Sharif Digital Repository

In this paper two methods are presented that can be used to determine the dynamic behavior of viscoelastic beams with different boundary conditions, carrying a moving mass. An analytical-numerical formulation that transforms the governing differential equation in viscoelastic media into a set of ordinary differential equations and thereafter a discrete element model based on assumption that continuous viscoelastic beam can be replaced by a system of rigid bars and joints which resist relative rotation of attached bars. The physical properties of the joints can be found through considering the viscoelastic model of beams material. Correctness of results has been ascertained by a comparison,... 

In this paper, the forced vibrations of the fractional viscoelastic beam with the Kelvin-Voigt fractional order constitutive relationship is studied. The equation of motion is derived from Newton’s second law and the Galerkin method is used to discretize the equation of motion in to a set of linear ordinary differential equations. For solving the discretized equations, the radial basis functions and Sinc quadrature rule are used. In order to show the effectiveness and accuracy of this method, some test problem are considered, and it is shown that the obtained results are in very good agreement with exact solution. In the following, the proposed numerical solution is applied to exploring the... 

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 the adolescent idiopathic scoliosis (AIS) treatment, a brace is prescribed to the patients who have 20 to 45° curves on their spines to prevent the disorder's advancement. For the analysis of Milwaukee brace effects during time, finite element models (FEMs) of the spine (the thoracolumbar region) and the ribcage (contained 10 pairs of the ribs and the sternum) were prepared for two patients. For modeling the spine part, a new element was used in which a disc (as viscoelastic 3D beam) and a vertebra (as rigid link) were modeled as an element and the ribs and the sternum modeled by 3D elastic beams. The gravity, Milwaukee brace constraints and the forces of the brace's different regions... 

This paper presents a numerical parametric study on design parameters of multispan viscoelastic shear deformable beams subjected to a moving mass via generalized moving least squares method (GMLSM). For utilizing Lagrange's equations, the unknown parameters of the problem are stated in terms of GMLSM shape functions and the generalized Newmark-β scheme is applied for solving the discrete equations of motion in time domain. The effects of moving mass weight and velocity, material relaxation rate, slenderness, and span number of the beam on the design parameters and possibility of mass separation from the base beam are scrutinized in some detail. The results reveal that for low values of beam...