On inertia nonlinearity in irregular-plan isolated structures under seismic excitations

The influence of nonlinear inertia as a function of acceleration, velocity, and displacement is investigated for an asymmetric isolated structure. Six degrees of freedom (6-DOFs) are defined to illustrate translational and rotational displacements of the superstructure and base isolation. Motion equations of such DOFs are derived using the Lagrangian formalism. Two coordinate systems of the reference are defined, one fixed on the building base (global coordinate) and the other at the torsional isolation level (local coordinate). The motion governing equations in the conventional approach is formulated on a linear form in the global coordinate system, whereas in the novel approach, the local coordinate system leads to a nonlinear form of dynamic equations. The difference between two linear and nonlinear models is appeared because of the existence of nonlinear inertia terms just in the nonlinear one. Afterwards, three particular types of isolated structures are employed with the peculiar ratio of torsional-lateral coupled frequency on symmetric frequency. Numerical analysis is applied to investigate the performance of two structural models by exerting harmonic excitations and earthquakes. The results are obtained while analyzing time history and frequency content and show that the coupling effects of nonlinear inertia lead to differences in the responses of linear and nonlinear models of such structures; also, some nonlinear phenomena such as energy transfer between modes, saturation, rigid displacement, and super-harmonic created due to geometrical (inertial) nonlinearities are studied.