基于阻尼耗能的薄板结构低噪声拓扑优化方法研究
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摘要
在进行薄板结构低噪声设计时,基于增加结构阻尼耗能的处理方法是最为直接、有效的,它不仅可以降低结构的响应峰值,还能提高机械系统在动态环境下的抗振性和稳定性。在阻尼复合结构的设计中,由于现代产品轻量化及结构动态耗能特性的要求,阻尼材料往往只能在特定位置局部覆盖,不同的分布对结构阻尼耗能特性影响很大,传统的优化手段很难得到最优的分布形式,材料利用率低,是限制阻尼技术发展的关键问题之一。本文以薄板结构为研究对象,在深入研究约束阻尼和压电分流阻尼复合板有限元建模和分布特性的基础上,将拓扑优化方法引入阻尼层在薄板结构上的分布优化问题中,提出了基于阻尼耗能的薄板结构低噪声拓扑优化方法。本文的研究成果主要体现在以下几个方面：
对约束阻尼层复合板结构的有限元建模方法进行了研究,提出了粘弹性层的界面有限单元模型,该模型可以与基于Love-Kirchhoff经典板壳理论建立的基础层和约束层单元直接耦合,提高了建模效率,采用模态应变能方法计算了模态损耗因子,并通过数值模型验证了建模方法的正确性；应用基于迭代格式的IRS (Improved Reduced System)动态缩聚IIRS方法对模型降阶,提高了计算速度,最后分析了约束阻尼层在悬臂梁上的分布形式对结构阻尼耗能特性的影响。
基于各向正交惩罚材料密度法(SIMP)密度-刚度插值方法,建立了阻尼复合板结构有限元模型,分析了惩罚因子的选择方法,以避免优化过程中产生局部模态,采用移动渐进线法(MMA)作为优化求解器,引入敏度过滤技术消除数值算法的不稳定性和模态跟踪方法保证模态阶次不发生变化,计算了模态损耗因子对设计变量的敏度,提出了拓扑优化一般流程,最后采用数值算例验证了优化方法的有效性。
采用有限元-边界元方法,给出了阻尼复合板结构辐射声功率的计算模型,引入了声阻抗矩阵概念,分析了声学灵敏度,采用SIMP插值模型和MMA算法,对典型约束阻尼复合板结构单频辐射声功率进行了拓扑优化并分析了优化结果；分析了板结构声辐射模态特性,提出了基于声辐射模态理论的拓扑优化目标函数,可以实现声功率在某阶模态峰值最小,但该方法仅适用于模态频率较低的情形。
基于分层线性位移假设,考虑了界面应力和位移连续条件,由Hamilton原理和第二类压电方程,推导了压电复合板的力电耦合动力学有限元方程,数值验证了建模方法的工程适用性；结合外部电路电压与电流的关系,建立了压电分流阻尼结构系统方程,分析了常见分流电路的减振特性。
采用闭路准静态能量循环方法,阐述了压电复合结构广义机电耦合系数(GEMCC)在能量层面的含义,分析了GEMCC与压电复合结构阻尼耗能之间的关系；建立了压电复合板的SIMP插值模型,根据GEMCC计算形式,提出了拓扑优化方法,并进行了数值分析；提出了压电片极化表面电荷量计算方法,根据设计连通性要求,基于植物根系形态形成机理,提出了压电复合板的仿生拓扑优化方法,给出了优化流程,结合数值算例,分析了优化方法的可行性。
最后,对约束阻尼复合板结构的最优拓扑结构进行了实验研究,验证了本文所提出的拓扑优化方法的有效性。
The method of increasing system damping energy dissipation is the most direct and effective approach in the design of low noise plate strucutres, as it not olny reduce the peak value of the structural resonance, but also enhance the vibration resistance and dynamic stability of the system. Light weight is very important in composite strucutre design, so the damping materials are only located on certain area partially. However, it is difficult to find the optimal location using traditional optimization methods considering the complexity of the system dynamic chacteristic. This dissertation analyze the finite element modeling and distribution characteristic of the composite plates with Passive constrained layer damping (PCLD) treatments or PZT shunt damping treatments, and use topology optimization method to find the optimal topology of damping layers. The features obtained in this dissertation are mainly as follows:
A general, accurate, easy-to-use interface finite element that can directly couple together the base structure plate elements, the viscoelastic layer and the constraining layer plate elements, is introduced. The base layer and constraining layer is modeled with plate elements based on Love-Kirchhoff classical plate theory. The modal loss factor is calculated by means of modal strain energy method. Then, Numerical model is adopted to verify the modeling method. In order to speed up, the improved reduced system based on iteration is used. Then, the relation between the distribution of PCLD and the damping effects of a cantilever beam is analyzed.
The finite element modeling is established based on the solid isotropic material with penalization (SIMP) model. To eliminate local mode, the penalization factors are analyzed. Then, the optimizer is chosen as the method of moving asymptote (MMA) approach. The design sensitivities filtering technology is applied to remove checkerboards and a mode-tracking method to avoid altering the order of the modal. The design sensitivities of the modal loss factor is then calculated. A general flow of topology optimization is proposed. The validation of the method is carried out by numerical cases.
The sound radiation power of the PCLD damped composite plate is obtained by finite element method-boundary element method (FEM-BEM) approach, and its sensitivity is analyzed then. By using the SIMP model and MMA optimizer, the topology of the PCLD is optimized to minimize the sound power of plates at a certain frequency. The sound radiation modal of the plate is studied and another objection function for sound power optimization is proposed. This method can minimize the sound power peak value of a certain structural modal, but it just suit for the case that the modal is in very low frequencies.
The layerwise linear of the laminated plates is assumed, and the displacements and transverse shear stresses in the interface of each layer are continuation. Then, the mechanical-electrical coupling model is deduced form Hamilton's principle and the second type piezoelectric equation, and then verified by two numerical example. Considering the relation of the circuit voltage and the current, the equation of the PZT shunt damping system is given. Some common shunt circuits are analyzed numerically.
A closed-loop quasi-static energy cycle method is introduced to demonstrate the meaning of the general electromechanical coupling coefficient (GEMCC. Then, the relation of the damping energy dissipation capability and the GEMCC is analyzed. The SIMP model and the topology optimization method of the PZT composite plate are proposed. After that, Two structures are studied numerically. The total charge of the polarization surface is calculated also. Considering the design connectivity of the PZT patch, a bionic topology optimization is proposed based on the growth process of root system of plants. The optimization flow is then illustrated. The feasibility of the method is validated by numerical examples.
Finally, the experimental validation is carried out for the plates with topology optimized PCLD treatments. The experimental results show that the proposed topology optimization is an efficient method for damped composite plates low noise design.
对约束阻尼层复合板结构的有限元建模方法进行了研究,提出了粘弹性层的界面有限单元模型,该模型可以与基于Love-Kirchhoff经典板壳理论建立的基础层和约束层单元直接耦合,提高了建模效率,采用模态应变能方法计算了模态损耗因子,并通过数值模型验证了建模方法的正确性；应用基于迭代格式的IRS (Improved Reduced System)动态缩聚IIRS方法对模型降阶,提高了计算速度,最后分析了约束阻尼层在悬臂梁上的分布形式对结构阻尼耗能特性的影响。
基于各向正交惩罚材料密度法(SIMP)密度-刚度插值方法,建立了阻尼复合板结构有限元模型,分析了惩罚因子的选择方法,以避免优化过程中产生局部模态,采用移动渐进线法(MMA)作为优化求解器,引入敏度过滤技术消除数值算法的不稳定性和模态跟踪方法保证模态阶次不发生变化,计算了模态损耗因子对设计变量的敏度,提出了拓扑优化一般流程,最后采用数值算例验证了优化方法的有效性。
采用有限元-边界元方法,给出了阻尼复合板结构辐射声功率的计算模型,引入了声阻抗矩阵概念,分析了声学灵敏度,采用SIMP插值模型和MMA算法,对典型约束阻尼复合板结构单频辐射声功率进行了拓扑优化并分析了优化结果；分析了板结构声辐射模态特性,提出了基于声辐射模态理论的拓扑优化目标函数,可以实现声功率在某阶模态峰值最小,但该方法仅适用于模态频率较低的情形。
基于分层线性位移假设,考虑了界面应力和位移连续条件,由Hamilton原理和第二类压电方程,推导了压电复合板的力电耦合动力学有限元方程,数值验证了建模方法的工程适用性；结合外部电路电压与电流的关系,建立了压电分流阻尼结构系统方程,分析了常见分流电路的减振特性。
采用闭路准静态能量循环方法,阐述了压电复合结构广义机电耦合系数(GEMCC)在能量层面的含义,分析了GEMCC与压电复合结构阻尼耗能之间的关系；建立了压电复合板的SIMP插值模型,根据GEMCC计算形式,提出了拓扑优化方法,并进行了数值分析；提出了压电片极化表面电荷量计算方法,根据设计连通性要求,基于植物根系形态形成机理,提出了压电复合板的仿生拓扑优化方法,给出了优化流程,结合数值算例,分析了优化方法的可行性。
最后,对约束阻尼复合板结构的最优拓扑结构进行了实验研究,验证了本文所提出的拓扑优化方法的有效性。
The method of increasing system damping energy dissipation is the most direct and effective approach in the design of low noise plate strucutres, as it not olny reduce the peak value of the structural resonance, but also enhance the vibration resistance and dynamic stability of the system. Light weight is very important in composite strucutre design, so the damping materials are only located on certain area partially. However, it is difficult to find the optimal location using traditional optimization methods considering the complexity of the system dynamic chacteristic. This dissertation analyze the finite element modeling and distribution characteristic of the composite plates with Passive constrained layer damping (PCLD) treatments or PZT shunt damping treatments, and use topology optimization method to find the optimal topology of damping layers. The features obtained in this dissertation are mainly as follows:
A general, accurate, easy-to-use interface finite element that can directly couple together the base structure plate elements, the viscoelastic layer and the constraining layer plate elements, is introduced. The base layer and constraining layer is modeled with plate elements based on Love-Kirchhoff classical plate theory. The modal loss factor is calculated by means of modal strain energy method. Then, Numerical model is adopted to verify the modeling method. In order to speed up, the improved reduced system based on iteration is used. Then, the relation between the distribution of PCLD and the damping effects of a cantilever beam is analyzed.
The finite element modeling is established based on the solid isotropic material with penalization (SIMP) model. To eliminate local mode, the penalization factors are analyzed. Then, the optimizer is chosen as the method of moving asymptote (MMA) approach. The design sensitivities filtering technology is applied to remove checkerboards and a mode-tracking method to avoid altering the order of the modal. The design sensitivities of the modal loss factor is then calculated. A general flow of topology optimization is proposed. The validation of the method is carried out by numerical cases.
The sound radiation power of the PCLD damped composite plate is obtained by finite element method-boundary element method (FEM-BEM) approach, and its sensitivity is analyzed then. By using the SIMP model and MMA optimizer, the topology of the PCLD is optimized to minimize the sound power of plates at a certain frequency. The sound radiation modal of the plate is studied and another objection function for sound power optimization is proposed. This method can minimize the sound power peak value of a certain structural modal, but it just suit for the case that the modal is in very low frequencies.
The layerwise linear of the laminated plates is assumed, and the displacements and transverse shear stresses in the interface of each layer are continuation. Then, the mechanical-electrical coupling model is deduced form Hamilton's principle and the second type piezoelectric equation, and then verified by two numerical example. Considering the relation of the circuit voltage and the current, the equation of the PZT shunt damping system is given. Some common shunt circuits are analyzed numerically.
A closed-loop quasi-static energy cycle method is introduced to demonstrate the meaning of the general electromechanical coupling coefficient (GEMCC. Then, the relation of the damping energy dissipation capability and the GEMCC is analyzed. The SIMP model and the topology optimization method of the PZT composite plate are proposed. After that, Two structures are studied numerically. The total charge of the polarization surface is calculated also. Considering the design connectivity of the PZT patch, a bionic topology optimization is proposed based on the growth process of root system of plants. The optimization flow is then illustrated. The feasibility of the method is validated by numerical examples.
Finally, the experimental validation is carried out for the plates with topology optimized PCLD treatments. The experimental results show that the proposed topology optimization is an efficient method for damped composite plates low noise design.
引文
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