VIBRATION AND STABILITY OF A HYPERELASTIC NEOHOOKEAN TRUSS

Resumo

Trusses are structural elements that present multi-stability, even under characteristic conditions of
geometry, contour and rigidity. Metamaterials, on the other hand, have been an increase motivation for studies
recently and their characteristics can be represented by hyperelastic constitutive models together with a
geometric shape of trusses. Thus, in this work, the behavior, linear and non-linear, of the stability and vibrations
of a hyperelastic neo-Hookean truss exhibiting Multistable behavior is investigated. For this, it is considered a
plane truss with two bars and geometric imperfections First an energetic formulation, considering large
displacements, is presented and the nonlinear equations of motion for a nodal load applied at the top node are
derived. Based on this formulation, the parametric buckling analysis of the truss under static load as a function of
the load and geometric imperfections. Then, the fundamental vibration frequency, nonlinear frequency–
amplitude relations and time history are obtained as a function of the static preload.