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Non-Linear Vibrations Analysis of Composite Cylindrical Shells Using Modal Method

Entezari, Ayoub | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 40959 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Kouchakzadeh, Mohammad Ali; Firouzabadi, Rohallah
  7. Abstract:
  8. With the recent trend to use thin shell structures in severe operational conditions, it is not sufficient to employ the classical linear theory to analyze their dynamic behavior, especially with large amplitudes. When the transverse deflection of a shell raise to the order of its thickness, the nonlinear effects grow significantly, leading to a variety of complex responses, such as the variable frequencies depending on the amplitude and the jump phenomenon. This dynamic behavior should be analyzed by the nonlinear theory of shells. In this research, the nonlinear vibration of composite shallow circular cylindrical shells is considered. The geometric nonlinear strains are of the von Karman type, the boundary condition is clamped-clamped and the shell is subjected to radial dynamic excitation. Here we use linear strains and eliminate nonlinear terms in the equations of motion to establish a system of three coupled linear partial differential equations. Then we obtain the natural frequency of vibration and mode shapes by applying Galerkin’s method. Approximate mode shapes for the clamped-clamped case may be obtained from related beam functions. The mode shapes from the linear free vibration solution, are used as the mode shapes of the assumed multi-mode displacement field. The displacement field is required to solve the nonlinear vibration equation of motion. By deriving the expressions for the strain energy, the kinetic energy and the virtual work done by the external forces and substitution into the Hamilton's principle, the nonlinear equation of motion for the shell based on the von Karman nonlinear strain is obtained. Substituting the obtained displacement field into the nonlinear equation of motion of the shell and applying Galerkin's method, yields to the governing nonlinear equations of motion in generalized coordinates. The equations are subsequently solved by the Runge-Kutta method. Using the presented model, the effects of lamination sequence and material properties on the vibration characteristics of the shell are studied and some conclusions are drawn
  9. Keywords:
  10. Vibration ; Nonlinear Equations ; Galerkin Method ; Composite Shells ; Modal Method

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