A new non-linear higher-order shear deformation theory for large-amplitude vibrations of laminated doubly curved shells |
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| Authors: | M. Amabili J.N. Reddy |
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| Affiliation: | a Department of Mechanical Engineering, McGill University, Macdonald Engineering Building, 817 Sherbrooke Street West, Montreal, PQ, Canada H3A 2K6
b Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA |
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| Abstract: | A consistent higher-order shear deformation non-linear theory is developed for shells of generic shape, taking geometric imperfections into account. The geometrically non-linear strain-displacement relationships are derived retaining full non-linear terms in the in-plane displacements; they are presented in curvilinear coordinates in a formulation ready to be implemented. Then, large-amplitude forced vibrations of a simply supported, laminated circular cylindrical shell are studied (i) by using the developed theory, and (ii) keeping only non-linear terms of the von Kármán type. Results show that inaccurate results are obtained by keeping only non-linear terms of the von Kármán type for vibration amplitudes of about two times the shell thickness for the studied case. |
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| Keywords: | Shells Nonlinear theory Shear deformation Vibrations Nonlinear vibrations Rotary inertia |
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