Nonlinear vibrations of laminated circular cylindrical shells: Comparison of different shell theories |
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| Affiliation: | 1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, PR China;2. Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu 610031, PR China;1. College of Mechanical and Electrical Engineering, Central South University, Changsha 410000, PR China;2. State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, PR China;3. Beijing Aerospace Technology Institute, China Aerospace Science & Industry Corp., Beijing 100074, PR China;4. Institute for Turbulence-Noise-Vibration Interaction and Control, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 51800, PR China |
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| Abstract: | The geometrically nonlinear forced vibrations of laminated circular cylindrical shells are studied by using the Amabili–Reddy higher-order shear deformation theory. An energy approach based on Lagrange equations, retaining modal damping, is used in order to obtain the equations of motion. An harmonic point excitation is applied in radial direction and simply supported boundary conditions are assumed. The equations of motion are studied by using the pseudo-arclength continuation method and bifurcation analysis. A one-to-one internal resonance is always present for a complete circular cylindrical shell, giving rise to pitchfork bifurcations of the nonlinear response with appearance of a second branch with travelling wave response and quasi-periodic vibrations. The numerical results obtained by using the Amabili–Reddy shell theory are compared to those obtained by using an higher-order shear deformation theory retaining only nonlinear term of von Kármán type and the Novozhilov classical shell theory. |
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