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The Analysis of Nonlinear Vibration of an Annular Thin Plate

Author: LiLei
Tutor: HouChaoSheng
School: Tianjin University
Course: Structural Engineering
Keywords: Annular thin circular plate Dynamic Von Karman Partial Differential Equations Hard spring type duffing Equations Periodic attractor
CLC: TU33
Type: Master's thesis
Year: 2004
Downloads: 116
Quote: 0
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Abstract


This paper analyzes the nonlinear vibration problem of thin circular ring board . Take four power function for the deflection test function , obtained through the compatibility equations Ereli (Airy) stress function , together with substituting dynamic von Karman partial differential equations , Galerkin method to eliminate residual value is derived fixed clamping can shift clamping ring under the hinge support , simply supported four boundary conditions of circular plate forced vibration control equations , hard spring Duffing equation . Then the asymptotic method (ie KBM method ) solution of this vibration control equations , obtained an approximate solution in the non-resonant and the main resonance both cases , and to explore and compare the main resonance case boundary conditions , damping ratio , the outer exciting of force, both inside and outside radius ratio of the four control parameters such as the amplitude change . In short , considering the nonlinear terms , the changes in the amplitude value and phase difference with the frequency of external excitation force jump phenomena and hysteresis . After this article further analysis of the stability of the hard spring Duffing equation , as a control parameter that is taken outside the excitation force , through theoretical analysis and numerical simulation we found that with the increase of the external excitation force power systems from around a focal point of the cycle movement into a periodic motion around the longitudinal axis of symmetry of the two focus .

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