A new non-linear higher-order shear deformation theory for large-amplitude vibrations of laminated doubly curved shells

Marco Amabili (1) , Junuthula Reddy (2)

1 Department of Mechanical Engineering [Montréal]
2 Texas A&M University [College Station]

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 Karman type. Results show that inaccurate results are obtained by keeping only non-linear terms of the von Ka´ma´ype for vibration amplitudes of about two times the shell thickness for the studied case.

Mots clés: Shells; Nonlinear theory; Shear deformation; Vibrations; Nonlinear vibrations; Rotary inertia

Domaines: Sciences de l'ingénieur [physics]

Marco Amabili, Junuthula Reddy. A new non-linear higher-order shear deformation theory for large-amplitude vibrations of laminated doubly curved shells. International Journal of Non-Linear Mechanics, 2010, ⟨10.1016/j.ijnonlinmec.2009.12.013⟩. ⟨hal-01302309⟩