Dynamic response of a non-uniform Timoshenko beam, subjected to moving mass

2014 ◽  
Vol 229 (14) ◽  
pp. 2499-2513 ◽  
Author(s):  
Davod Roshandel ◽  
Massood Mofid ◽  
Amin Ghannadiasl
Keyword(s):  
Dynamic Response ◽  
Timoshenko Beam ◽  
Expansion Method ◽  
Mode Shapes ◽  
Natural Mode ◽  
Moving Mass ◽  
Orthonormal Polynomial ◽  
Eigenfunction Expansion Method ◽  
Polynomial Series ◽  
Series Expansion Method

In this article, the dynamic response of a non-uniform Timoshenko beam acted upon by a moving mass is extensively investigated. To this end, the eigenfunction expansion method is adapted to the problem, employing the natural mode shapes of a uniform Timoshenko beam. Moreover, the orthonormal polynomial series expansion method is successfully applied to the coupled set of governing differential equations pertaining to the dynamic behavior of non-uniform Timoshenko beam actuated by a moving mass. Some numerical examples are solved in which the excellent agreement of the two presented methods is illustrated.

Vibration analysis of a Mindlin elastic plate under a moving mass excitation by eigenfunction expansion method

2013 ◽  
Vol 62 ◽  
pp. 53-64 ◽  
Author(s):  
Javad Vaseghi Amiri ◽  
Ali Nikkhoo ◽  
Mohammad Reza Davoodi ◽  
Mohsen Ebrahimzadeh Hassanabadi
Keyword(s):  
Elastic Plate ◽  
Eigenfunction Expansion ◽  
Vibration Analysis ◽  
Expansion Method ◽  
Moving Mass ◽  
Eigenfunction Expansion Method

scholarly journals Dynamic response of Timoshenko beam under moving mass

2012 ◽  
Author(s):  
S. Eftekhar Azam ◽  
M. Mofid ◽  
R. Afghani Khoraskani
Keyword(s):  
Dynamic Response ◽  
Timoshenko Beam ◽  
Moving Mass

Extraction of mode shapes of beam-like structures from the dynamic response of a moving mass

2019 ◽  
Vol 35 (3) ◽  
pp. 664-673
Author(s):  
Yao Zhang ◽  
Longqi Wang ◽  
Haisheng Zhao ◽  
Seng Tjhen Lie
Keyword(s):  
Dynamic Response ◽  
Mode Shapes ◽  
Moving Mass

Dynamic Response of a Nonuniform Timoshenko Beam with Elastic Supports, Subjected to a Moving Spring-Mass System

2018 ◽  
Vol 18 (05) ◽  
pp. 1850066 ◽  
Author(s):  
Guojin Tan ◽  
Wensheng Wang ◽  
Yongchun Cheng ◽  
Haibin Wei ◽  
Zhigang Wei ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Timoshenko Beam ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Summation Method ◽  
Mode Shapes ◽  
Response Analysis ◽  
Timoshenko Beams ◽  
Mass System ◽  
Elastic Supports

This paper is concerned with the dynamic response of a nonuniform Timoshenko beam with elastic supports subjected to a moving spring-mass system. The modal orthogonality of nonuniform Timoshenko beams and the corresponding overall matrix of undetermined coefficients are derived. Then the natural frequencies and mode shapes of nonuniform Timoshenko beams are obtained by the Runge–Kutta method and cubic spline interpolation method. By using the Newmark-[Formula: see text] method and the mode summation method, the vibration equation of Timoshenko beams subjected to a moving spring-mass system was established. A comparison of results between the proposed method and finite element method reveals that this method possesses favorable accuracy for dynamic response analysis. In numerical examples, the effects of the support spring and moving spring-mass system on Timoshenko beams have been examined in detail.

scholarly journals Nonlinear Dynamic Analysis of a Timoshenko Beam Resting on a Viscoelastic Foundation and Traveled by a Moving Mass

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ahmad Mamandi ◽  
Mohammad H. Kargarnovin
Keyword(s):  
Dynamic Response ◽  
Timoshenko Beam ◽  
Nonlinear Dynamic Analysis ◽  
Dynamic Responses ◽  
Moving Mass ◽  
Viscoelastic Foundation ◽  
Cross Sectional ◽  
Nonlinear Viscoelastic ◽  
Fixed End ◽  
Traveling Mass

The dynamic response of a Timoshenko beam with immovable ends resting on a nonlinear viscoelastic foundation and subjected to motion of a traveling mass moving with a constant velocity is studied. Primarily, the beam’s nonlinear governing coupled PDEs of motion for the lateral and longitudinal displacements as well as the beam’s cross-sectional rotation are derived using Hamilton’s principle. On deriving these nonlinear coupled PDEs the stretching effect of the beam’s neutral axis due to the beam’s fixed end conditions in conjunction with the von-Karman strain-displacement relations is considered. To obtain the dynamic responses of the beam under the act of a moving mass, derived nonlinear coupled PDEs of motion are solved by applying Galerkin’s method. Then the beam’s dynamic responses are obtained using mode summation technique. Furthermore, after verification of our results with other sources in the literature a parametric study on the dynamic response of the beam is conducted by changing the velocity of the moving mass, damping coefficient, and stiffnesses of the foundation including linear and cubic nonlinear parts, respectively. It is observed that the inclusion of geometrical and foundation stiffness nonlinearities into the system in presence of the foundation damping will produce significant effect in the beam’s dynamic response.

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