中文摘要：

主动减振系统由3个以上减振器构成，其固有频率直接决定了系统隔振带宽，且减振器水平向隔振广泛采用摆机构。柔性杆直径及杆长是影响摆机构水平向刚度的主要几何参数。根据材料弹性变形理论建立了摆机构的水平向刚度模型及最大拉应力模型。在给定的负载质量范围内，以主动减振系统水平向固有频率与目标值的均方差最小作为优化目标，将许用拉应力和最大尺寸作为设计约束，应用序列二次规划法求解该非线性优化模型，得出摆机构的最优设计参数及对应的均方差。基于30准则，可估计主动减振系统的水平向固有频率分布范围。在许用固有频率范围约束下，得到摆机构参数的允许范围。实验结果表明：减振系统固有频率的测试值与理论分析值的差异小于10％；加入主动控制后，振动传递率的共振峰小于0dB，大于6Hz的振动传递率小于-20dB。

英文摘要：

An active vibration isolation system（AVIS） consists of more than three isolators, of which natural frequency is the key factor in determining the horizontal vibration isolation bandwidth. A pendulum is commonly employed in an active vibration isolator. The beam diameter and beam length are main geometry parameters in determining the horizontal stiffness of pendu- lum. In this paper, the stiffness model and the peak tensile stress model of the pendulum are presented according to the me- chanics of materials. Within the allowable mass range of the upload, the root mean square （RMS） error of the horizontal natu- ral frequency between the actual values and the target value is set as the optimization objective, and the allowable tensile stress and maximum geometry sizes are used as constraints. Then, the nonlinear optimization model is built with multivariable con- straints, and the optimal values and the RMS error are obtained with a sequential quadratic programming （SQP） method. The horizontal natural frequency range can be estimated according to the 3a rule and the structure parameters range of the pendulum can also be estimated with the allowable natural frequency range restriction. The experiment results show that the relative error of natural frequency between the experiment values and the theoretical values is no more than 10~. With active control of the AVIS, the vibration resonance is less than 0 dB, and the vibration transmissibility is less, than --20 dB when the vibration fre- quency is greater than 6 Hz.