Abstract
The use of viscous damping terms to simplify the damping of a vibrating system has been well established for decades. For solid materials whose energy dissipated per cycle is frequency-independent, an equivalent viscous damping has often been used. However, this may give inaccurate results, especially at higher excitation frequencies. Alternatively, a complex stiffness term can be used. In this case, a challenge arises for the time domain analysis due to the unstable poles in the resulting model. Several methods have been proposed to deal with this issue. The use of an analytic signal along with Hilbert transform and a time reversal technique is one of the first introduced methods. In this paper, we extend the method so that it can be used for solving the system equations of motion using the numerical integration algorithm solvers that are available in MATLAB. We also present the application of this extended method to simulate a multi-degree-of-freedom (MDOF) structure with supplemental passive vibration suppression systems using linear hysteretic damping in the time domain.
Highlights
In civil engineering applications, solid materials, such as rubber, are one of the most widely used materials for dampers and base isolations
We extend the method so that it can be used for solving the system equations of motion using the numerical integration algorithm solvers that are available in MATLAB
We present the application of this extended method to simulate a multi-degree-of-freedom (MDOF) structure with supplemental passive vibration suppression systems using linear hysteretic damping in the time domain
Summary
Solid materials, such as rubber, are one of the most widely used materials for dampers and base isolations. Some methods have been proposed to solve the equation of motion of a system with hysteretic damping in the time domain. One of the first was introduced by Inaudi and Makris [2] In this method, the hysteretic characteristic of the material damping in the equation of motion is modelled by using the Hilbert transform. Using the state space formulation, the equation of motion can be solved by using time-reversal technique to avoid the instability problems associated with the unstable pole Some improvement of this method were given by Bae et al [3, 4]. Note that in this case, as the system is relatively simple, a comparison can be made between the numerical method proposed in this paper and the analytical solution. Figure 3. 3-storey structure with (a) a TMhD at the top storey (b) a TIhD at the base storey
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