Sharif Digital Repository

A micro scale Timoshenko beam was modeled with strain gradient theory in "A micro scale Timoshenko beam model based on strain gradient elasticity theory" by Wang et al., European Journal of Mechanics - A/Solids, vol. 29, pp. 591-599, 7//2010. Looking at the modeling of the beam, a mistake in deriving the effect of classical moment has occurred. The classical boundary conditions of a Timoshenko beam could not be derived going backward from the strain gradient Timoshenko beam theory which has been presented in aforementioned paper. In this comment, the contradiction has been shown and the correct form of the boundary conditions and final equations has been derived  

A micro scale Timoshenko beam was modeled with strain gradient theory in “A micro scale Timoshenko beam model based on strain gradient elasticity theory” by Wang et al., European Journal of Mechanics – A/Solids, vol. 29, pp. 591–599, 7//2010. Looking at the modeling of the beam, a mistake in deriving the effect of classical moment has occurred. The classical boundary conditions of a Timoshenko beam could not be derived going backward from the strain gradient Timoshenko beam theory which has been presented in aforementioned paper. In this comment, the contradiction has been shown and the correct form of the boundary conditions and final equations has been derived  

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... 

The response of an infinite Timoshenko beam subjected to a harmonic moving load based on the thirdorder shear deformation theory (TSDT) is studied. The beam is made of laminated composite, and located on a Pasternak viscoelastic foundation. By using the principle of total minimum potential energy, the governing partial differential equations of motion are obtained. The solution is directed to compute the deflection and bending moment distribution along the length of the beam. Also, the effects of two types of composite materials, stiffness and shear layer viscosity coefficients of foundation, velocity and frequency of the moving load over the beam response are studied. In order to... 

The objective of this paper is to apply He's homotopy perturbation method (HPM) to analyze nonlinear free vibration of simply supported Timoshenko beams considering the effects of rotary inertia and shear deformation. First, the equation governing the nonlinear free vibration of a Timoshinko beam is nondimensionalized. Galerkin's projection method is utilized to reduce the governing nonlinear partial differential equation to a nonlinear ordinary differential equation. HPM is then used to find analytic expressions for nonlinear natural frequencies of the pre-stretched beam. A parametric study has also been applied in order to investigate the effects of design parameters such as applied axial... 

Natural frequencies are important dynamic characteristics of a structure where they are required for the forced vibration analysis and solution of resonant response. Therefore, the exact solution to free vibration of elastically restrained Timoshenko beam on an arbitrary variable elastic foundation using Green Function is presented in this paper. An accurate and direct modeling technique is introduced for modeling uniform Timoshenko beam with arbitrary boundary conditions. The applied method is based on the Green Function. Thus, the effect of the translational along with rotational support flexibilities, as well as, the elastic coefficient of Winkler foundation and other parameters are... 

In this paper, we consider the exponential stabilization problem of a Timoshenko beam with interior local controls with input delays. In the past, most of the stabilization results for the Timoshenko beam were on the boundary control with input delays. In the present paper we shall extend the method treating the boundary control with delays to the case of interior local control with delays. Essentially we design a new dynamic feedback control laws that stabilizes exponentially the system. Detail of the design procedure of the dynamic feedback controller and analysis of the exponential stability are given. © 2018 World Scientific and Engineering Academy and Society. All Rights Reserved  

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... 

Since the classical continuum theory is neither able to evaluate the accurate stiffness nor able to justify the size-dependency of micro-scale structures, the non-classical continuum theories such as the modified couple stress theory have been developed. In this paper, a new comprehensive Timoshenko beam element has been developed on the basis of the modified couple stress theory. The shape functions of the new element are derived by solving the governing equations of modified couple stress Timoshenko beams. Subsequently, the mass and stiffness matrices are developed using energy approach and Hamilton's principle. The formulations of the modified couple stress Euler-Bernoulli beam element... 

This paper presents the dynamic response of uniform Timoshenko beams with arbitrary boundary conditions using Dynamic Green Function. An exact and direct modeling technique is stated to model beam structures with arbitrary boundary conditions subjected to the external load that is an arbitrary function of time t and coordinate x and the concentrated moving load. This technique is based on the Dynamic Green Function. The effect of different boundary conditions, load, and other parameters is assessed. Finally, some numerical examples are shown to illustrate the efficiency and simplicity of the new formulation based on the Dynamic Green Function  

In this paper the non-planar nonlinear dynamic responses of an axially loaded rotating Timoshenko beam subjected to a three-directional force traveling with a constant velocity is studied. On deriving the nonlinear coupled partial differential equations (PDEs) of motion the stretching effect of the beam's neutral axis due to the pinned-pinned ends' condition in conjunction with the von Karman strain-displacement relation are considered. The beam's nonlinear governing coupled PDEs of motion for the bending rotations of warped cross-section, longitudinal and lateral displacements are derived using Hamilton's principle. To obtain the dynamic responses of the beam, derived PDEs of motion are... 

A composite beam with single delamination traveled by a constant amplitude moving force is modeled accounting for the Poisson's effect, shear deformation and rotary inertia. The mechanical behavior between the delaminated surfaces is modeled using a piecewise-linear spring foundation. The governing differential equations of motion for such system are derived. Primarily, eigen-solution technique is used to obtain the natural frequencies and their corresponding mode shapes of such beam. Then, the Ritz method is employed to derive the dynamic response of the beam due to the moving force. The obtained results for the free and forced vibrations of beams are verified against reported similar... 

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... 

In this paper, the predictions of different beam theories for the behavior of a shape memory polymer (SMP) beam in different steps of a thermomechanical cycle are compared. Employing the equilibrium equations, the governing equations of the deflection of a SMP beam in the different steps of a thermomechanical cycle, for higher order beam theories (Timoshenko Beam Theory and von-Kármán Beam Theory), are developed. For the Timoshenko Beam Theory, a closed form analytical solution for various steps of the thermomechanical cycle is presented. The nonlinear governing equations in von-Kármán Beam theory are numerically solved. Results reveal that in the various beam length to beam thickness... 

We have conducted Molecular Dynamics (MD) simulations with the Environment-Dependent Interatomic Potential (EDIP) to obtain the natural frequency of ultra-thin Silicon Nanowires (SiNWs) with various crystallographic structures, boundary conditions and dimensions. As expected, results show that the mechanical properties of SiNWs are size-/orientation-dependent. The observed phenomena are ascribed to the surface effects which become dominant due to the large surface-to-volume number of atoms at the investigated range of dimensions. Due to their accuracy, atomistic simulations are widely accepted for the investigations of such nano-scaled systems; however, they suffer from high computational... 

The free vibration analysis of rotating axially functionally graded nanobeams under an in-plane nonlinear thermal loading is provided for the first time in this paper. The formulations are based on Timoshenko beam theory through Hamilton’s principle. The small-scale effect has been considered using the nonlocal Eringen’s elasticity theory. Then, the governing equations are solved by generalized differential quadrature method. It is supposed that the thermal distribution is considered as nonlinear, material properties are temperature dependent, and the power-law form is the basis of the variation of the material properties through the axial of beam. Free vibration frequencies obtained are... 

Timoshenko beam model is widely exploited in the literature to examine the mechanical behavior of stubby beam-like components. Timoshenko beam theory is well-known to require the shear correction factor in order to recognize the non-uniform shear distribution at a section. While a variety of shear correction factors are appeared in the literature so far, there is still no consensus on the most appropriate form of the shear correction factor. The Saint-Venant's flexure problem is first revisited in the frame work of the classical theory of elasticity and a highly accurate approximate closed-form solution is presented employing the extended Kantorovich method. The resulted approximate solution...