Viscoelastic material is widely used in automotive structures due to its outstanding vibration-damping characteristics with appropriate stiffness. Viscoelastic material, which has viscosity and elasticity, shows energy absorption and dissipation. The material properties of viscoelastic material are dependent upon time, temperature, and loading path. Hence, these characteristics have to be considered when performing structural optimization. Studies on the constitutive equations of viscoelastic material are widely carried out, and structural optimization using harmonic excitation in the frequency-domain is often reported. However, structural optimization in the time-domain is rarely performed. One of the reasons is that the cost of sensitivity analysis is quite expensive. The Equivalent Static Loads Method (ESLM) is a linear/nonlinear dynamic response structural optimization method. In this research, a practical structural optimization method to consider the characteristics of viscoelastic material is proposed using ESLM. Equivalent static loads (ESLs) are defined as the static loads that generate the same displacement field as that from dynamic analysis. In ESLM, dynamic analysis and linear static response optimization are alternatively repeated until convergence is achieved. Viscoelastic material reduces the vibration amplitude and the stored energy in a structural system. Thus, excellent damping performance is required for a part with viscoelastic material, while the proper stiffness is maintained. An appropriate design formulation is made for the design of viscoelastic material. In this research, the sum of damping ratios, the sum of weighted damping ratios, and the sum of squared displacements are considered as the objective functions. These three objective functions deal with the peak displacements of damped vibration. Three case studies are defined by optimizations of some typical automotive parts with viscoelastic material. They are a sandwich panel, a rubber bushing, and a seat cushion. The damping performances of the objective functions are compared and discussed.

中文翻译：

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基于等效静载荷法的粘弹性材料结构动力响应优化

粘弹性材料因其出色的减振特性和适当的刚度而广泛应用于汽车结构中。粘弹性材料具有粘性和弹性，表现出能量的吸收和耗散。粘弹性材料的材料特性取决于时间、温度和加载路径。因此，在进行结构优化时必须考虑这些特性。对粘弹性材料本构方程的研究得到广泛开展，并且经常报道使用频域中的谐波激励进行结构优化。然而，很少执行时域中的结构优化。原因之一是敏感性分析的成本相当昂贵。等效静载荷法 (ESLM) 是一种线性/非线性动态响应结构优化方法。在这项研究中，使用 ESLM 提出了一种考虑粘弹性材料特性的实用结构优化方法。等效静载荷 (ESL) 定义为产生与动态分析相同的位移场的静载荷。在 ESLM 中，动态分析和线性静态响应优化交替重复，直到达到收敛。粘弹性材料降低了结构系统中的振动幅度和储存的能量。因此，具有粘弹性材料的零件需要出色的阻尼性能，同时保持适当的刚度。为粘弹性材料的设计制定了适当的设计公式。在这项研究中，阻尼比之和、加权阻尼比之和和位移平方和被视为目标函数。这三个目标函数处理阻尼振动的峰值位移。三个案例研究是通过使用粘弹性材料对一些典型汽车零件进行优化来定义的。它们是夹心板、橡胶衬套和座垫。比较和讨论了目标函数的阻尼性能。和一个座垫。比较和讨论了目标函数的阻尼性能。和一个座垫。比较和讨论了目标函数的阻尼性能。