Browse > Article
http://dx.doi.org/10.5050/KSNVE.2013.23.11.943

Harmonic Response Estimation Method on the Lévy Plate with Two Opposite Edges Having Free Boundary Conditions  

Park, Nam-Gyu (KEPCO NF)
Suh, Jung-Min (KEPCO NF)
Jeon, Kyeong-Lak (KEPCO NF)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.23, no.11, 2013 , pp. 943-950 More about this Journal
Abstract
This paper discusses a harmonic response estimation method on the L$\acute{e}$vy plate with two opposite edges simply supported and the other two edges having free boundary conditions. Since the equation of motion of the plate is not self-adjoint, the modes are not orthogonal to each other on the domain. Noting that the L$\acute{e}$vy plate can be expressed using one term sinusoidal function that is orthogonal to other sinusoidal functions, this paper suggested the calculation method that is equivalent to finding a least square error minimization solution of the finite number of algebraic equations. Example problems subjected to a distributed area loading and a distributed line loading are defined and their solutions are provided. The solutions are compared to those of the commercial code, ANSYS. According to the verification results, it is expected that the suggested method will be useful to predict the forced response on the L$\acute{e}$vy plate with the distributed area or line loading conditions.
Keywords
L$\acute{e}$vy Plate; Harmonic Response; Mode Superposition Method; Algebraic Equation; Least Mean Square Error;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 Lee, K. H., Lim, G. T. and Wang, C. M., 2002, Thick Levy Plates Re-visited, Int. J. Solids and Structures, Vol. 39, No. 1, pp. 127-144.   DOI   ScienceOn
2 Lee, J. and Lee, U., 1998, Vibration Analysis of the Plates Subject to Dynamic Concentrated Loads by Using Spectral Element Method, Transactions of the KSME(A), Vol. 22, No. 3, pp. 635-643.   과학기술학회마을
3 Lee, J. H. and Lee, K. H., 1996, The Reduction of Harmonic Dynamic Response of Plate Structure Using Continuum Design Sensitivity Analysis, Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 6, No. 1, pp. 27-34.   과학기술학회마을
4 Doyle, J. F., 1997, Wave Propagation in Structures, Springer.
5 Soedel, W., 1993, Vibrations of Shells and Plates, Marcel Decker Inc.
6 Kulla, P. H., 1997, High Precision Finite Elements, Finite element in Analysis and Design, Vol. 26, No. 2, pp. 997-114.
7 Xiang, Y., Zhao, Y. B. and Wei, G. W., 2002, Levy Solutions for Vibration of Multi-span Rectangular Plates, International Journal of Mechanical Sciences, Vol. 44, No. 6, pp. 1195-1218.   DOI   ScienceOn
8 Xiang, Y. and Wei, G. W., 2004, Exact Solutions for Buckling and Vibration of Stepped Rectangular Mindlin plates, International Journal of Solids and Structures, Vol. 41, No. 1, pp. 279-294.   DOI   ScienceOn
9 Marynowski, K., 2010, Free Vibration Analysis of the Axially Moving Levy-type Viscoelastic Plate, European J. Mechanics-A/Solids, Vol. 29, No. 5, pp. 879-886.   DOI   ScienceOn
10 Thai, H. T. and Kim, S. E., 2012, Levy-type Solution for Free Vibration Analysis of Orthotropic Plates Based on Two Variable Refined Plate Theory, Applied Mathematical Modelling, Vol. 36, No. 8, pp. 3870-3882.   DOI   ScienceOn
11 Lellep, J. and Kago, E., 2011, Vibrations of Elastic Stretched Strips with Cracks, Intl. J. of Mechanics, Vol. 5, No. 1, pp. 27-34.
12 Leissa, A. W., 1973, The Free Vibration of Rectangular Plate, J. Sound & Vibration, Vol. 31, No. 3, pp. 257-293.   DOI   ScienceOn
13 Ryu, J. Y., Eom, K. B., Jeon, S. Y. and Suh, J. M., 2012, An Analysis on the Flow Induced Vibration Characteristics of Protective Grids in Nuclear Fuel Assembly, Proceedings of the KSNVE Annual Spring Conference, pp. 739-740.   과학기술학회마을
14 Noble, B. H. and Daniel, J. W., 1988, Applied Linear Algebra, Prentice-Hall.
15 Oh, J. E. and Rhee, D. I., 1997, A Free Vibration Analysis of Sound-structure Interaction Plate Having a Small Cut-out, Transactions of the KSME(A), Vo. 21, No. 10, pp. 1666-1673.   과학기술학회마을
16 Venstel, E. and Krauthammer, T., 2001, Thin Plates and Shells, Marcel Dekker Inc.
17 Kim, J. O. and Moo, B. H., 2001, Flexural Vibration of a Rectangular Plate with Orthotropically and Harmonically Varying Material Properties, Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 11, No. 2, pp. 323-328.   과학기술학회마을
18 Yu, Y. Y., 1996, Vibrations of Elastic Plates, Springer.
19 Youn, J. O. and Lee, J. M., 1996, Double Fourier Sine Series Method for the Free Vibration of a Rectangular Plate, Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 6, No. 6, pp. 771-779.   과학기술학회마을
20 Hur, S. C. and Yoo, H. H., 2000, Dynamic Modeling and Vibration Analysis of Rotating Plate Structures with Stiffeners, Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 10, No. 2, pp. 312-318.   과학기술학회마을
21 Lee, Y. S. and Choi, M. H., 1999, A Study on the Vibration Characteristics of Steel and Plain Weave Composite Cylindrical Shells Combined with Internal Plate Structures, Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 9, No. 1, pp. 149-162.   과학기술학회마을