Vibration of Damped Plate‐Oscillator Systems
Publication: Journal of Engineering Mechanics
Volume 112, Issue 1
Abstract
A classical method for obtaining the exact natural frequencies, natural modes, orthogonality relation and response due to arbitrary loading of undamped beam‐oscillator systems presented earlier by the writers is extended to viscously damped plate‐oscillator systems. The natural modes are expressed in terms of the Green's function for the vibrating plate. Damping is present in both the plate and oscillators. Modal analysis allows the determination of a closed form expression for the system response to arbitrary loading. Oscillators attached to a simply supported rectangular plate have been considered, but the method is applicable to any plate‐oscillator system, provided the Green's function for the undamped vibrating plate is known. An example involving a single oscillator attached to the plate shows the natural frequencies, natural modes and response due to two special types of loading.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Amba‐Rao, C. L., “On the Vibration of a Rectangular Plate Carrying a Concentrated Mass,” Journal of Applied Mechanics, Vol. 31, 1964, pp. 550–551.
2.
Andreev, L. V., Dyshko, A. L., and Pavlenko, I. D., “Estimation of the Fundamental Vibration Frequencies of Plates and Shells Carrying Shock‐Mounted Masses,” Isvestiya VUZ. Aviatsionnaya Tekhnika, Vol. 23, 1980, pp. 72–75.
3.
Banerjee, B., “Large Amplitude Vibrations of a Clamped Orthotopic Square Plate Carrying a Concentrated Mass,” Journal of Sound and Vibration, Vol. 82, 1982, pp. 329–333.
4.
Bergman, L. A., and Nicholson, J. W., “Forced Vibration of a Damped Combined Linear System,” Journal of Vibration, Acoustics, Stress, and Reliability in Design, ASME, Vol. 107, No. 3, July, 1985, pp. 275–281.
5.
Das, Y. C., and Navaratna, D. R., “Vibrations of a Rectangular Plate with Concentrated Mass, Spring, and Dashpot,” Journal of Applied Mechanics, Vol. 30, 1963, pp. 31–36.
6.
Dowell, E. H., “On Some General Properties of Combined Dynamical Systems,” Journal of Applied Mechanics, Vol. 46, 1979, pp. 206–209.
7.
Gajendar, N., “Free Vibrations of Composite Elastic Systems,” Journal of Science and Engineering Research, Vol. 11, 1967, pp. 45–50.
8.
Gladwell, G. M. L., and Bishop, R. E. D., “Interior Receptances of Beams,” Journal of Mechanical Engineering Science, Vol. 2, 1960, pp. 1–15.
9.
Goyal, S. K., and Sinha, P. K., “Transverse Vibrations of Sandwich Plates with Concentrated Mass, Spring and Dashpot,” Journal of Sound and Vibration, Vol. 51, 1977, pp. 570–573.
10.
Hildebrand, F. B., Advanced Calculus for Applications, Prentice‐Hall, Inc., Englewood Cliffs, NJ, 1976.
11.
Iyengar, K. T. S. R., and Jagadish, R. S., “The Vibrations of a Clamped Rectangular Plate with Concentrated Mass, Spring and Dashpot,” Indian Society of Earthquake Technology: Bulletin, Vol. 1, 1964, pp. 27–35.
12.
Jacquot, R. G., “The Forced Vibration of Singly Modified Damped Elastic Surface Systems,” Journal of Sound and Vibration, Vol. 48, 1976, pp. 195–201.
13.
Jacquot, R. G., and Soedel, W., “Vibrations of Elastic Surface Systems Carrying Dynamic Elements,” Journal of the Acoustical Society of America, Vol. 47, 1970, pp. 1354–1358.
14.
Karmakar, B. M., “Nonlinear Vibrations of Orthotropic Plates Carrying Concentrated Mass,” Journal of Engineering for Industry, Vol. 100, 1978, pp. 293–294.
15.
Karmaker, B. M., “Amplitude‐Frequency Characteristics of Nonlinear Vibrations of Clamped Elliptic Plates Carrying a Concentrated Mass,” International Journal of Nonlinear Mechanics, Vol. 13, 1979, pp. 351–359.
16.
Kishor, B., “Nonlinear Transverse Vibration Analysis of a Rectangular Plate with Lumped M‐S‐D Systems,” Journal of Applied Mechanics, Vol. 40, 1973, pp. 825–826.
17.
Klein, L. R., and Dowell, E. H., “Analysis of Modal Damping by Component Modes Method Using Lagrange Multipliers,” Journal of Applied Mechanics, Vol. 41, 1974, pp. 527–528.
18.
Kozlov, S. V., “Determination of the Natural Frequencies and Mode Configurations for Small Vibrations of an Orthotropic Cylindrical Shell with Attached Masses,” Soviet Applied Mechanics, Vol. 17, 1981, pp. 46–51.
19.
Laura, P. A. A., Arias, A., and Luisoni, L. E., “Fundamental Frequency of Vibration of a Circular Plate Elastically Restrained Against Rotation and Carrying a Concentrated Mass,” Journal of Sound and Vibration, Vol. 45, 1976, pp. 298–301.
20.
Laura, P. A. A., and Gutierrez, R. H., “Transverse Vibrations of Thin, Elastic Plates with Concentrated Masses and Internal Elastic Supports,” Journal of Sound and Vibration, Vol. 75, 1981, pp. 135–143.
21.
Magrab, E. B., “Vibration of a Rectangular Plate Carrying a Concentrated Mass,” Journal of Applied Mechanics, Vol. 35, 1968, pp. 411–412.
22.
Meirovitch, L., Analytical Methods in Vibrations, The MacMillan Co., New York, NY, 1967.
23.
Nicholson, J. W., and Bergman, L. A., “Free Vibration of Combined Dynamical Systems,” Journal of Engineering Mechanics, ASCE, Vol. 112, No. 1, Jan., 1986, pp. 1–13.
24.
Nicholson, J. W., and Bergman, L. A., “Forced Response of a Combined Dynamical System,” Report UILU‐ENG‐84‐6005, Univ. of Illinois at Urbana‐Champaign, Apr., 1984.
25.
Ramachandran, J., “Nonlinear Vibrations of a Rectangular Plate Carrying a Concentrated Mass,” Journal of Applied Mechanics, Vol. 40, 1973, pp. 630–632.
26.
Saczalski, K. J., and Huang, T. C., “Coupled Response of Spatial Vibratory Structures Mounted to Isotropic Plate Elements,” Journal of Engineering for Industry, Vol. 94, 1972, pp. 15–22.
27.
Shah, A. H., and Datta, S. K., “Normal Vibrations of a Rectangular Plate with Attached Masses,” Journal of Applied Mechanics, Vol. 36, 1969, pp. 130–132.
28.
Stanisic, M. M., and Payne, J. G., “A Rapidly Converging Technique for Vibration Analysis of Plates with a Discrete Mass Distribution,” Ingenieur‐Archive, Vol. 37, 1968, pp. 189–195.
29.
Stokey, W. F., and Zorowski, C. F., “Normal Vibrations of a Uniform Plate Carrying Any Number of Finite Masses,” Journal of Applied Mechanics, Vol. 26, 1959, pp. 210–216.
30.
Timoshenko, S., and Woinowsky‐Krieger, S., Theory of Plates and Shells, McGraw‐Hill Co., Inc., New York, NY, 1959.
31.
Wah, T., “Natural Frequencies of Plate‐Mass Systems,” Proceedings of the 7th Congress on Theoretical and Applied Mechanics, Bombay, India, 1961, pp. 157–168.
32.
Whaley, P. W., “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.
Information & Authors
Information
Published In
Copyright
Copyright © 1986 ASCE.
History
Published online: Jan 1, 1986
Published in print: Jan 1986
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.