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http://dx.doi.org/10.12989/sem.2003.16.3.341

On the eigenvalues of a uniform rectangular plate carrying any number of spring-damper-mass systems  

Chen, Der-Wei (Department of Naval Architecture and Marine Engineering, Chung Cheng Institute of Technology, National Defense University)
Publication Information
Structural Engineering and Mechanics / v.16, no.3, 2003 , pp. 341-360 More about this Journal
Abstract
The goal of this paper is to determine the eigenvalues of a uniform rectangular plate carrying any number of spring-damper-mass systems using an analytical-and-numerical-combined method (ANCM). To this end, a technique was presented to replace each "spring-damper-mass" system by a massless equivalent "spring-damper" system with the specified effective spring constant and effective damping coefficient. Then, the mode superposition approach was used to transform the partial differential equation of motion into the matrix equation, and the eigenvalues of the complete system were determined from the associated characteristic equation. To verify the reliability of the presented theory, all numerical results obtained from the ANCM were compared with those obtained from the conventional finite element method (FEM) and good agreement was achieved. Since the order of the property matrices for the equation of motion obtained from the ANCM is much lower than that obtained from the FEM, the CPU time required by the ANCM is much less than that by the FEM.
Keywords
analytical-and-numerical-combined method (ANCM); eigenvalues; equivalent "spring-damper" system; finite element method (FEM);
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  • Reference
1 Avalos, D.R., Larrondon, H.A. and Laura, P.A.A. (1993), "Vibration of a simply supported plate carrying an elastically mounted concentrated mass", Ocean Engng., 20(2), 95-200.
2 Goldfracht, E. and Rosenhouse, G. (1984), "Use of Lagrange multipliers with polynominal series for dynamicanalysis of constrained plates, Part I: Polynominal series", J. Sound Vib., 92(1), 83-93.   DOI   ScienceOn
3 Meirovitch, L. (1967), Analytical Methods in Vibrations, New York: Macmillan Company.
4 Warburton, G.B. (1976), The Dynamical Behavior of Structure, New York, Pergmaon Press.
5 Wu, J.S. and Luo, S.S. (1997b), "Free vibration of a rectangular plate carrying any number of point masses andtranslational springs by using the modified and quasi analytical-and-numerical-combined methods", Int. J.Numer. Meth. Eng., 40, 2171-2193.   DOI   ScienceOn
6 Das, Y.C. and Nazarena, D.R. (1963), "Vibration of a rectangular plate with concentrated mass, spring, anddashpot", J. Appl. Mech., 30(1), 1-36.   DOI
7 Inman, Daniel J. (1994), Engineering Vibration, Prentice-Hall, Inc.
8 Rosenhouse, G. and Goldfracht, E. (1984), "Use of Lagrange multipliers with polynomial series for dynamicanalysis of constrained plates, Part II: Lagrange multipliers", J. Sound Vib., 92(1), 95-106.   DOI   ScienceOn
9 Avalos, D.R., Larrondon, H.A. and Laura, P.A.A. (1994), "Transverse vibration of a circular plate carrying anelastically mounted mass", J. Sound Vib., 177(2), 251-258.   DOI   ScienceOn
10 Librescu, L. and Na, S.S. (1997), "Vibration and dynamic response control of cantilevers carrying externallymounted stores", Journal Acoustics, Society of America, 102(6), 3516-3522.   DOI   ScienceOn
11 Przemieniecki, J.S. (1968), Theory of Matrix Structural Analysis, New York, McGraw-Hill, Inc.
12 Weaver, R.L. (1997), "Multiple-scattering theory for mean responses in a plate with sprung masses", J. Acoust.Soc. Am., 101(6), 3466-3474.   DOI   ScienceOn
13 Wu, J.S. and Luo, S.S. (1997c), "Author's reply: Use of the analytical-and-numerical-combined method in freevibration of a rectangular plate with any number of point masses and translational springs", J. Sound Vib.,207(4), 591-592.   DOI   ScienceOn
14 Weaver, R.L. (1998), "Mean-square responses in a plate with sprung masses, energy flow and diffusion", J.Acoust. Soc. Am., 103(1), 414-427.   DOI   ScienceOn
15 Wu, J.S. and Luo, S.S. (1997a), "Use of the analytical-and-numerical-combined method in free vibration of arectangular plate with any number of point masses and translational springs", J. Sound Vib., 200(2), 179-194.   DOI   ScienceOn
16 Faires, J.D. and Burden, R.L. (1993), Numerical Methods, Pws Publishing Company.
17 Clough, R.W. and Penzien, J. (1975), Dynamics of Structures, McGraw-Hill, Inc.
18 Wu, J.S., Chou, H.M. and Chen, D.W. (2002), "Free vibration analysis of a uniform rectangular plate carryingany number of elastically mounted masses", J. Multi-body Dynamic, (accepted).
19 Tse, F.S., Morse, I.E. and Hinkle, R.T. (1978), Mechanical Vibration Theory and Applications, Allyn and Bacon,Inc.
20 Goyal, S.K. and Sinha, P.K. (1977), "Transverse vibrations of sandwich plates with concentrated mass, spring,and dashpot", J. Sound Vib., 51, 570-573.   DOI   ScienceOn
21 Laura, P.A.A., Susemihl, E.A., Pombo, J.L., Luisoni, L.E. and Gelos, R. (1977), "On the dynamic behaviour ofstructural elements carrying elastically mounted concentrated masses," Applied Acoustics, 10, 121-145.   DOI   ScienceOn
22 Nicholson, J.W. and Bergman, L.A. (1986), "Vibration of damped plate-oscillator systems", J. Eng. Mech.,American Society of Civil Engineers, 112(1), 14-30.   DOI   ScienceOn
23 Bergman, L.A., Hall, J.K. and Lueschen, G.G.G. (1993), "Dynamic Green's functions for Levy plates", J. SoundVib., 162(2), 281-310.   DOI   ScienceOn