局部非线性结构分析方法及其在航天器结构分析中的应用
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摘要
合理准确地计算和分析航天器结构的动力学特性,可以为航天器结构及其控制系统提供正确的设计参考依据,进而可以保证航天器设计的合理性并提高其技术性能。一些现代航天器的结构正变得日益复杂和庞大,这类结构通常可以视为由若干简单子结构通过各种连接结构组合而成。连接结构通常对航天器结构的动力学特性有明显的影响,它们的存在增加了航天器结构动力学分析的复杂性,特别是当它们包含的非线性因素不可忽略时。在航天器工程中,通常借助于有限元方法来计算分析航天器结构的动力学特性,因而得到的数学模型通常具有大量的自由度。但是,在这类模型中,与非线性因素相关联的自由度数目通常却只占整个模型自由度数目的很小一部分。从航天器结构的分析和设计角度,如果直接将得到的数学模型按照一般的非线性问题处理并分析,将会增加航天器结构的设计周期和研制成本。因此,本文从局部非线性结构的角度对大型航天器结构动力学问题进行分析与讨论。
本文首先针对航天器结构中的非线性因素具有局部性和离散性的特点,基于广义动力缩聚方法和直接积分方法中的Newmark方法提出了一种求解大型局部非线性结构瞬态响应的方法。在结构降阶时,将感兴趣的自由度、激励自由度和非线性自由度保留在物理空间,而将剩余自由度转换至模态空间。通过这种处理不仅可以使该方法适用于求解强非线性问题,而且可以提高计算结果的精度。此外,在利用Newmark方法求解结构瞬态响应时,为了降低计算量,通过变换将每个时间步的迭代计算量减少至仅与非线性自由度相关。
基于描述函数和频响函数提出了一种求解大型局部非线性结构简谐激励响应的方法。利用该方法分别研究了简谐激励下局部非线性结构的基础谐波响应和多谐波响应。该方法首先结合描述函数将结构动力学常微分方程转化为非线性复代数方程组,然后采用频响函数将代数方程组的迭代计算量减小到只与非线性自由度相关。因此,该方法可以适用于分析大型局部非线性结构。此外,该方法还可以用于分析简谐激励下局部非线性结构的稳态响应。在计算频响函数时,由于采用了线性模态叠加方法,所以该方法可以与现有商业有限元软件有效的结合起来。
讨论了现有组合结构分析方法的优缺点。基于描述函数提出了一种非线性组合结构分析方法,用于分析含有复杂非线性连接子结构的情形。文中分别讨论了基础谐波和多谐波情形下的拟线性频响函数耦合方法。在该方法中,首先利用描述函数将非线性连接拟线性化,得到非线性连接的拟线性阻抗方程,然后将一种线性频率响应函数耦合方法扩展并推广,从而得到组合结构的拟线性频响函数方程。与现有的频域综合方法相比,该方法更具有一般性。
论文最后将局部非线性结构简谐激励响应的计算和伪弧长延拓方法结合,讨论了局部非线性结构简谐激励响应的参数化计算问题。该方法可以比较容易的计算非线性参数变化和激励幅值变化对结构简谐激励响应的影响,还可以用于修改非线性参数后的结构稳态响应的计算。此外,还讨论了大型局部非线性结构简谐激励响应的灵敏度分析问题,并针对两类典型频率响应函数曲线的共振点、简单转折点及其幅值的计算问题和它们对非线性参数和激励幅值的灵敏度计算问题进行了相关讨论。
Reasonable and accurate calculation and analysis of dynamic characteristics of spacecraft can provide an accurate reference for the design of structure and control system of spacecraft, and thus can ensure the design quality and enhance the performance of spacecraft. To achieve better performances and integrate more functions, many spacecraft structures have been becoming larger and more complicated. In general, spacecraft can be considered as an assembled structure of which several physically existing substructures that are connected by different kinds of connectors. These connectors usually have obvious influences on the dynamic characteristics of spacecraft, especially when their nonlinearities cannot be ignored. Thus they make the dynamic analysis of spacecraft more complicated. In engineering practices, spacecraft are often idealized as finite element models with many degrees of freedom (DOFs). However, the number of DOFs associated with nonlinear connectors usually constitutes only a small part of the model. If such structures are taken as globally nonlinear in the dynamic analysis, great difficulties will be certainly brought to the analysis and design process. And it is unavoidable that design costs will be added and design time will be extended. Therefore, an alternative approach is to take them as local nonlinear structures. From this point of view, the structural dynamics of spacecraft is investigated.
As the nonlinearities of spacecraft are usually distributed and local, an approach is proposed to calculate the transient response of large-scale structure with local nonlinearities. The approach is based on general dynamic reduction method and the Newmark’s method, which is commonly used in direct time integration method. DOFs that are of interest, those on which external forces act, and those associated with nonlinearities are expressed in physical coordinates, but the remaining DOFs are transformed into modal coordinates. In this way, the proposed method can solve strongly nonlinear problems and improve the accuracies of the results. With a transformation, the iterations in each time step are only related to nonlinear DOFs. Consequently, the computational effort of the approach can be significantly reduced.
A method is proposed to study the forced harmonic response of large-scale structures with local nonlinearities. It is combining the describing function (DF) and frequency response function (FRF). With the method, fundamental and multi-harmonic response analysis is discussed, respectively. In the method, the dynamical equations of motion are firstly converted into a set of nonlinear algebra equations. Subsequently, with FRF, the computational efficiency of the approach can be significantly enhanced, and only associated with nonlinear DOFs. In addition, the method can be also used to study the steady state periodic response of nonlinear structures. In the approach, FRF are obtained by using linear normal modes (LNMs). As the LNMs can be obtained by the well developed standard linear modal analysis procedures, the method can be easily cooperated with commercial finite element (FE) softwares.
Following a brief review of most commonly used coupling methods with their merits and shortcomings, a quasilinear FRF coupling method is established by using the DF. The purpose of the method is the treatment of complicated nonlinear joints, which are called general nonlinear joints. Fundamental and multi-harmonic receptance coupling are discussed. In the method, the dynamical equations of motion of general nonlinear joints are firstly quasi-linearized with the DF. Then a linear FRF coupling method is extended, modified and adopted to calculate the forced harmonic response. In comparison with current nonlinear coupling methods in the frequency domain, the present method is more general.
In the last part of the dissertation, parametric study for the forced harmonic response of local nonlinear structures is presented. By using the pseudo-arclength continuation scheme, the effects of modifying nonlinear parameters and/or changing excitation levels on the forced harmonic response can be easily obtained. The approach can be also used to calculate the steady state periodic response of a local nonlinear structure when its nonlinear parameter is modified. Besides, sensitivity analysis (SA) of the forced harmonic response with respect to nonlinear parameters and excitation levels are presented. Moreover, focused on two kinds of typical frequency response cure, the calculations of simple turning points, resonant points, and their corresponding amplitudes are discussed. Their SA with respect to nonlinear parameters and excitation levels is presented.
本文首先针对航天器结构中的非线性因素具有局部性和离散性的特点,基于广义动力缩聚方法和直接积分方法中的Newmark方法提出了一种求解大型局部非线性结构瞬态响应的方法。在结构降阶时,将感兴趣的自由度、激励自由度和非线性自由度保留在物理空间,而将剩余自由度转换至模态空间。通过这种处理不仅可以使该方法适用于求解强非线性问题,而且可以提高计算结果的精度。此外,在利用Newmark方法求解结构瞬态响应时,为了降低计算量,通过变换将每个时间步的迭代计算量减少至仅与非线性自由度相关。
基于描述函数和频响函数提出了一种求解大型局部非线性结构简谐激励响应的方法。利用该方法分别研究了简谐激励下局部非线性结构的基础谐波响应和多谐波响应。该方法首先结合描述函数将结构动力学常微分方程转化为非线性复代数方程组,然后采用频响函数将代数方程组的迭代计算量减小到只与非线性自由度相关。因此,该方法可以适用于分析大型局部非线性结构。此外,该方法还可以用于分析简谐激励下局部非线性结构的稳态响应。在计算频响函数时,由于采用了线性模态叠加方法,所以该方法可以与现有商业有限元软件有效的结合起来。
讨论了现有组合结构分析方法的优缺点。基于描述函数提出了一种非线性组合结构分析方法,用于分析含有复杂非线性连接子结构的情形。文中分别讨论了基础谐波和多谐波情形下的拟线性频响函数耦合方法。在该方法中,首先利用描述函数将非线性连接拟线性化,得到非线性连接的拟线性阻抗方程,然后将一种线性频率响应函数耦合方法扩展并推广,从而得到组合结构的拟线性频响函数方程。与现有的频域综合方法相比,该方法更具有一般性。
论文最后将局部非线性结构简谐激励响应的计算和伪弧长延拓方法结合,讨论了局部非线性结构简谐激励响应的参数化计算问题。该方法可以比较容易的计算非线性参数变化和激励幅值变化对结构简谐激励响应的影响,还可以用于修改非线性参数后的结构稳态响应的计算。此外,还讨论了大型局部非线性结构简谐激励响应的灵敏度分析问题,并针对两类典型频率响应函数曲线的共振点、简单转折点及其幅值的计算问题和它们对非线性参数和激励幅值的灵敏度计算问题进行了相关讨论。
Reasonable and accurate calculation and analysis of dynamic characteristics of spacecraft can provide an accurate reference for the design of structure and control system of spacecraft, and thus can ensure the design quality and enhance the performance of spacecraft. To achieve better performances and integrate more functions, many spacecraft structures have been becoming larger and more complicated. In general, spacecraft can be considered as an assembled structure of which several physically existing substructures that are connected by different kinds of connectors. These connectors usually have obvious influences on the dynamic characteristics of spacecraft, especially when their nonlinearities cannot be ignored. Thus they make the dynamic analysis of spacecraft more complicated. In engineering practices, spacecraft are often idealized as finite element models with many degrees of freedom (DOFs). However, the number of DOFs associated with nonlinear connectors usually constitutes only a small part of the model. If such structures are taken as globally nonlinear in the dynamic analysis, great difficulties will be certainly brought to the analysis and design process. And it is unavoidable that design costs will be added and design time will be extended. Therefore, an alternative approach is to take them as local nonlinear structures. From this point of view, the structural dynamics of spacecraft is investigated.
As the nonlinearities of spacecraft are usually distributed and local, an approach is proposed to calculate the transient response of large-scale structure with local nonlinearities. The approach is based on general dynamic reduction method and the Newmark’s method, which is commonly used in direct time integration method. DOFs that are of interest, those on which external forces act, and those associated with nonlinearities are expressed in physical coordinates, but the remaining DOFs are transformed into modal coordinates. In this way, the proposed method can solve strongly nonlinear problems and improve the accuracies of the results. With a transformation, the iterations in each time step are only related to nonlinear DOFs. Consequently, the computational effort of the approach can be significantly reduced.
A method is proposed to study the forced harmonic response of large-scale structures with local nonlinearities. It is combining the describing function (DF) and frequency response function (FRF). With the method, fundamental and multi-harmonic response analysis is discussed, respectively. In the method, the dynamical equations of motion are firstly converted into a set of nonlinear algebra equations. Subsequently, with FRF, the computational efficiency of the approach can be significantly enhanced, and only associated with nonlinear DOFs. In addition, the method can be also used to study the steady state periodic response of nonlinear structures. In the approach, FRF are obtained by using linear normal modes (LNMs). As the LNMs can be obtained by the well developed standard linear modal analysis procedures, the method can be easily cooperated with commercial finite element (FE) softwares.
Following a brief review of most commonly used coupling methods with their merits and shortcomings, a quasilinear FRF coupling method is established by using the DF. The purpose of the method is the treatment of complicated nonlinear joints, which are called general nonlinear joints. Fundamental and multi-harmonic receptance coupling are discussed. In the method, the dynamical equations of motion of general nonlinear joints are firstly quasi-linearized with the DF. Then a linear FRF coupling method is extended, modified and adopted to calculate the forced harmonic response. In comparison with current nonlinear coupling methods in the frequency domain, the present method is more general.
In the last part of the dissertation, parametric study for the forced harmonic response of local nonlinear structures is presented. By using the pseudo-arclength continuation scheme, the effects of modifying nonlinear parameters and/or changing excitation levels on the forced harmonic response can be easily obtained. The approach can be also used to calculate the steady state periodic response of a local nonlinear structure when its nonlinear parameter is modified. Besides, sensitivity analysis (SA) of the forced harmonic response with respect to nonlinear parameters and excitation levels are presented. Moreover, focused on two kinds of typical frequency response cure, the calculations of simple turning points, resonant points, and their corresponding amplitudes are discussed. Their SA with respect to nonlinear parameters and excitation levels is presented.
引文
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