FEA for vibrated structures with non-linear concentrated spring having hysteresis

This paper describes vibration analysis using finite element method for structures connected with non-linear concentrated spring. The restoring force of the spring is assumed to be expressed as power series of displacement. The restoring force also has linear hysteresis damping. Thus, complex stiffness is introduced for the linear component of the restoring force. Finite element for the spring is expressed and is connected to viscoelastic structures modelled by linear solid finite elements. Further, the discretised equations in physical coordinate are transformed into the non-linear ordinary coupled equations using normal coordinate corresponding to linear natural modes. Note that modal damping is also transformed in this procedure. The transformed equations were integrated numerically in fairly small degree of freedom. This transformation yields computation efficiency. Effectiveness of this analysis was shown for a basic block-spring model. And then, this numerical method was applied for a sophisticated measurement system named as the Levitation Mass Method proposed by Fujii for evaluating viscoelastic parameters.