Mathematical design and graphical solution of the multiple bifurcation equations of a 4-DoF benchmark model

A 4 degree-of-freedom (DoF) benchmark model of multiple bifurcation (MB) in compound stability problems of nonlinear structures is proposed. In the MB model, the governing equations are designed to be highly simplified when two critical modes exist in the singular Jacobian matrix. The resulting MB equations can be solved analytically through manual calculation. To verify the applicability, graphical solution methods are applied to solve the MB...