Abstract
This paper describes vibration analysis using FEM for frame structures supported by multiple nonlinear concentrated springs with hysteresis damping. The restoring forces of the springs have cubic nonlinearity, and the springs have complex spring constants. Finite elements for the nonlinear springs with hysteresis are expressed and are connected to the frame structures modeled by linear solid finite elements. The frame structures have complex modulus of elasticity. The discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. By using Modal Strain Energy Method, modal loss factors are approximately computed from complex eigenvalue problem and are introduced into the nonlinear coupled equations. Harmonic balance method is applied to the equations to obtain nonlinear resonance responses. The calculated responses by the proposed method are verified. As numerical examples, influences of rigidity of the frames on nonlinear resonance responses are investigated.
