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首页> 外文期刊>Bulletin of earthquake engineering >Mechanical formulations for bilinear and trilinear hysteretic models used in base isolators
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Mechanical formulations for bilinear and trilinear hysteretic models used in base isolators

机译：基本隔离器中使用的双线性和三线性滞后模型的机械公式

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The best known model for numerically simulating the hysteretic behavior of various structural components is the bilinear hysteretic system. There are two possible mechanical formulations that correspond to the same bilinear model from a mathematical viewpoint. The first one consists of a linear elastic spring connected in series with a parallel system comprising a plastic slider and a linear elastic spring, while the second one comprises a linear elastic spring connected in parallel with an elastic-perfectly plastic system. However, the bilinear hysteretic model is unable to describe either softening or hardening effects in these components. In order to account for this, the bilinear model is extended to a trilinear one. Thus, two trilinear hysteretic models are developed and numerically tested, and the analysis shows that both exhibit three plastic phases. More specifically, the first system exhibits one elastic phase, while the second one exhibits two elastic phases according to the level of strain amplitude. Next, the change of slope between the plastic phases in unloading does not occur at the same displacement level in the two models. Furthermore, the dissipated energy per cycle in the first trilinear model, as proven mathematically and explained physically, decreases in the case of hardening and increases in the case of softening, while in the second trilinear model the dissipated energy per cycle remains unchanged, as is the case with the bilinear model. Numerical examples are presented to quantify the aforementioned observations made in reference to the mechanical behavior of the two trilinear hysteretic models. Finally, a set of cyclic shear tests over a wide range of strain amplitudes on a high damping rubber bearing is used in the parameter identification of the two different systems, namely (a) trilinear hysteretic models of the first type connected in parallel, and (b) trilinear hysteretic models of the second type also connected in parallel. The results show that the complex nonlinear shear behavior of high damping rubber bearings can be correctly simulated by a parallel system which consists of only one component, namely the trilinear hysteretic system of the first type. The second parallel system was not able to describe the enlargement of the dissipated hysteresis area for large strain amplitudes.
机译：用于数值模拟各种结构部件的磁滞行为的最著名模型是双线性磁滞系统。从数学观点来看，有两种可能的机械公式对应于相同的双线性模型。第一个由与包括塑料滑块和线性弹性弹簧的并联系统串联连接的线性弹性弹簧组成，而第二个由与与弹性完美的塑料系统并联连接的线性弹性弹簧组成。但是，双线性滞后模型无法描述这些组件中的软化或硬化效果。为了解决这个问题，将双线性模型扩展为三线性模型。因此，建立了两个三线性滞后模型并进行了数值测试，分析表明它们都表现出三个塑性相。更具体地，根据应变幅度的水平，第一个系统表现出一个弹性相，而第二个系统表现出两个弹性相。其次，在两个模型中，在相同位移水平下，卸载时塑性相之间的斜率变化不会发生。此外，如数学上证明和物理上解释的那样，在第一三线性模型中，每个周期的耗散能量在硬化情况下减少，而在软化情况下则增加，而在第二三线性模型中，每个周期的耗散能量保持不变。双线性模型的情况。给出了数值示例，以量化参照两个三线性滞后模型的力学行为所做的上述观察。最后，在两个不同系统的参数识别中使用了一组在高阻尼橡胶轴承上的宽应变幅度范围内的循环剪切测试，即（a）并联的第一类三线性滞后模型，以及（ b）第二类型的三线性滞后模型也并联连接。结果表明，高阻尼橡胶轴承的复杂非线性剪切行为可以通过仅由一个分量组成的并行系统（即第一类三线性滞后系统）正确模拟。第二个并行系统无法描述大应变幅度下耗散磁滞面积的扩大。

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