Analytical and Experimental Study for Vibration of Laminated Rectangular Plates with Point Masses

Abstract:

An analytical method is presented for free vibration of a symmetrically laminated rectangular plate with point masses, and experimental modal analysis is conducted to compare both sets of the frequency data. The problem is solved by an extending Ritz method to include kinetic energy caused by added point masses under any sets of edge conditions, and a frequency equation is derived by minimizing the energy functional. In numerical computation, the accuracy of the solution is studied by convergence test and comparison with the existing result in the specific case. Then, the experimental modal analysis is applied to measure the natural frequencies and mode shapes. The two sets of results are compared, and the validity of both theoretical and experimental approaches is established.

• Periodical: Construction Technologies and Architecture (Volume 7)
• Pages: 1-10
• DOI: https://doi.org/10.4028/p-fg323A
• Online since: June 2023
• Authors: Shinya Honda*, Katsuhiko Sasakir, Yoshihiro Narita
• Keywords: Composite, Experimental Modal Analysis, Point Mass, Ritz Method, Vibration

References

[1] P.W. Whaley, Prediction of the change in natural frequency of a cantilevered flat plate with added lumped mass, Journal of Sound and Vibration, Vol.69, (1980), pp.519-529.

DOI: 10.1016/0022-460x(80)90622-7

[2] P. A. A. Laura, R.H. Gutierrez, Transverse vibrations of thin, elastic plates with concentrated masses and internal elastic supports, Journal of Sound and Vibration, Vol.75, (1981), pp.135-143.

DOI: 10.1016/0022-460x(81)90241-8

[3] J.W. Nicholson, L.A. Bergman, Vibration of thick plates carrying concentrated masses, Journal of Sound and Vibration, Vol.3, (1985), pp.357-369.

DOI: 10.1016/0022-460x(85)90428-6

[4] M. Mukhopadhyay, Vibration analysis of elastically restrained rectangular plates with concentrated mass, Journal of Sound and Vibration, Vol.113, (1987), pp.547-558.

DOI: 10.1016/s0022-460x(87)80136-0

[5] M.S. Ingber, A.L. Pate, J.M. Salazar, Vibration of a clamped plate with concentrated mass and spring attachments, Journal of Sound and Vibration, Vol.153, (1992), pp.143-166.

DOI: 10.1016/0022-460x(92)90633-9

[6] K.H. Low, G.B. Chai, T.M. Lim, S.C. Sue, Comparisons of experimental and theoretical frequencies for rectangular plates with various boundary conditions and added masses, International Journal of Mechanical Sciences, Vol.40, (1998), pp.1119-1131.

DOI: 10.1016/s0020-7403(98)00013-7

[7] K.H Low, An improved model for the frequency estimate of mass-loaded plates by a combined use of equivalent center mass and stiffness factors, International Journal of Mechanical Sciences, Vol.43, (2001), pp.581-594.

DOI: 10.1016/s0020-7403(99)00116-2

[8] R.R. Reynolds, B.D. Provencher, S.A. Shesterikov, The high frequency, transient response of a panel with attached masses, Journal of Sound and Vibration, Vol.266, (2003), pp.833-846.

DOI: 10.1016/s0022-460x(02)01449-9

[9] Q.S. Li, An exact approach for free vibration analysis of rectangular plates with line-concentrated mass and elastic line-support, International Journal of Mechanical Sciences, Vol.45, (2003), pp.669-685.

DOI: 10.1016/s0020-7403(03)00110-3

[10] T. Kocat.urka, S. Sezerb, C. Demirb, Determination of the steady state response of viscoelastically point-supported rectangular specially orthotropic plates with added concentrated masses, Journal of Sound and Vibration, Vol.278, (2004), p.789–806.

DOI: 10.1016/j.jsv.2003.10.059

[11] M. Amabili, M. Pellegrini, F. Righi, F. Vinci, Effect of concentrated masses with rotary inertia on vibrations of rectangular plates, Journal of Sound and Vibration, Vol.295, (2006), pp.1-12.

DOI: 10.1016/j.jsv.2005.11.035

[12] D.V. Bambill, D.H. Felix, C.A. Rossit, Natural frequencies of thin, rectangular plates with holes or orthotropic "patches" carrying an elastically mounted mass, International Journal of Solids and Structures, Vol.43, (2006), pp.4116-4135.

DOI: 10.1016/j.ijsolstr.2005.03.051

[13] P.M. Ciancioa, C.A. Rossitb and P.A.A. Laura, Approximate study of the free vibrations of a cantilever anisotropic plate carrying a concentrated mass, Journal of Sound and Vibration, Vol. 302, (2007), p.621–628.

DOI: 10.1016/j.jsv.2006.11.027

[14] S.D. Yu, Free and forced flexural vibration analysis of cantilever plates with attached point mass, Journal of Sound and Vibration, 321, (2009), p.270–285.

DOI: 10.1016/j.jsv.2008.09.042

[15] J.R. Vinson and R.L. Sierakowski, The Behavior of Structures Composed of Composite Materials, Martinus Nijhoff, Dordrecht, (1986)

[16] Y. Narita and J.M. Hodgkinson, Layerwise optimization for maximizing the fundamental frequencies of point-supported rectangular laminated composite plates, Composite Structures, Vol.69, (2005), pp.127-135.

DOI: 10.1016/j.compstruct.2004.05.021

[17] Y. Narita, Combinations for the free-vibration behaviors of anisotropic rectangular plates under general edge conditions, Trans. ASME Journal Applied Mechanics, Vol.67, (2000), pp.568-573.

DOI: 10.1115/1.1311959