SINGLE-DEGREE-OF-FREEDOM NONLINEAR HOMOGENEOUS SYSTEMS

A Class Of nonlinear oscillator that scales input-output relations is identified and studied in this paper. This type 01 system shows variab le stiffness, variable damping, or both, and is piecewise linear in co nical regions of the state space. The following passive and semiactive mechanical systems, which exhibit this variable structure, are used t o motivate the discussion: structures containing energy-dissipating de vices with different loading and unloading stiffnesses, structures wit h variable dampers, and structures with active variable stiffness. The free-vibration response of single-degree-of-freedom systems with vari able stiffness and variable damping is computed. It is demonstrated th at the period of oscillation and the decay ratio between consecutive p eaks of this type of nonlinear system are independent of the amplitude of oscillation. The statistical-linearization method is used to estim ate the mean-square response of structures containing nonlinear homoge neous devices and subjected to random excitation. Excellent accuracy i s achieved in the estimation of the mean-square response of these osci llators using the statistical-linearization method.