Keywords: cylindrical shells, spherical shells, free vibration, refined theories, Love, Donnell, Flugge, thickness approximation, curvature approximation, vehicle vibration, automotive structures, thin shells, shear deformation, displacement components, shell geometry
Evaluation of various theories of the thickness and curvature approximations for free vibrational analysis of cylindrical and spherical shells
Cylindrical and spherical shells are largely used in several engineering fields, especially in aerospace vehicles as structural elements and in automotive vehicles as shafts or exhaust and induction systems. Due to their particular relations with vibrations of automotive structures, this work compares various significant shell theories to evaluate the free vibration response. Thin shell theories and shear deformation shell theories are compared with refined theories for both in-plane and out-of-plane displacement components (including transverse normal strain effects). As far as approximation of the curvature terms is concerned, Donnell, Love and exact Flugge theories are been considered. A quite comprehensive analysis has been conducted for the case of simply supported shells. Fundamental and higher frequency parameters are compared by varying the various geometrical parameters of the considered cylindrical and spherical shells. Conclusions are drawn on the use of the most appropriate shell theories for a given shell geometry.