Design sensitivity analysis (DSA) of transient responses, which are indispensable in gradient-based time domain optimization, often requires excessive computational resources for viscoelastically damped systems to directly differentiate and integrate the full-order model (FOM). In this paper, an efficient model-order reduction (MOR)–based DSA framework is developed for capturing the 1st- and 2nd-order derivatives of the transient responses and response functions for viscoelastically damped systems. The damping force is represented by a non-viscous damping model, which depends on the past history of motion via convolution integrals over suitable kernel functions. The direct differentiation method (DDM) is used to derive the DSA. Three robust modal reduction bases, namely multi-model (MM) method, modal strain energy modified by displacement residuals (MSER) method and improved approximation method (IAM) are introduced to reduce the system dimension. Based on a generalized damping model in expression of fraction formula, a reduced state-space formulation without convolution integral term is derived. The 1st- and 2nd-order derivatives of the transient responses and response functions are calculated using a modified precise integration method and the DDM on the reduced stage. The computational efficiency and accuracy of the presented methods are illustrated and compared by two examples. The results indicate that the computational time is significantly reduced by the proposed MOR methods maintaining fairly good accuracy. Among these methods, the MM method represents the most compromise between precise and efficiency and would be the best candidate to be the reduction basis for calculating the time domain DSA of large-scale viscoelastically damped systems.

在基于梯度的时域优化中必不可少的瞬态响应的设计灵敏度分析 (DSA) 通常需要过多的计算资源来让粘弹性阻尼系统直接区分和整合全阶模型 (FOM)。在本文中，开发了一种有效的基于模型阶数减少 (MOR) 的 DSA 框架，用于捕获粘弹性阻尼系统的瞬态响应和响应函数的一阶和二阶导数。阻尼力由非粘性阻尼模型表示，该模型依赖于通过在合适核函数上进行卷积积分的过去运动历史。直接微分法 (DDM) 用于导出 DSA。三个鲁棒模态约简基础，即多模型（MM）方法，引入位移残差(MSER)法和改进逼近法(IAM)修正模态应变能以减小系统维数。基于分数公式表达式中的广义阻尼模型，推导出了一个没有卷积积分项的约简状态空间公式。瞬态响应和响应函数的一阶和二阶导数是使用改进的精确积分方法和简化阶段的 DDM 计算的。通过两个例子说明和比较了所提出方法的计算效率和准确性。结果表明，所提出的 MOR 方法显着减少了计算时间，并保持了相当好的准确性。在这些方法中，