In this article, torsional control has been studied in the plan-mass asymmetric vertical seismic isolation (VSI) system considering the three-dimensionally analytical model. In the 3D VSI, a structure is partitioned by vertical isolation planes into two inner and outer substructures interconnected by links for lateral response reduction. In an ideal analytical model of plan-mass asymmetric VSI, plan-wise distribution of damping and stiffness have been provided for more torsional control. Seismic responses of the non-classically 3D VSI were obtained by Runge-Kutta numerical method, considering a large number of isolation ratios. In this investigation, the mass and stiffness ratios of substructures are defined with respect to the original structure which provides a novel method of graphic presentation for analysis results. In this manner, contour graphs create comprehensive and worthwhile insight into the 3D VSI behavior and can also serve as a design tool for the preliminary design of the system. The results show that in the case that the inner substructure is the flexible one, torsional control is nearly effective in both substructures satisfactorily, regardless of plan-wise damping distribution. However, in the second case that is the outer flexible substructure, torsional control is nearly effective in the stiff substructure while the response in flexible substructure is satisfactory just in a limited range of isolation ratios.

在本文中，考虑了三维分析模型，在平面质量非对称垂直地震隔离（VSI）系统中研究了扭转控制。在3D VSI中，结构通过垂直隔离平面划分为两个内部和外部子结构，这些内部和外部子结构通过链接相互连接以减少横向响应。在平面质量非对称VSI的理想分析模型中，已经提供了阻尼和刚度的平面方向分布，以便进行更多的扭转控制。考虑到大量的隔离比，通过Runge-Kutta数值方法获得了非经典3D VSI的地震响应。在这项研究中，相对于原始结构定义了子结构的质量和刚度比，这为分析结果提供了一种新颖的图形表示方法。以这种方式，等高线图可为3D VSI行为提供全面而有价值的见解，并且还可以用作系统初步设计的设计工具。结果表明，在内部子结构为柔性结构的情况下，无论平面阻尼分布如何，扭转控制在两个子结构中均能令人满意地发挥作用。然而，在第二种情况下，即外部柔性子结构中，扭转控制在刚性子结构中几乎是有效的，而柔性子结构中的响应仅在有限的隔离比范围内令人满意。无论平面阻尼分布如何，扭转控制在两个子结构中都几乎令人满意。然而，在第二种情况下，即外部柔性子结构中，扭转控制在刚性子结构中几乎是有效的，而柔性子结构中的响应仅在有限的隔离比范围内令人满意。无论平面阻尼分布如何，扭转控制在两个子结构中都几乎令人满意。然而，在第二种情况下，即外部柔性子结构中，扭转控制在刚性子结构中几乎是有效的，而柔性子结构中的响应仅在有限的隔离比范围内令人满意。