Development and Validation of a Nonlinear Model to Describe the Tension–Compression Behavior of Rubber-Like Base Isolators

Seismic analysis of 3D train–wheel–bridge–bearing systems: Modeling

“…The adopted strategy to create the displacement‐input bearing subsystem is to virtually set an extra mass block between the bridge and bearing to reverse the order of input and output signals in the bearing subsystem. We have demonstrated in our previous work [ 20 ] that the error caused by the extra block is negligible when the block mass is far smaller ($$\le 0.5\,\%$$) than the bridge mass.…”

“…The state‐space representation of the core pad tension/compression model is [ 20 ] $$$$\begin{equation} \begin{aligned} \mathbf {x}_{z,k+1}&=\mathbf {A}_{z,k}\mathbf {x}_{z,k}+\mathbf {B}_z\hat{z}_{1s\imath ,k}^g-\displaystyle \sum _{j=1}^{{\min (k+1,{\rm UL}_z)}}{{\rm GL}(\beta ,j)\mathbf {x}_{z,k+1-j}},\\ & F_{c1s\imath z,k}^b =\mathbf {C}_{z,k}\mathbf {x}_{z,k}+\mathbf {D}_{z,k}\hat{z}_{1s\imath ,k}^g, \end{aligned} \end{equation}$$$$where $$$$\begin{equation} \mathbf {A}_{z,k}=-\frac{E_{1,k}+E_{2,k}}{\kappa _k}\Delta t^\beta ,\,\mathbf {B}_z=\Delta t^\beta ,\,\mathbf {C}_{z,k}=-\frac{A_cE_{1,k}^2}{h_c\kappa _k},\,\mathbf {D}_{z,k}=\frac{A_cE_{1,k}}{h_c...$$…”

“…Figure 14 shows the construction of the multidimensional bearing, which has been modeled, designed, manufactured, and tested in our previous work. [19,20] Viscoelastic rubber-like materials have been widely used in dampers or bearings in engineering practice. [49,50] The core pad and four cylindrical dampers of the bearing in this paper are filled with the same viscoelastic rubber-like material to dissipate energy during vibration.…”

“…The fractional-order derivative Zener model was adopted and modified to build the bearing's nonlinear horizontal and vertical dynamic models, which showed good agreement with experimental results. [19,20] Detailed bearing description and its modeling can be found in the publications. [19,20] All the bearings are assumed to have the same sizes.…”

“…The high computational efficiency of the TWBB coupled model can be achieved because (1) the bridge state-space equations (SSEs) are built on the generalized modal coordinates by using the modal decomposition method, which generates far fewer DOF compared to traditional finite element methods; and (2) no iterations are involved in the calculations. The multidimensional viscoelastic bearing behaviors in vertical and horizontal directions are governed by the modified fractional Zener model proposed by Li et al [19,20] Nevertheless, other bearing models with state-space representations could also be adopted, making the proposed numerical model of the TWBB system very flexible. The efficiency of the proposed model makes it possible to conduct comprehensive and detailed performance-based design of TWBB system's bearings in engineering practice.…”