Dynamic analysis of rectangular plates crossed by distributed moving loads

Abstract

This study investigates the dynamic behaviour of plates crossed by distributed moving gravitational and inertial loads, in the case in which the relative magnitude of the moving mass introduces a coupling effect with the structure, with possible applications to the vibration analysis of railway bridges. A rectangular Kirchhoff plate is considered, simply supported on two opposite edges and free on the other two edges, loaded by a partially distributed mass travelling in the parallel direction with respect to the free edges. The formulation includes damping, and it is accomplished by the Rayleigh–Ritz method, expressing the solution in semi-analytical form. The shape functions for describing the transverse displacement field of the plate are selected as tensor products of linearly independent eigenfunctions of homogeneous uniform beams in flexural vibration, yielding a low-order model with time-dependent coefficients. Numerical examples are then presented and discussed, aimed at investigating the effects of each of the model governing parameters.

Keywords

Rectangular plate distributed moving inertial load Rayleigh–Ritz method

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References

Fryba

. Vibration of solids and structures under moving loads. 3rd ed.London: Telford, 1999.

Fryba

. Dynamics of railway bridges. London: Telford, 1996.

Humar

Kashif

. Dynamic response analysis of slab–type bridges. J Struct Eng 1995; 121: 48–62.

Lin

. Vibration analysis of Timoshenko beams traversed by moving loads. J Marine Sci Technol 1994; 2: 25–35.

Stancioiu

Ouyang

Mottershead

. Vibration of a continuous beam excited by a moving mass and experimental validation. J Phys Conf Ser 2009; 181: 1–9.

Adetunde

. Dynamical behavior of Euler-Bernoulli beam traversed by uniform partially distributed moving masses. Res J Appl Sci 2007; 2: 476–483.

Lin

Cho

. Vibration suppression of beam structures traversed by multiple moving loads using a damped absorber. J Marine Sci Technol 1993; 1: 39–48.

Dyniewicz

Bajer

. New feature of the solution of a Timoshenko beam carrying the moving mass particle. Arch Mech 2010; 62: 327–341.

Dyniewicz

. Space–time finite element approach to general description of a moving inertial load. Finite Elem Anal Des 2012: 62: 8–17.

10.

Nikkhoo

Hassanabadi

Azam

. Vibration of a thin rectangular plate subjected to series of moving inertial loads. Mech Res Commun 2014; 55: 105–113.

11.

Marchesiello

Fasana

Garibaldi

. Dynamics of multi–span continuous straight bridges subject to multi–degrees of freedom moving vehicle excitation. J Sound Vib 1999; 224: 541–561.

12.

Gbadeyan

Oni

. Dynamic behaviour of beams and rectangular plates under moving loads. J Sound Vib 1995; 182: 677–695.

13.

De Faria

Oguamanam

. Finite element analysis of the dynamic response of plates under traversing loads using adaptive meshes. Thin Wall Struct 2004; 42: 1481–1493.

14.

Dyniewicz

Pisarski

Bajer

. Vibrations of a Mindlin plate subjected to a pair of inertial loads moving in opposite directions. J Sound Vib 2017; 386: 265–282.

15.

Gbadeyan

Dada

. Dynamic response of a Mindlin elastic rectangular plate under a distributed moving mass. Int J Mech Sci 2006; 48: 323–340.

16.

. Use of moving distributed mass element for the dynamic analysis of a flat plate undergoing a moving distributed load. Int J Numer Meth Eng 2007; 71: 347–362.

17.

Amiri

Nikkhoo

Davoodi

. Vibration analysis of a Mindlin elastic plate under a moving mass excitation by eigenfunction expansion method. Thin Wall Struct 2013; 62: 53–64.

18.

Meirovitch

. Principles and techniques of vibrations, Upper Saddle River, NJ: Prentice Hall, 1997.

19.

Warburton

. The vibration of rectangular plates. Proc Inst Mech Eng Ser A168 1954; 168: 371-384.

20.

Catania

Sorrentino

. Spectral modeling of vibrating plates with general shape and general boundary conditions. J Vib Contr 2012; 18: 1607–1623.

21.

Leissa

. Vibration of plates. Washington DC: Nasa SP 160, U.S. Government Printing Office, 1969.

22.

Butcher

. Numerical methods for ordinary differential equations. New York: John Wiley & Sons, 2008.