弹性约束边界条件下耦合结构振动特性研究
发布时间：2018-07-22 10:17
【摘要】：边界条件是影响耦合结构振动的重要因素,研究边界条件对耦合结构动态特性的影响,有利于探索边界条件在耦合结构减振降噪方面的潜力,为结构减振降噪提供新的思路。本文围绕弹性约束边界条件下耦合结构振动问题,针对常见的耦合结构开展了如下研究工作:提出了一种弹性约束边界条件下多段耦合梁横向弯曲振动问题的解析方法。与传统的“傅里叶余弦级数+辅助多项式”梁位移表达式相比,本文提出使用三角函数作为梁位移表达式的辅助函数,简化了公式推导过程。利用耦合边界的位移连续和力平衡条件建立了多段耦合梁的边界方程,联立梁振动方程,将梁振动求解转变为一个标准的矩阵特征值问题,获得了弹性边界条件下多段耦合梁的模态以及振动响应,并使用数值仿真和实验方法验证了本文多段耦合梁弹性边界理论。本文进一步在加筋耦合结构变形协调条件模型基础上加入了弹性约束边界条件,建立了具有弹性约束边界条件加筋板振动理论模型。利用改进的二维傅里叶级数作为加筋板位移假设函数,使得加筋板振动控制方程离散为可求解的线性方程组,利用矩阵运算实现了弹性约束边界条件下加筋板自由振动以及稳态声振响应的求解。通过与已有文献和有限元结果对比,验证了本文方法的稳定性和有效性。通过引入Rayleigh阻尼,求解获得了弹性约束边界条件下带阻尼加筋板稳态振动响应。将弹性边界理论由单个平板结构推广到了多平接板耦合振动系统。利用耦合板耦合部位的平衡条件和连续性条件,推导了田字型耦合平板边界耦合方程,使用改进的傅里叶级数作为每个子板的弯曲位移函数,离散边界耦合方程和各子板的振动方程为求解方便的线性方程组。通过数值仿真和实验方法验证了本文所建立理论模型的正确性。利用本文建立的理论模型,分析了耦合边界阻尼对耦合板声振响应的影响,结果表明:耦合边界阻尼可以在一定程度上削弱声振响应共振峰,而且其抑振效果受耦合边界刚度影响。进一步仿真研究了耦合板结构内的振动功率流传递特性,结果表明:增大横向弹性边界刚度能有效抑制功率流在边界处的流动;当外激励频率为低阶共振频率时,功率流更容易流向与受激板相同材质的接受板。本文利用耦合部位的平衡条件和连续性条件,完整地考虑了面内剪切力、面内纵向力、弯矩和横向剪切力的耦合效应,建立了多段耦合圆柱壳结构的耦合边界方程,解决了弹性边界条件下边界耦合方程不易表达的难题,将弹性边界理论从单段圆柱壳推广到多段耦合圆柱壳。使用本文改进的傅里叶级数作为圆柱壳位移表达式,使得微分形式的边界耦合方程和各个壳体的振动方程离散为求解方便的线性方程组。使用有限元方法和实验方法验证了多段耦合圆柱壳理论模型的有效性,并分析了边界约束刚度对多段耦合圆柱壳结构振动响应的影响,结果表明:相比轴向和旋转边界刚度,环向和径向边界刚度对耦合圆柱壳结构振动响应影响更大。将发展的弹性边界计算方法应用于水下敷瓦加筋圆柱壳振动响应与传递分析。分别利用等效单层理论和正交各向异性理论,建立了弹性边界条件下敷瓦圆柱壳和加筋圆柱壳振动理论模型。结合弹性边界理论,引入了水流体负载的影响,得到了弹性边界条件下水下敷瓦加筋圆柱壳的振动响应计算方法。开展了加筋圆柱壳和敷瓦加筋圆柱壳实验研究。获得了加筋圆柱壳以及水下敷瓦加筋圆柱壳的振动响应,测试结果与理论结果一致性良好。
[Abstract]:The boundary condition is an important factor affecting the vibration of coupled structures. The study of the influence of boundary conditions on the dynamic characteristics of coupled structures is beneficial to the exploration of the potential of boundary conditions in the vibration and noise reduction of coupled structures, and provides a new idea for the vibration and noise reduction of the structure. The coupling structure has carried out the following research work: an analytical method for the lateral bending vibration of multi segment beams under the elastic confinement boundary condition is proposed. Compared with the traditional "Fourier cosine series + auxiliary polynomial" beam displacement expression, this paper proposes a triangular function as the auxiliary function of the beam displacement expression. By using the displacement continuity and force balance conditions of the coupled boundary, the boundary equation of the multi segment coupling beam is established and the vibration equation of the joint beam is established. The solution of the beam vibration is transformed into a standard matrix eigenvalue problem. The modal and vibration response of the multi segment beam under the elastic boundary condition are obtained, and the numerical simulation and experimental side are used. In this paper, the elastic boundary theory of the multi segment coupling beam is verified. In this paper, the elastic constrained boundary condition is added to the deformation coordination condition model of the stiffened coupling structure, and the theoretical model of the stiffened plate with elastic constraint boundary condition is established. The improved two-dimensional Fu Liye series is used as the displacement hypothesis function of the stiffened plate. The vibration control equation of the stiffened plate is discrete to the solution of the linear equations. The matrix calculation is used to solve the free vibration of the stiffened plate and the steady sound vibration response under the elastic constrained boundary condition. The stability and effectiveness of the proposed method are verified by the comparison with the existing literature and finite element results. The solution is solved by introducing the Rayleigh damping. The steady vibration response of a stiffened stiffened plate with elastic constraint boundary conditions is obtained. The elastic boundary theory is extended from a single plate structure to a multi flat plate coupled vibration system. The coupling equation of the field type coupling plate boundary boundary is derived by using the balance condition and the continuity condition of the coupling plate. The improved Fourier series is used. As the flexural displacement function of each sub plate, the discrete boundary coupling equation and the vibration equation of each sub plate are the convenient linear equations. The correctness of the theoretical model is verified by numerical simulation and experimental method. The acoustic vibration response of coupling plate with coupled boundary damping is analyzed by using the theoretical model established in this paper. The results show that the coupling boundary damping can weaken the resonant peak of the acoustic vibration response to a certain extent, and its vibration suppression effect is affected by the coupling boundary stiffness. The vibration power flow transmission characteristics in the coupling plate structure are further simulated and studied. The results show that the increase of the lateral elastic boundary stiffness can effectively restrain the flow of power flow at the boundary. When the external excitation frequency is low order resonance frequency, the power flow is easier to flow to the plate with the same material as the excited plate. In this paper, the coupling effect of the in-plane shear force, the longitudinal force, the bending moment and the transverse shear force of the plane is considered, and the coupling of the multi section coupled cylindrical shell structure is established by using the equilibrium condition and the continuity condition of the coupling. The boundary equation solves the problem that the boundary coupling equation is not easy to express under the elastic boundary condition. The elastic boundary theory is extended from a single cylindrical shell to a multi section cylindrical shell. The Fourier series is used as the displacement expression of the cylindrical shell, which makes the boundary coupling equation of differential form and the vibration equation of each shell discrete into the equation. The finite element method and experimental method are used to verify the validity of the multi section coupled cylindrical shell theory model and the influence of the boundary constraint stiffness on the vibration response of the multi section coupled cylindrical shell structure. The results show that the stiffness of the circumferential and radial boundary and the stiffness of the circumferential and radial boundary on the coupled cylindrical shell junction are compared. The elastic boundary calculation method is applied to the vibration response and transfer analysis of the stiffened cylindrical shells under water. By using the equivalent monolayer theory and the orthotropic theory, the vibration theory model of the cylindrical shell and stiffened cylindrical shell under the elastic boundary condition is established, and the elastic boundary theory is introduced. The effect of water load on the vibration response of a cylindrical shell with elastic reinforcement under the elastic boundary condition is obtained. The experimental study on the stiffened cylindrical shell and the stiffened cylindrical shell is carried out. The vibration response of the stiffened cylindrical shell and the stiffened cylindrical shell under water is obtained. The results of the test are in good agreement with the theoretical results.
【学位授予单位】：西北工业大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：U661.44
，
本文编号：2137081
[Abstract]:The boundary condition is an important factor affecting the vibration of coupled structures. The study of the influence of boundary conditions on the dynamic characteristics of coupled structures is beneficial to the exploration of the potential of boundary conditions in the vibration and noise reduction of coupled structures, and provides a new idea for the vibration and noise reduction of the structure. The coupling structure has carried out the following research work: an analytical method for the lateral bending vibration of multi segment beams under the elastic confinement boundary condition is proposed. Compared with the traditional "Fourier cosine series + auxiliary polynomial" beam displacement expression, this paper proposes a triangular function as the auxiliary function of the beam displacement expression. By using the displacement continuity and force balance conditions of the coupled boundary, the boundary equation of the multi segment coupling beam is established and the vibration equation of the joint beam is established. The solution of the beam vibration is transformed into a standard matrix eigenvalue problem. The modal and vibration response of the multi segment beam under the elastic boundary condition are obtained, and the numerical simulation and experimental side are used. In this paper, the elastic boundary theory of the multi segment coupling beam is verified. In this paper, the elastic constrained boundary condition is added to the deformation coordination condition model of the stiffened coupling structure, and the theoretical model of the stiffened plate with elastic constraint boundary condition is established. The improved two-dimensional Fu Liye series is used as the displacement hypothesis function of the stiffened plate. The vibration control equation of the stiffened plate is discrete to the solution of the linear equations. The matrix calculation is used to solve the free vibration of the stiffened plate and the steady sound vibration response under the elastic constrained boundary condition. The stability and effectiveness of the proposed method are verified by the comparison with the existing literature and finite element results. The solution is solved by introducing the Rayleigh damping. The steady vibration response of a stiffened stiffened plate with elastic constraint boundary conditions is obtained. The elastic boundary theory is extended from a single plate structure to a multi flat plate coupled vibration system. The coupling equation of the field type coupling plate boundary boundary is derived by using the balance condition and the continuity condition of the coupling plate. The improved Fourier series is used. As the flexural displacement function of each sub plate, the discrete boundary coupling equation and the vibration equation of each sub plate are the convenient linear equations. The correctness of the theoretical model is verified by numerical simulation and experimental method. The acoustic vibration response of coupling plate with coupled boundary damping is analyzed by using the theoretical model established in this paper. The results show that the coupling boundary damping can weaken the resonant peak of the acoustic vibration response to a certain extent, and its vibration suppression effect is affected by the coupling boundary stiffness. The vibration power flow transmission characteristics in the coupling plate structure are further simulated and studied. The results show that the increase of the lateral elastic boundary stiffness can effectively restrain the flow of power flow at the boundary. When the external excitation frequency is low order resonance frequency, the power flow is easier to flow to the plate with the same material as the excited plate. In this paper, the coupling effect of the in-plane shear force, the longitudinal force, the bending moment and the transverse shear force of the plane is considered, and the coupling of the multi section coupled cylindrical shell structure is established by using the equilibrium condition and the continuity condition of the coupling. The boundary equation solves the problem that the boundary coupling equation is not easy to express under the elastic boundary condition. The elastic boundary theory is extended from a single cylindrical shell to a multi section cylindrical shell. The Fourier series is used as the displacement expression of the cylindrical shell, which makes the boundary coupling equation of differential form and the vibration equation of each shell discrete into the equation. The finite element method and experimental method are used to verify the validity of the multi section coupled cylindrical shell theory model and the influence of the boundary constraint stiffness on the vibration response of the multi section coupled cylindrical shell structure. The results show that the stiffness of the circumferential and radial boundary and the stiffness of the circumferential and radial boundary on the coupled cylindrical shell junction are compared. The elastic boundary calculation method is applied to the vibration response and transfer analysis of the stiffened cylindrical shells under water. By using the equivalent monolayer theory and the orthotropic theory, the vibration theory model of the cylindrical shell and stiffened cylindrical shell under the elastic boundary condition is established, and the elastic boundary theory is introduced. The effect of water load on the vibration response of a cylindrical shell with elastic reinforcement under the elastic boundary condition is obtained. The experimental study on the stiffened cylindrical shell and the stiffened cylindrical shell is carried out. The vibration response of the stiffened cylindrical shell and the stiffened cylindrical shell under water is obtained. The results of the test are in good agreement with the theoretical results.
【学位授予单位】：西北工业大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：U661.44
，
本文编号：2137081
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