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eigenfunction-expansion-methods
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A new simplified formula in prediction of the resonance velocity for multiple masses traversing a thin beam
, Article Scientia Iranica ; Volume 23, Issue 1 , 2016 , Pages 133-141 ; 10263098 (ISSN) ; Mofid, M ; Eftekhar Azam, S ; Ebrahimzadeh Hassanabadi, M ; Sharif University of Technology
Abstract
In this article, transverse vibration of an Euler-Bernoulli beam carrying a series of traveling masses is analyzed. A semi-analytical approach based on eigenfunction expansion method is employed to achieve the dynamic response of the beam. The inertia of the traveling masses changes the fundamental period of the base beam. Therefore, a comprehensive parametric survey is required to reveal the resonance velocity of the traversing inertial loads. In order to facilitate resonance detection for engineering practitioners, a new simplified formula is proposed to approximate the resonance velocity
Parametric study of the dynamic response of thin rectangular plates traversed by a moving mass
, Article Acta Mechanica ; Volume 223, Issue 1 , September , 2012 , Pages 15-27 ; 00015970 (ISSN) ; Rofooei, F. R ; Sharif University of Technology
2012
Abstract
The governing differential equation of motion of a thin rectangular plate excited by a moving mass is considered. The moving mass is traversing on the plate's surface at arbitrary trajectories. Eigenfunction expansion method is employed to solve the constitutive equation of motion for various boundary conditions. Approximate and exact expressions of the inertial effects are adopted for the problem formulation. In the approximate formulation, only the vertical acceleration component of the moving mass is considered while in the exact formulation all the convective acceleration components are included in the problem formulation as well. Parametric studies are carried out to investigate the...
Dynamic response of a non-uniform Timoshenko beam, subjected to moving mass
, Article Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science ; Volume 229, Issue 14 , October , 2015 , Pages 2499-2513 ; 09544062 (ISSN) ; Mofid, M ; Ghannadiasl, A ; Sharif University of Technology
SAGE Publications Ltd
2015
Abstract
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
Modal analysis of the dynamic response of Timoshenko beam under moving mass
, Article Scientia Iranica ; Volume 22, Issue 2 , 2015 , Pages 331-344 ; 10263098 (ISSN) ; Mofid, M ; Ghannadiasl, A ; Sharif University of Technology
Sharif University of Technology
2015
Abstract
In this study, the dynamic response of a Timoshenko beam under moving mass is investigated. To this end, vectorial form orthogonality property of the Timoshenko beam free vibration modes is applied to the EEM (Eigenfunction Expansion Method). The implication of the vectorial form series and an appropriate inner product of mode shapes in combination are focused for a beam with arbitrary boundary conditions. Consequently, significant simplifications and efficacy in the utilization of the EEM in eliminating the spatial domain is achieved. In order to comprise validation, the present study is compared with the DET (Discrete Element Technique) and the RKPM (Reproducing Kernel Particle Method)