Sharif Digital Repository

The response of a Timoshenko beam with uniform cross-section and infinite length supported by a generalized Pasternak-type viscoelastic foundation subjected to an arbitrary-distributed harmonic moving load is studied in this paper. Governing equations are solved using complex Fourier transformation in conjunction with the residue and convolution integral theorems. The solution is directed to compute the deflection, bending moment and shear force distribution along the beam length. A parametric study is carried out for an elliptical load distribution and influences of the load speed and frequency on the beam responses are investigated. © 2004 Elsevier Ltd. All rights reserved  

In this paper, a continuous model for vibration analysis of a beam with an open edge crack including the effects of shear deformation and rotary inertia is presented. A displacement field is suggested for the beam and the strain, and stress fields are calculated. The governing equation of motion for the beam has been obtained using Hamilton's principle. The equation of motion is solved with a modified Galerkin method and the natural frequencies and mode shapes are obtained. A good agreement has been observed between the results of this research and the results of previous work done in this fiels. The results are also compared to results of a similar model with Euler-Bernoulli assumptions to... 

In this study, the homotopy analysis method is used to obtain an accurate analytical solution for fundamental non-linear natural frequency and corresponding displacement of tapered beams. Comparison between the obtained results and numerical solutions shows that the first-order approximation of present study leads to accurate solutions with a maximum relative error less than 0.5%  

In this paper, a continuous model for flexural vibration of beams with a vertical edge crack including the effects of shear deformation and rotary inertia is presented. The crack is assumed to be an open-edge crack perpendicular to the neutral plane. A quasi-linear displacement filed is suggested for the beam, and the strain and stress fields are calculated. The governing equation of motion for the beam has been obtained using Hamilton principle. The equation of motion is solved with a modified weighted residual method, and the natural frequencies and mode shapes are obtained. The results are compared to the results of similar model with Euler–Bernoulli assumptions and finite element model... 

On the basis of the modified couple stress theory, some analytical results are obtained for vibrational parameters of micro-spinning Rayleigh beams with an axial mass-eccentricity distribution. The modified couple stress theory is a nonclassical continuum theory capable to capture the size effects in small-scale structures. After writing the governing equations of motion, they are transformed to the complex form. Then by utilizing the Galerkin method, analytical expressions for natural frequencies of the micro-spinning beam in forward and backward whirl motions are obtained. Critical speeds are also analytically presented in the two whirl motions for different modes. Moreover, the... 

In this study, a periodic beam-like structure consisting of the horizontal and inclined beam elements is proposed. Three models with three different angles of inclination are considered. The generalized differential quadrature (GDQ) and generalized differential quadrature rule (GDQR) methods are used to solve the differential equations of longitudinal and transverse vibrations, respectively. The effects of two geometrical parameters on the first three band gaps of each model are investigated, comprehensively. Results show that this periodic structure has wide band gaps at low frequency ranges. Furthermore, the band gaps can get close to each other by changing the geometrical parameters.... 

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... 

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... 

This paper presents a nonlinear size-dependent Timoshenko beam model based on the modified couple stress theory, a non-classical continuum theory capable of capturing the size effects. The nonlinear behavior of the new model is due to the present of induced mid-plane stretching, a prevalent phenomenon in beams with two immovable supports. The Hamilton principle is employed to determine the governing partial differential equations as well as the boundary conditions. A hinged-hinged beam is chosen as an example to delineate the nonlinear size-dependent static and free-vibration behaviors of the derived formulation. The solution for the static bending is obtained numerically. The solution for... 

Laminated composite beams with non-uniform thickness are being used as primary structural elements in a wide range of advanced engineering applications. Tapered composite structures, formed by terminating some of the plies, create geometry and material discontinuities that act as sources for delamination initiation and propagation. Any small damage or delamination in these structures can progress rapidly without any visible external signs. Due to this reason early detection of damage in these systems during their service life is receiving increasing attention. The presence of a crack in a component or structure leads to changes in its global dynamic characteristics results in decreases in... 

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... 

The resonant frequency of flexural vibration for a dagger shaped atomic force microscope (AFM) cantilever has been investigated using the Timoshenko beam theory. Generally, three distinct regions are considered for dagger shaped cantilevers, one region with constant cross section and height and two double tapered regions. In this paper, the effects of the contact position, contact stiffness, the height of the tip, thickness of the beam, the height and breadth taper ratios of cantilever and the angle between the cantilever and the sample surface based on Timoshenko beam theory on the non-dimensional frequency and sensitivity to the contact stiffness have been studied. The differential... 

Passive control of vibration of beams subjected to moving loads is studied in which, an optimal tuned mass damper (TMD) system is utilized to suppress the undesirable beam vibration. Timoshenko beam theory is applied to the beam model having three types of boundary conditions, namely, hinged-hinged, hinged-clamped, and the clamped-clamped ends, and the governing equations of motion are solved using the Galerkin method. For every set of boundary conditions, a minimax problem is solved using the sequential quadratic programming method and the optimum values of the frequency and damping ratios for the TMD system are obtained. To show the effectiveness of the designed TMD system, simulations of...