基于分布参数传递函数方法的被动约束层阻尼结构动力学分析
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摘要
被动约束层阻尼(Passive Constrained Layer Damping,PCLD)被广泛地应用在航空航天结构的振动控制中,它具有控制频率宽、可靠性高、鲁棒性强、结构简单和成本低的优点。本文研究工作的重点是建立PCLD结构动力学问题的分布参数传递函数方法(简称传递函数方法)求解体系,并在此基础上进行PCLD结构动力学优化、阻尼层粘弹性材料模型的随机性分析和粘弹性材料模型参数修正等一系列专题研究,主要研究内容如下:
提出了求解PCLD全部覆盖和局部覆盖梁动力学问题的传递函数方法。利用Hamilton原理推导了PCLD梁的运动微分方程和边界条件,建立了系统的状态空间方程,采用传递函数方法求解得到动力学方程的封闭形式解。
提出了求解PCLD板动力学问题的传递函数方法。推导了PCLD全部覆盖板的运动方程和边界条件,通过三角级数展开,得到了对边简支PCLD全部覆盖板动力学问题的解析解。为了适应任意边界条件,将PCLD板在宽度方向离散成多个条形单元,推导了PCLD条形传递函数单元的刚度矩阵和质量矩阵,得到了PCLD全部覆盖和局部覆盖板动力学问题的半解析解。
提出了求解PCLD圆柱壳的动力学问题的传递函数方法。基于Donnell薄壳简化理论,推导了PCLD全部覆盖圆柱壳运动方程与边界条件,利用传递函数方法进行求解,并在此基础上进一步分析了局部覆盖环状PCLD圆柱壳动力学问题。
建立了PCLD设计参数的单目标和多目标优化模型。单目标优化中以结构模态损耗因子最大为优化目标;多目标优化中以各阶模态损耗因子最大、各阶固有频率改变量最小和PCLD附加的结构质量最小为优化目标。优化变量选择为PCLD起始位置、覆盖长度、阻尼层厚度和约束层厚度。
研究了阻尼层粘弹性材料模型参数的随机性对PCLD结构动力学特性的影响,修正了粘弹性材料模型参数。
本文研究既拓展了传递函数方法的应用范围,又为航空航天工业部门中PCLD结构的工程应用和参数设计提供了理论支持,具有重要的理论和实用价值。
Passive constrained layer damping (PCLD) is broadly used in aerospace structures for vibration control, which has many advantages such as wide control frequency, high reliability, good robustness, simple structural form and low cost. The emphasis of this dissertation is to establish a methodological system for PCLD structure dynamic analysis with distributed parameter transfer function method (shortened as transfer function method), and to solve a series of special subject problems based on the methodological system such as dynamic optimization of PCLD structure, parameter random analysis and model updating of viscoelastic material. The main achievements are summarized as follows:
For dynamic problems of the beam with full and partial PCLD treatment, the transfer function method is proposed. The motion differential equations and boundary conditions are derived for PCLD beam by the Hamilton principle. The system equation in state space is then established, and the closed-form solutions are obtained by the transfer function method.
For dynamic problems of the PCLD plate, the transfer function method is proposed. The motion equations and boundary conditions are deduced for the plate with full PCLD treatment, and the analytical solutions of the plate with two opposite simply-supported edges are presented through trigonometric series expansion. In order to adapt to arbitrary boundary conditions, the PCLD plate is divided into several strip elements in breadth, and the element stiffness matrix and element mass matrix are deduced. Then, the semi-analytical solutions of the plate with full and partial PCLD treatment are obtained
For dynamic problems of the PCLD cylindrical shell, the transfer function method is proposed. Based on Donnell assumptions, the motion equations and boundary conditions are derived for the cylindrical shell with full PCLD treatment, and the equations are solved by the transfer function method. Furthermore, the dynamic problem of the cylindrical shell with partial ring-shape PCLD treatment is analyzed.
Optimization models of single-objective and multi-objective are established for PCLD design parameters. In single-objective optimization, the aim is to maximize each mode loss factor. In multi-objective optimization, the aims are to maximize each mode loss factor, to minimize each frequency's shift and to minimize the PCLD mass. The PCLD start placement, PCLD length, constrained layer thickness and viscoelastic layer thickness are chosen as design variables.
The influences of parameter randomness in viscoelastic material model are researched on dynamic characteristics of PCLD structure. The model parameters are updated.
This dissertation has important value on both theory and practical application, which extends the applied range of the transfer function method and provides a theoretical basis for the use and design of PCLD structure in aerospace industrial fields.
提出了求解PCLD全部覆盖和局部覆盖梁动力学问题的传递函数方法。利用Hamilton原理推导了PCLD梁的运动微分方程和边界条件,建立了系统的状态空间方程,采用传递函数方法求解得到动力学方程的封闭形式解。
提出了求解PCLD板动力学问题的传递函数方法。推导了PCLD全部覆盖板的运动方程和边界条件,通过三角级数展开,得到了对边简支PCLD全部覆盖板动力学问题的解析解。为了适应任意边界条件,将PCLD板在宽度方向离散成多个条形单元,推导了PCLD条形传递函数单元的刚度矩阵和质量矩阵,得到了PCLD全部覆盖和局部覆盖板动力学问题的半解析解。
提出了求解PCLD圆柱壳的动力学问题的传递函数方法。基于Donnell薄壳简化理论,推导了PCLD全部覆盖圆柱壳运动方程与边界条件,利用传递函数方法进行求解,并在此基础上进一步分析了局部覆盖环状PCLD圆柱壳动力学问题。
建立了PCLD设计参数的单目标和多目标优化模型。单目标优化中以结构模态损耗因子最大为优化目标;多目标优化中以各阶模态损耗因子最大、各阶固有频率改变量最小和PCLD附加的结构质量最小为优化目标。优化变量选择为PCLD起始位置、覆盖长度、阻尼层厚度和约束层厚度。
研究了阻尼层粘弹性材料模型参数的随机性对PCLD结构动力学特性的影响,修正了粘弹性材料模型参数。
本文研究既拓展了传递函数方法的应用范围,又为航空航天工业部门中PCLD结构的工程应用和参数设计提供了理论支持,具有重要的理论和实用价值。
Passive constrained layer damping (PCLD) is broadly used in aerospace structures for vibration control, which has many advantages such as wide control frequency, high reliability, good robustness, simple structural form and low cost. The emphasis of this dissertation is to establish a methodological system for PCLD structure dynamic analysis with distributed parameter transfer function method (shortened as transfer function method), and to solve a series of special subject problems based on the methodological system such as dynamic optimization of PCLD structure, parameter random analysis and model updating of viscoelastic material. The main achievements are summarized as follows:
For dynamic problems of the beam with full and partial PCLD treatment, the transfer function method is proposed. The motion differential equations and boundary conditions are derived for PCLD beam by the Hamilton principle. The system equation in state space is then established, and the closed-form solutions are obtained by the transfer function method.
For dynamic problems of the PCLD plate, the transfer function method is proposed. The motion equations and boundary conditions are deduced for the plate with full PCLD treatment, and the analytical solutions of the plate with two opposite simply-supported edges are presented through trigonometric series expansion. In order to adapt to arbitrary boundary conditions, the PCLD plate is divided into several strip elements in breadth, and the element stiffness matrix and element mass matrix are deduced. Then, the semi-analytical solutions of the plate with full and partial PCLD treatment are obtained
For dynamic problems of the PCLD cylindrical shell, the transfer function method is proposed. Based on Donnell assumptions, the motion equations and boundary conditions are derived for the cylindrical shell with full PCLD treatment, and the equations are solved by the transfer function method. Furthermore, the dynamic problem of the cylindrical shell with partial ring-shape PCLD treatment is analyzed.
Optimization models of single-objective and multi-objective are established for PCLD design parameters. In single-objective optimization, the aim is to maximize each mode loss factor. In multi-objective optimization, the aims are to maximize each mode loss factor, to minimize each frequency's shift and to minimize the PCLD mass. The PCLD start placement, PCLD length, constrained layer thickness and viscoelastic layer thickness are chosen as design variables.
The influences of parameter randomness in viscoelastic material model are researched on dynamic characteristics of PCLD structure. The model parameters are updated.
This dissertation has important value on both theory and practical application, which extends the applied range of the transfer function method and provides a theoretical basis for the use and design of PCLD structure in aerospace industrial fields.
引文
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