An isogeometric FSDT approach for the study of nonlinear vibrations in truncated viscoelastic conical shells

Nonlinear vibrations of truncated viscoelastic conical shell (TVCS) structures are studied using an isogeometric formulation based on non-uniform rational B-spline (NURBS) basis functions. The governing equations of motion for the TVCS are formulated in terms of meridional, circumferential, and transverse deformation components, using the first-order shear deformation theory (FSDT). The TVCS domain is modeled using a non-periodic knot vector along its meridional direction due to its bounded form and a periodic knot vector along the circumferential direction due to its periodicity. Assuming the generalized form of the Maxwell model for visco-elastic material, a system of coupled nonlinear equations for the isogeometric patch is obtained. Displacement functions are approximated using quadratic and cubic NURBS resulting in a generalized time-varying nonlinear problem. The effects of patch refinements, partial loading, and asymmetric hysteresis behavior on the nonlinear vibration of the TVCS structures with different geometries and load functions are investigated.