Influence of aspect ratio on the linear and non-linear steady state forced vibration response of cylindrical open shells

Abstract

The paper deals with the linear and non-linear steady state periodic response estimation of isotropic cylindrical open shells. The displacement field of first order shear deformation theory has been employed and the analysis is based on finite element method. CO continuous, eight-noded serendipity quadrilateral shear flexible element with five nodal degrees of freedom has been used for the analysis. The geometric non-linearity is included in the analysis using von Karman’s assumption for small strains and moderately large deflection. The governing equations of motion have been obtained in the time domain and the nonlinear periodic responses are obtained using shooting technique. The entire non-linear steady state frequency response curve consisting of stable and unstable regimes has been obtained employing shooting technique along with arc length and pseudo-arc length continuation schemes. The present method does not involve any apriori assumption on the participating modes. The comparison of linear and nonlinear frequency response curves reveals large differences between the two. Frequency response curve, response history and the phase plane plots have been obtained, for different aspect ratio (L/b), to explore the linear and non-linear forced vibration characteristics of cylindrical open shells. The asymmetric nature of the phase plane plots reveal significant higher harmonic contributions. With the increase in aspect ratio, thin open shells reveal increased peak amplitude in both linear and nonlinear analysis. The presence of secondary peak in the nonlinear frequency response for greater aspect ratio is due to modal interaction between first and higher modes.