NURBS-based isogeometric vibration analysis of generally laminated deep curved beams with variable curvature

Abstract

In this paper, the NURBS-based isogeometric analysis is developed for the free vibration analysis of the generally laminated Timoshenko-type of deep curved beams with arbitrary curvature. The equivalent modulus of elasticity is utilized to account for the material couplings of the beam and the deepness term is exactly integrated into ABD parameters of the curved beam. The geometry and the curvature of the laminated free-form curved beams are modeled by NURBS so that the gap between the analysis of the laminated curved beam with constant curvature and the analysis of that with variable curvature is bridged. All the effects of the axis extensibility, the shear deformation and the rotary inertia are taken into account. Results of the non-dimensional frequencies for the laminated elliptic and circular curved beams with different lay-ups are compared with other available results in order to demonstrate the validity of the present isogeometric model. The free vibration analysis of the laminated parabolic curved beams and the laminated elliptic ring are presented. Particularly, the laminated Tschirnhausen’s cubic curved beam is considered to study the dynamic responses as an example of the laminated free-form curved beam.