Abstract
The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condition were established by von Karman plate theory, and then accordingly exact solution of static load and its numerical results were given. Based on time mode hypothesis and the variational method, the control equation of the space mode was derived, and then the amplitude frequency-load character relation of circular sandwich plate was obtained by the modified iteration method. Consequently the rule of the effect of the two kinds of load on the vibration character of the circular sandwich plate was investigated. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.
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Liu Renhuai, Li Dong, Yuan Hong. Axisymmetric nonlinear vibration of orthotropic shallow spherical shell[J]. Journal of Vibration Engineering, 2005, 18(4):395–405 (in Chinese).
Chen Yan, Liu Renhuai. Nonlinear force vibration of piezoelectric rectangular thin plate[J]. Journal of South China University of Technology, 2003, 31(Suppl):63–66 (in Chinese).
Liu Renhuai. Analysis and application of plates and shells[J]. China Engineering Science, 2000, 2(11):60–67.
Liu Renhuai. Nonlinear bending of circular sandwich plate[J]. Applied Mathematics and Mechanics (English Edition), 1981, 2(2):173–190.
Liu Renhuai, Shi Yunfang. Exact solution for circular sandwich plate with large amplitude[J]. Applied Mathematics and Mechanics (English Edition), 1982, 3(1):11–24.
Du Guojun, Li Huijian. Nonlinear vibration of circular sandwich plate under the uniformed load[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(2):217–226.
Chen Chunsheng. Large amplitude vibration of an initially stressed cross ply laminated plates[J]. Applied Acoustics, 2002, 63(9):939–956.
Abde Rahman. Axisymmetric natural frequencies of statically loaded annular plates[J]. Shock and Vibration, 2003, 10(5/6):301–312.
Nayfeh Ali H. Dynamic behavior of circular structural elements under thermal loads[C]. In: Proceeding of the 44th AIAA/ASME/ASCE/AHS/ASC Stuctures, Structural Dynamics and Materials Conference, Norfolk, Virginia, Apr. 7–10, 2003.
Chung J. Nonlinear vibration of a flexible spinning disc with angular acceleration[J]. Journal of Sound and Vibration, 2000, 231(2):375–391.
Kimura Koichi. Vibration of pressure loaded nonlinear rectangular plates with cross stiffener[J]. Journal of Engineering Mechanics, 2002, 128(7):788–794.
Yeh Kaiyuan, Ye Zhiming, Wang Xinzhi. A discussion on “the large deflection problem of circular thin plate with variable thickness under uniformly distributed loads”[J]. Applied Mathematics and Mechanics (English Edition), 1985, 6(3):291–292.
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Du, Gj., Ma, Jq. Nonlinear vibration and buckling of circular sandwich plate under complex load. Appl Math Mech 28, 1081–1091 (2007). https://doi.org/10.1007/s10483-007-0810-z
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DOI: https://doi.org/10.1007/s10483-007-0810-z
Key words
- circular sandwich plate
- nonlinear vibration
- buckling
- complex load
- amplitude frequency-load characteristic relation