复杂边界条件下旋转结构统一动力学模型的构建与研究
发布时间：2019-06-04 16:45
【摘要】：旋转结构作为独立的结构或组合结构的部件,被广泛应用于航空航天、海洋工程、土木工程以及机械工程等工程应用领域,其相关动力学问题的求解一直是工程领域研究的一个重要内容。在传统求解分析方法中,需要建立不同几何配置参数下旋转结构的求解方案,并对位移容许函数进行修改以适用于各种不同的边界条件。为了实现模型的参数化,本文针对旋转结构,构建了一种适用于复杂边界条件的统一动力学分析模型,对工程实际应用领域中旋转结构的设计提供必要的理论和技术支持,并从本质上研究结构振动特性和声场的形成机理。本文围绕着复杂边界条件下旋转结构动力学建模问题,开展了如下的研究工作:建立了复杂边界条件下旋转板(扇形板、环板和圆板)结构横向振动统一分析模型,采用二维谱几何法来描述旋转板结构横向振动位移容许函数。为了消除位移容许函数及其空间导数在边界处存在的不连续或跳跃现象,构建的位移函数分量表示为一个标准的单余弦级数与四项正弦函数之和。在旋转板各边界上均匀分布具有独立刚度系数的线性和旋转约束弹簧,模拟板结构系统的复杂边界条件,通过修改边界约束弹簧的刚度系数值即可求解复杂边界条件下旋转板结构的振动问题。采用基于能量原理的瑞利-里兹法求解位移容许函数的未知级数展开系数。通过数值分析对所构建的位移容许函数和统一分析模型进行了验证,对旋转板横向振动特性影响因素进行了研究分析。构建了复杂边界条件下旋转板结构面内振动问题的统一分析模型。为了确保面内振动位移容许函数及其导数在各边界处的连续性,采用二维谱几何法对旋转板结构径向和周向的位移容许函数进行了统一描述。采用沿各边界均匀分布的切向和法向约束弹簧来描述面内振动问题的复杂边界条件。基于瑞利-里兹法推导了复杂边界条件下旋转板结构面内振动特征方程,并通过求解一个标准特征值问题来获得面内自由振动特征参数。通过将本文数值计算结果与其它分析方法结果进行对比分析,检验了本文方法及统一分析模型。提出了一种三维谱几何法,并建立了复杂边界条件下旋转板结构三维振动统一分析模型。采用三维谱几何法将旋转板结构三维振动位移容许函数描述为三重三角级数形式,以消除位移容许函数及其空间导数在结构各边界面上可能存在的间断点。通过修改各边界面上三个方向的边界约束弹簧刚度系数,模拟各种不同的边界条件及其任意组合。采用基于能量原理的瑞利-里兹法推导了旋转板结构系统的三维自由振动运动方程,通过求解该方程获得结构系统的振动特性,即通过求解同一个边值问题而获得不同几何形状旋转结构的振动特性。通过对不同边界条件下旋转结构自由振动特性的求解,并与相关文献结果及有限元法结果进行对比分析来验证所提方法及构建的统一分析模型。构建了复杂边界条件/耦合连接条件下旋转板-圆柱壳耦合结构系统动力学问题的统一分析模型。采用二维谱几何法来描述旋转板和圆柱壳结构的六种位移容许函数,分别对各自外在的复杂边界条件进行建模。在连接公共边,采用具有线性刚度和旋转刚度的三维弹性耦合器来描述板壳连接的相容性条件。三维弹性耦合器由沿公共边界分布的四类耦合弹簧来描述,详尽地考虑了弯矩、横向剪切、面内剪切与纵向剪切的耦合效应,通过改变相应弹簧刚度值来实现结构系统各种不同的耦合连接条件。最后采用瑞利-里兹法求解得到板-壳耦合结构动力学问题相应的双重改进三角级数解。将本文数值计算结果与其它文献解及有限元法结果进行对比分析来检验构建的分析模型。在此基础上,对旋转板-圆柱壳耦合结构的强迫振动响应进行了计算分析,并研究了各种不同耦合连接条件、耦合位置及其它结构参数对板-壳耦合结构振动响应特性的影响。最后,设计并搭建了相关实验台架,对旋转板(凹角环扇形板和圆板)以及弹性圆板-圆柱壳耦合结构的振动特性开展了相关的实验研究。通过将实验测试结果与本文方法的预测结果进行对比分析来检验了所提出的分析方法,并对特殊的实验现象和实验误差原因进行了分析。
[Abstract]:As a component of independent structure or combined structure, the rotating structure is widely used in the application fields of aerospace, ocean engineering, civil engineering and mechanical engineering, and the solution of the related dynamic problems has been an important content in the field of engineering. In the traditional solution analysis method, the solution scheme of the rotation structure under different geometric configuration parameters needs to be established, and the displacement tolerance function can be modified to be suitable for various boundary conditions. In order to parameterize the model, a unified dynamic analysis model for complex boundary conditions is built, and the necessary theory and technical support are provided for the design of the rotating structure in the practical application field of the project. The characteristics of structural vibration and the formation mechanism of sound field are studied from the essence. In this paper, the problem of the dynamic modeling of the rotating structure under complex boundary conditions is studied. The unified analytical model of the transverse vibration of the rotating plate (the sector plate, the ring plate and the circular plate) under the complex boundary conditions is established. A two-dimensional spectral method is used to describe the allowable function of the lateral vibration displacement of the rotating plate structure. In order to eliminate the discontinuity or jumping phenomenon of the displacement tolerance function and its spatial derivative at the boundary, the constructed displacement function component is expressed as a standard single-cosine series and the sum of the four sine functions. The linear and rotational constraint springs with independent stiffness coefficients are uniformly distributed on each boundary of the rotating plate, and the complex boundary conditions of the plate structure system are simulated, and the vibration problem of the rotating plate structure under the complex boundary conditions can be solved by modifying the rigidity coefficient value of the boundary constraint spring. An energy-based Rayleigh-Ritz method is used to solve the unknown series expansion coefficient of the displacement tolerance function. The displacement tolerance function and the unified analytical model are verified by numerical analysis, and the influence factors of the transverse vibration characteristics of the rotating plate are analyzed. The unified analytical model of the in-plane vibration of the rotating plate structure under complex boundary conditions is constructed. In order to ensure the continuity of the in-plane vibration displacement tolerance function and its derivative at each boundary, a two-dimensional spectral geometry method is used to describe the displacement tolerance function in the radial and circumferential direction of the rotating plate structure. The complex boundary conditions of the in-plane vibration problem are described by tangential and normal constraint springs which are uniformly distributed along the boundary. In this paper, the in-plane vibration characteristic equation of a rotating plate structure under complex boundary conditions is derived based on the Rayleigh-Ritz method, and a standard characteristic value problem is solved to obtain the in-plane free vibration characteristic parameters. In this paper, the numerical results of this paper and other analytical methods are compared and analyzed, and the method and the unified analytical model of this paper are examined. In this paper, a three-dimensional spectral geometry method is proposed, and a three-dimensional vibration unified analysis model of the rotating plate structure under complex boundary conditions is established. The three-dimensional vibration displacement tolerance function of the rotating plate structure is described by the three-dimensional spectral geometry as a triple triangular series form, so as to eliminate the discontinuity points that the displacement tolerance function and the space derivative may exist on each boundary surface of the structure. Various boundary conditions and any combination thereof are simulated by modifying the boundary constraint spring rate coefficient of the three directions on each boundary surface. The three-dimensional free-vibration motion equation of a rotating plate structure system is derived by the energy-based Rayleigh-Ritz method, and the vibration characteristics of the structure system are obtained by solving the equation, that is, by solving the same boundary value problem, the vibration characteristics of the rotating structure of different geometric shapes are obtained. By solving the free vibration characteristics of the rotating structure under different boundary conditions, and comparing with the results of the relevant literature and the results of the finite element method, the proposed method and the unified analysis model of the proposed method are verified. A unified analytical model of the dynamics of a rotating plate-cylindrical shell coupled structure under complex boundary conditions/ coupling conditions is constructed. The six displacement tolerance functions of the rotating plate and the cylindrical shell structure are described by the two-dimensional spectral method, and the complex boundary conditions of the rotating plate and the cylindrical shell are respectively modeled. A three-dimensional elastic coupler with a linear stiffness and a rotational stiffness is used to describe the compatibility condition of the plate-shell connection prior to connecting the common side. The three-dimensional elastic coupler is described by four kinds of coupling springs distributed along the common boundary, and the coupling effect of bending moment, transverse shearing, in-plane shearing and longitudinal shearing is considered in detail, and various coupling conditions of the structural system can be realized by changing the value of the corresponding spring. In the end, the method of Rayleigh-Ritz method is used to solve the double-modified triangular solution of the dynamic problem of the plate-shell coupling structure. The numerical results of this paper are compared with other literature and the results of the finite element method to test and construct the analytical model. In this paper, the forced vibration response of the coupling structure of the rotating plate and the cylindrical shell is calculated and analyzed, and the effects of various coupling conditions, coupling positions and other structural parameters on the vibration response of the plate-shell coupling structure are studied. Finally, the relevant experimental bench is designed and built, and the vibration characteristics of the rotating plate (the concave-angle ring sector plate and the circular plate) and the elastic circular plate-cylindrical shell coupling structure are studied. The results of the experiment and the prediction results of this method are compared and analyzed to verify the proposed analytical method, and the special experimental phenomena and the cause of the experimental error are analyzed.
【学位授予单位】：哈尔滨工程大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TH113
，
本文编号：2492852
[Abstract]:As a component of independent structure or combined structure, the rotating structure is widely used in the application fields of aerospace, ocean engineering, civil engineering and mechanical engineering, and the solution of the related dynamic problems has been an important content in the field of engineering. In the traditional solution analysis method, the solution scheme of the rotation structure under different geometric configuration parameters needs to be established, and the displacement tolerance function can be modified to be suitable for various boundary conditions. In order to parameterize the model, a unified dynamic analysis model for complex boundary conditions is built, and the necessary theory and technical support are provided for the design of the rotating structure in the practical application field of the project. The characteristics of structural vibration and the formation mechanism of sound field are studied from the essence. In this paper, the problem of the dynamic modeling of the rotating structure under complex boundary conditions is studied. The unified analytical model of the transverse vibration of the rotating plate (the sector plate, the ring plate and the circular plate) under the complex boundary conditions is established. A two-dimensional spectral method is used to describe the allowable function of the lateral vibration displacement of the rotating plate structure. In order to eliminate the discontinuity or jumping phenomenon of the displacement tolerance function and its spatial derivative at the boundary, the constructed displacement function component is expressed as a standard single-cosine series and the sum of the four sine functions. The linear and rotational constraint springs with independent stiffness coefficients are uniformly distributed on each boundary of the rotating plate, and the complex boundary conditions of the plate structure system are simulated, and the vibration problem of the rotating plate structure under the complex boundary conditions can be solved by modifying the rigidity coefficient value of the boundary constraint spring. An energy-based Rayleigh-Ritz method is used to solve the unknown series expansion coefficient of the displacement tolerance function. The displacement tolerance function and the unified analytical model are verified by numerical analysis, and the influence factors of the transverse vibration characteristics of the rotating plate are analyzed. The unified analytical model of the in-plane vibration of the rotating plate structure under complex boundary conditions is constructed. In order to ensure the continuity of the in-plane vibration displacement tolerance function and its derivative at each boundary, a two-dimensional spectral geometry method is used to describe the displacement tolerance function in the radial and circumferential direction of the rotating plate structure. The complex boundary conditions of the in-plane vibration problem are described by tangential and normal constraint springs which are uniformly distributed along the boundary. In this paper, the in-plane vibration characteristic equation of a rotating plate structure under complex boundary conditions is derived based on the Rayleigh-Ritz method, and a standard characteristic value problem is solved to obtain the in-plane free vibration characteristic parameters. In this paper, the numerical results of this paper and other analytical methods are compared and analyzed, and the method and the unified analytical model of this paper are examined. In this paper, a three-dimensional spectral geometry method is proposed, and a three-dimensional vibration unified analysis model of the rotating plate structure under complex boundary conditions is established. The three-dimensional vibration displacement tolerance function of the rotating plate structure is described by the three-dimensional spectral geometry as a triple triangular series form, so as to eliminate the discontinuity points that the displacement tolerance function and the space derivative may exist on each boundary surface of the structure. Various boundary conditions and any combination thereof are simulated by modifying the boundary constraint spring rate coefficient of the three directions on each boundary surface. The three-dimensional free-vibration motion equation of a rotating plate structure system is derived by the energy-based Rayleigh-Ritz method, and the vibration characteristics of the structure system are obtained by solving the equation, that is, by solving the same boundary value problem, the vibration characteristics of the rotating structure of different geometric shapes are obtained. By solving the free vibration characteristics of the rotating structure under different boundary conditions, and comparing with the results of the relevant literature and the results of the finite element method, the proposed method and the unified analysis model of the proposed method are verified. A unified analytical model of the dynamics of a rotating plate-cylindrical shell coupled structure under complex boundary conditions/ coupling conditions is constructed. The six displacement tolerance functions of the rotating plate and the cylindrical shell structure are described by the two-dimensional spectral method, and the complex boundary conditions of the rotating plate and the cylindrical shell are respectively modeled. A three-dimensional elastic coupler with a linear stiffness and a rotational stiffness is used to describe the compatibility condition of the plate-shell connection prior to connecting the common side. The three-dimensional elastic coupler is described by four kinds of coupling springs distributed along the common boundary, and the coupling effect of bending moment, transverse shearing, in-plane shearing and longitudinal shearing is considered in detail, and various coupling conditions of the structural system can be realized by changing the value of the corresponding spring. In the end, the method of Rayleigh-Ritz method is used to solve the double-modified triangular solution of the dynamic problem of the plate-shell coupling structure. The numerical results of this paper are compared with other literature and the results of the finite element method to test and construct the analytical model. In this paper, the forced vibration response of the coupling structure of the rotating plate and the cylindrical shell is calculated and analyzed, and the effects of various coupling conditions, coupling positions and other structural parameters on the vibration response of the plate-shell coupling structure are studied. Finally, the relevant experimental bench is designed and built, and the vibration characteristics of the rotating plate (the concave-angle ring sector plate and the circular plate) and the elastic circular plate-cylindrical shell coupling structure are studied. The results of the experiment and the prediction results of this method are compared and analyzed to verify the proposed analytical method, and the special experimental phenomena and the cause of the experimental error are analyzed.
【学位授予单位】：哈尔滨工程大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TH113
，
本文编号：2492852
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