Modelling Wave Propagation in Thin Plates with the pectral Modal Method
Authors
Abstract
In this article spectral modal method is developed for studying wave propagation in thin plates with constant or variable thickness. Theses plates are subjected to the impact forces and different boundary conditions. Spectral modal method can be considered as the combination of Dynamic Stiffness Method (DSM), Fourier Analysis Method (FAM) and Finite Stripe Method (FSM). Using modeling of continuous distribution of mass and an exact stiffness causes solutions in frequency domain. Unlike the most numerical methods, in this method refining meshes is no longer necessary in which the cost and computational time is decreased. In this paper the important parameters of the method and their effects on results are studied through different examples.
Keywords
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7. Danial, A. N., and Doyle, J. F., “Transverse Impact a Damped Plate near a Straight Edge”, Journal of Vibration and Acoustics, Vol. 117, pp. 103-108, 1995.
8. Chakraborty, A., and Gopalakrishnan, S., “Wave Propagation in Inhomogeneous Layered Media: Solution of Forward and Inverse Problems”, Journal of Acta Mechanica, Vol. 169, No. 1-4, pp. 153-185, 2004.
9. Chakraborty, A., and Gopalakrishnan, S., “A Spectrally Formulated Plate Element for Wave Propagation Analysis in Anisotropic Material,” International Journal of Computer Methods in Applied Mechanics and Engineering, Vol. 194, No. 42-44, pp. 4425-4446, 2005.
10. Lee, J., and Lee, U., “Spectral Element Analysis of the Structure under Dynamic Distributed Loads”, AIAA, American Institute of Aeronautics and Astronautics, Reston, Va, pp. 1494-96, 1996.
11. Lee, U., and Lee, J., “Spectral-Element Method for Levy-Type Plates Subjected to Dynamic Loads”, Journal of Engineering Mechanics, Vol. 125, No. 2, pp. 243-247 1999.
12. Lee, U., “Dynamic Continuum Modelling of Beamlike Space Structures Using Finite-Element Matrices”, AIAA Journal, Vol. 28, No. 4, pp. 725-731, 1990.
13. Lee, U., and Lee, C., “Spectral Element Modelling for Extended Timoshenko Beams”, Journal of Sound and Vibration, Vol. 319, pp. 993-1002, 2009.
14. Szilard, R., Theories and Applications of Plate Analysis: Classical, Numericaland Engineering Methods, John Wiley & Sons, 2004.
15. Doyle, J. F., Wave Propagation in Structure, Springer, NewYork, 1997.
16. Lee, U., Spectral Element Method in Structural Dynamics, John Wiley & Sons (Asia), Singapore, 2009.
17. Paz, M., Structural Dynamics: Theory and Computation, 3rd Ed., Van Nostrand Reinhold, New York, 1991.
2. Doyle, J. F., and Farris, T. N., “A Spectrally Formulated Element for Wave Propagation in 3-D Frame Structures”, Journal of Analytical and Experimental Modal Analysis, Vol. 5, No. 4, pp. 223-237, 1990.
3. Rizzi, S. A., and Doyle, J. F., “A Spectral Element Approach to Wave Motion in Layered Solids”, Journal of Vibration and Acoustics, Vol. 114, pp. 569-576, 1992.
4. Gopalakrishnan, S., Martin, M., and Doyle, J. F., “A Matrix Methodology for Spectral Analysis of Wave Propagation in Multiple Connected Timoshenko Beam”, Journal of Sound and Vibration, Vol. 158, No. 4, pp. 11-24, 1992.
5. Martin, M., Gopalakrishnan, S., and Doyle, J. F., “Wave Propagation in Multiply Connected Deep Waveguides”, Journal of Sound and Vibration, Vol. 174, No. 4, pp. 521-538, 1994.
6. Gopalakrishnan, S., and Doyle, J. F., “Wave Propagation in Connected Waveguides of Varying Cross-Section”, Journal of Sound and Vibration, Vol. 175, No. 3, pp. 347-363, 1994.
7. Danial, A. N., and Doyle, J. F., “Transverse Impact a Damped Plate near a Straight Edge”, Journal of Vibration and Acoustics, Vol. 117, pp. 103-108, 1995.
8. Chakraborty, A., and Gopalakrishnan, S., “Wave Propagation in Inhomogeneous Layered Media: Solution of Forward and Inverse Problems”, Journal of Acta Mechanica, Vol. 169, No. 1-4, pp. 153-185, 2004.
9. Chakraborty, A., and Gopalakrishnan, S., “A Spectrally Formulated Plate Element for Wave Propagation Analysis in Anisotropic Material,” International Journal of Computer Methods in Applied Mechanics and Engineering, Vol. 194, No. 42-44, pp. 4425-4446, 2005.
10. Lee, J., and Lee, U., “Spectral Element Analysis of the Structure under Dynamic Distributed Loads”, AIAA, American Institute of Aeronautics and Astronautics, Reston, Va, pp. 1494-96, 1996.
11. Lee, U., and Lee, J., “Spectral-Element Method for Levy-Type Plates Subjected to Dynamic Loads”, Journal of Engineering Mechanics, Vol. 125, No. 2, pp. 243-247 1999.
12. Lee, U., “Dynamic Continuum Modelling of Beamlike Space Structures Using Finite-Element Matrices”, AIAA Journal, Vol. 28, No. 4, pp. 725-731, 1990.
13. Lee, U., and Lee, C., “Spectral Element Modelling for Extended Timoshenko Beams”, Journal of Sound and Vibration, Vol. 319, pp. 993-1002, 2009.
14. Szilard, R., Theories and Applications of Plate Analysis: Classical, Numericaland Engineering Methods, John Wiley & Sons, 2004.
15. Doyle, J. F., Wave Propagation in Structure, Springer, NewYork, 1997.
16. Lee, U., Spectral Element Method in Structural Dynamics, John Wiley & Sons (Asia), Singapore, 2009.
17. Paz, M., Structural Dynamics: Theory and Computation, 3rd Ed., Van Nostrand Reinhold, New York, 1991.
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