layers. Through energy approach the kinetic and potential energies of the system are written and using the Lagrange equation the discretized form of the governing equation is derived based on the Ritz method. The free vibration analysis is carried out to obtain the natural frequency and the corresponding loss factor of the beam. Finally, after validating the formulation in order to provide a deep insight the effects of different parameters on the free... 

A powerful and now theoretical approach is used to obtain an expression for the effect of creep on reinforced concrete shear deform able beams. First, a method is proposed for Ruler-Bernoulli beam to analyze the long-term behavior of concrete beams based on linear strain theory. Second, a formulation has been developed to analyze the strain distribution in shear deformablo concrete beams. Finally, three numerical examples are included in order to compare well-known codes with the proposed method. The comparison of the proposed method, FEM, codes, and experimental works demonstrates that the proposed analytical procedure can effectively simulate creep behavior of reinforced concrete beams.... 

A powerful and now theoretical approach is used to obtain an expression for the effect of creep on reinforced concrete shear deform able beams. First, a method is proposed for Ruler-Bernoulli beam to analyze the long-term behavior of concrete beams based on linear strain theory. Second, a formulation has been developed to analyze the strain distribution in shear deformablo concrete beams. Finally, three numerical examples are included in order to compare well-known codes with the proposed method. The comparison of the proposed method, FEM, codes, and experimental works demonstrates that the proposed analytical procedure can effectively simulate creep behavior of reinforced concrete beams.... 

In this paper, the tip tracking control problem of a Timoshenko micro-cantilever beam is investigated. The beam is actuated by a piezoelectric layer laminated on one side of the beam. Dynamic equations of the beam and piezoelectric layer are found using the Hamilton principle. By employing the Galerkin projection method, state space representation of the system is derived. Then, a cascade control loop is used for tracking control of the beam's tip. The cascade control structure consists of an inner loop stabilizer and an outer loop proportional-integral-derivative controller. The stabilizer has a linear feedback form whose states are obtained through a linear observer which is based on the... 

In this article, OPSEM (Orthonormal Polynomial Series Expansion Method) is developed as a new computational approach for the evaluation of thin beams of variable thickness transverse vibration. Capability of the OPSEM in assessing the free vibration frequencies and mode shapes of an Euler-Bernoulli beam with varying thickness is discussed. Multispan continuous beams with various classical boundary conditions are included. Contribution of BOPs (Basic Orthonormal Polynomials) in capturing the beam vibrations is also illustrated in numerical examples to give a quantitative measure of convergence rate. Furthermore, OPSEM is adopted for the forced vibration of a thin beam caused by a moving mass.... 

In this paper, a simple method for detection of multiple edge cracks in Euler-Bernoulli beams having two different types of cracks is presented based on energy equations. Each crack is modeled as a massless rotational spring using Linear Elastic Fracture Mechanics (LEFM) theory, and a relationship among natural frequencies, crack locations and stiffness of equivalent springs is demonstrated. In the procedure, for detection of m cracks in a beam, 3m equations and natural frequencies of healthy and cracked beam in two different directions are needed as input to the algorithm. The main accomplishment of the presented algorithm is the capability to detect the location, severity and type of each... 

In this paper, the tip tracking control problem of a Timoshenko micro-cantilever beam is investigated. The beam is actuated by a piezoelectric layer laminated on one side of the beam. Dynamic equations of the beam and piezoelectric layer are found using the Hamilton principle. By employing the Galerkin projection method, state space representation of the system is derived. Then, a cascade control loop is used for tracking control of the beam's tip. The cascade control structure consists of an inner loop stabilizer and an outer loop proportional-integral-derivative controller. The stabilizer has a linear feedback form whose states are obtained through a linear observer which is based on the... 

A size-dependent functionally graded Euler-Bernoulli beam model is developed based on the strain gradient theory, a non-classical theory capable of capturing the size-effect in micro-scaled structures. The governing equation and both classical and non-classical boundary conditions are obtained using variational approach. To develop the new model, the previously used simplifying assumption which considered the length scale parameter to be constant through the thickness is avoided in this work. As a consequence, equivalent length scale parameters are introduced for functionally graded microbeams as functions of the constituents' length scale parameters. Moreover, a generally valid closed-form... 

This paper deals with the dynamic analysis of a delaminated composite beam under the action of moving oscillatory mass. The beam is analyzed as four interconnected sub-beams using the delamination limits as their boundaries. The constrained model is used to model the delamination region. The continuity and equilibrium conditions are satisfied between the adjoining beams. The beam response variation due to the delamination with respect to the intact beam has been investigated. Furthermore, the possible separation of the moving oscillator from the beam during the course of the motion is investigated by monitoring the contact force between the oscillator and the beam. The effect of the... 

This article investigates the free vibration of the rotating, tapered, thin-walled, composite box beam. The structural model incorporates a number of non-classical effects, such as transverse shear, warping inhibition, non-uniformtorsional model, and rotary inertia.The results obtained in this article seek to clarify the effect of flap-twist coupling, taper ratio, slenderness ratio, angular velocity, fibre orientation, and hub ratio on natural frequencies and mode shapes of the rotating thin-walled composite beams. The results are expected to offer better predictions of the vibrational behaviour of these kinds of structures in general, and in the design of rotor blades of turbo machinery, in... 

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....