Nonlinear Solution of Tuned Liquid Column Dampers Compared to Linearized Analytical Solution

Resumo

This article compares the nonlinear and equivalent linearized solutions of an isolated Tuned Liquid
Column Dampers (TLCD), a kind vibration control device. A numerical simulation of the nonlinear behavior of
the structure under harmonic excitation was performed to determine the frequency response function (FRF). The
stepped sweep-sine procedure was performed to numerical estimation of nonlinear transmissibility FRF. With
TLCD’s transmissibility FRF due to base acceleration, the equivalent damping coefficient was determined using
the linearized solution proposed by Gao et al. [1]. Both non-linear and linearized FRF was compared to verify the
precision of Gao’s equivalent damping technique. The present implementation were done in Python programming
language and its native scientific libraries Numpy, Scypy and Matplotlib. The solution of nonlinear TLCD ODE
was calculated with the Odeint tool, a general-purpose integrator developed under the LSODA procedure

(Livermore Solver for Ordinary Differential Equations with the automatic switching method for rigid and non-
rigid problems).