Random vibration of structures with strong non-linearities subjected to seismic excitation

The response of nonlinear structures subjected to earthquake excitation modeled by white noise random process is calculated. The non-linearity of structural elements is modeled by a first order differential equation representing a curvilinear relationship between the restoring force and the displacement, that is suitable for the dynamic analysis of structures. The spectral method of analysis is used to obtain the Root Mean Square response of the structure using the complex frequency function of the structural system. The equivalent linearization technique is used to obtain the equivalent linear parameters for stiffness and damping of the non-linear structure. The degree of nonlinearity, and the damping ratio of the structure are investigated through the parametric study.