Geometrically Nonlinear Random Vibration of Structures Using Finite Element Method

Dabouee Moshkabadi, Mehdi | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53165 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hosseini Kordkheili, Ali
  7. Abstract:
  8. Indeterminate behavior of some forces in the aerospace industry due to flight at high speeds, gust, combustion, etc., has led to the exposure of structures to dynamic loads with random behavior in the nonlinear manner. To analyze problems in which the loading is random or the system parameters are random, the only possible way is to describe the system response in statistical values.Since most modern structures have complex geometry and the number of degrees of freedom is very high, advanced numerical solution methods are used to obtain the system response. In this study, the geometric nonlinear vibrations of structures under random loading are investigated by the finite element method.First, using the concepts of of continuum mechanics and by virtue of appropriate and conjugate stress and strain tensors, the nonlinear governing equation of structures is obtained. Random loading on structures is modeled by random processes. In many cases, for easy access to the answer, it is assumed that the stimulation is white noise with zero mean. Then, according to the various solution methods available, the equivalent linearization method is used in the analysis of nonlinear problems of random vibrations to obtain the statistical characteristics of the system response. In the next step, the finite element code is developed to solve the structure under uniform random loading with zero mean, and several examples in the linear and nonlinear domains are solved
  9. Keywords:
  10. Geometric Nonlinearity ; Finite Element Method ; Random Loading ; Random Vibration ; Continuum Mechanics ; Stress Tensor ; Structural Stability

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