Theoretical analysis and a parametric study on forced vibration of large statically deformed curved beam with rigid links and moving support

Abstract

Forced vibration characteristics around large statically deformed configuration of curved beam system with rigid links and moving support are analyzed. In addition, the paper also investigates various parametric effects of height to span ratio and roller radius to height ratio coupled with support connection mechanism and profile shape, on dynamic characteristics of the curved beam system. The subject problem includes two interrelated problems: determining deformed configuration under static load and dynamic response of the loaded beam under harmonic excitation. The static problem is analyzed incrementally through the variational principle-based energy method in body-embedded curvilinear frame considering geometric nonlinearities due to combined bending-stretching and non-uniform initial curvature. In each incremental step, the nonlinear governing equation is solved iteratively, and kinematic constraints due to interactive deformation of the flexible curved beam with rigid links are imposed to obtain the global solution. Concerning the statically deformed configuration, governing equation for forced vibration is derived through Hamilton’s principle in curvilinear frame. Nonlinear effects caused by combined bending-stretching modes of vibration, non-uniform curvature, and lumped mass of the dead static load are considered. The set of inhomogeneous governing equations is solved through Broyden’s method. A direct substitution technique through successive relaxation is also employed to obtain an initial guess solution. Besides the forced vibration, free vibration analysis at static deformed configuration is also carried out for the completeness of the study. The theoretical model is validated through comparisons of loaded natural frequency results with finite element package. After the validation study, the effects of the mentioned geometric parameters on the dynamic response of the curved beam system are investigated and presented suitably. The physically insightful framework along with the parametric study may facilitate simulation and design of several practical structures involving moving support and rigid links subjected to continuous excitation around large statically deformed configurations.