Nonlinear Resonance Analysis of Slender Portal Frames under Base Excitation

Abstract

The dynamic nonlinear response and stability of slender structures in the main resonance regions are a topic of importance in structural analysis. In complex problems, the determination of the response in the frequency domain indirectly obtained through analyses in time domain can lead to huge computational effort in large systems. In nonlinear cases, the response in the frequency domain becomes even more cumbersome because of the possibility of multiple solutions for certain forcing frequencies. Those solutions can be stable and unstable, in particular saddle-node bifurcation at the turning points along the resonance curves. In this work, an incremental technique for direct calculation of the nonlinear response in frequency domain of plane frames subjected to base excitation is proposed. The transformation of equations of motion to the frequency domain is made through the harmonic balance method in conjunction with the Galerkin method. The resulting system of nonlinear equations in terms of the modal amplitudes and forcing frequency is solved by the Newton-Raphson method together with an arc-length procedure to obtain the nonlinear resonance curves. Suitable examples are presented, and the influence of the frame geometric parameters and base motion on the nonlinear resonance curves is investigated.

Nonlinear dynamic P‐delta interaction between TMD and the frame structure under proportional internal resonances

“…The lateral behavior of tall RC buildings with height irregularities under secondary analysis has also been investigated in two studies 18,19 . Moreover, Paullo Muñoz et al 20 have carried out a nonlinear resonance analysis of the slender portal frame under base excitation. Tuned mass dampers (TMDs), also known as harmonic absorbers, are devices mounted on structures to reduce mechanical vibrations.…”

“…The effect of axial force in dynamic analysis of structures appeared in stiffness matrix as stability coefficients, attained by Chen and Lui 10 for a flexible beam with axial force. Recent works on secondary analysis include several references 11–20 . Brazil and Mazzilli 11 have presented a general FEM formulation of planar frames with a geometrically nonlinear behavior, constituted by a linear elastic material.…”