Investigation into the Dynamics of Layered and Jointed Cantilevered Beams

Abstract

Damping occurring at the joints due to interfacial relative motion is the major source of inherent damping in fabricated structures. In the present investigation, the dynamic analysis of layered cantilever beams jointed with rivets was carried out using the finite element approach for the Euler—Bernoulli beam model. The solution is based on one-dimensional beam elements, with each element consisting of two nodes having two degrees of freedom (i.e. transverse displacement and rotation) at each node. The cubic shape functions are considered for the transverse vibration of the beam in terms of nodal variables. The stiffness and mass matrices are evaluated from the bending strain energy and kinetic energy of the beam, respectively, which are further used to determine the natural frequency and mode shapes by modal analysis. The damping capacity of the cantilever specimens was computed using the energy approach. Experiments were conducted for validating the numerical results. The results establish that the damping capacity of built-up structures having lower beam thickness ratio and higher cantilever length can be improved substantially using larger diameter rivets at lower amplitude of excitation.