复合结构基座减振特性的理论与实验研究
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摘要
军、民船舶的振动与噪声的预报与控制是船舶工程中一个重要的技术领域。该领域相关技术的研究与应用对改进民船的质量与安全性,提高舰船的作战与生存能力有重要的意义。机械激励引起船舶振动与水中声辐射的控制技术的研究在国内外已有悠久的历史和丰富的成果。为进一步提高船舶减振降噪的成效,发展基于复合材料结构动力学特征的新型隔振技术成为一个有吸引力的研究方向。
机械设备的基座结构是设备振动传递到船体结构的最重要通道。为更好地发挥该通道在减振降噪中的作用,本文突破了船舶机械设备钢质基座的传统形式,设计了复合结构基座,并从理论和实验两方面研究了其隔振效果。本文的结构及主要研究内容如下:
(1)课题相关研究领域的综述——从声学的角度,分析了机械噪声控制的整体框架和思路。在该框架内,从轮机设计的角度,综述了船舶柔性隔振系统的研究方法;从结构设计的角度,综述了船体基座及船体结构中声传递的研究方法;最后,综述了纤维增强树脂基复合材料阻尼的研究进展。
(2)基本元件动力学特性的矩阵描述法——在元件坐标系下,分别推导了连续元件(欧拉—伯努利梁、杆)和离散元件(质量、弹簧、阻尼、刚体)输入端状态向量与输出端状态向量之间的关系。在状态向量正方向的定义相同时,给出了向前传递矩阵、向后传递矩阵、阻抗矩阵和导纳矩阵的解析公式,研究了四种矩阵的特性。结合欧拉梁和杆的相关公式,得到了一般二维梁的传递矩阵和广义阻抗矩阵的解析公式。数值算例表明:在激励频率较低时,本文方法与有限元法的结果基本相同。当激振频率趋近于零时,获得了位移阻抗矩阵和静力学有限元刚度矩阵之间的关系。讨论了动力学中的矩阵描述法(阻抗矩阵法、导纳矩阵法和传递矩阵法)与静力学中的矩阵描述法(位移法、力法和混合法)的对应关系。
(3)组合结构动力学特性的阻抗综合法——给出了机械阻抗的基本定义和广义定义。给出了无源线性振动系统的四端参数矩阵的一般形式,给出了四端系统的串联和并联运算法则。介绍了阻抗综合法的基本原理,采用传递矩阵法推导了单层隔振模型的振动方程。本文分别采用传递矩阵法和导纳矩阵法推导了加固型阻振基座的纵向振动方程,得到了纵向力传递率的解析公式,两种方法得到的结果相同,但传递矩阵法的推导过程更简洁。本文还采用传递矩阵法推导了悬臂型阻振基座的横向振动方程,得到了横向力传递率的解析公式。矩阵描述法有利于利用计算机编程计算动力学问题,本文所导得的公式可用于指导阻振基座的动力学设计,计算工作量不大且精度较高。
(4)复合材料杆件动力学实验及分析——推导了杆在不同边界下原点阻抗和传递阻抗的公式,分析了阻尼和材料对杆阻抗数值的影响。在机械阻抗测试平台上,采用常用的单点激振法进行实验,得到频域内复合材料杆件的机械阻抗数据,频率高于100Hz时,理论预测值和实验值基本吻合,证明了该实验方法的正确性。用实验方法、解析方法和混合方法进行了模态参数的初步识别,并用非线性最小二乘方法中的Levenberg-Marquardt和Trust region算法分别求得了模态参数的最优值,比较了两种算法的结果。由采用优化参数的单自由度离散模型求得的机械阻抗值与实验值吻合良好,该模型可以较好地描述复合材料试件的动力学特性。
(5)复合材料T型胶接接头动力学实验及分析——设计了典型的船用T型胶接接头,利用前一章的实验及分析方法,借助设计的夹具,在阻抗测试平台上测得了正装和反装的机械阻抗数据,获得了T型接头的离散系统数学模型。
(6)胶接元件的动力学特性——采用理论结合实验的方法研究了T型接头的胶接结合部在法线方向上的线性动力学特性。根据粘弹性力学原理,推导了由3个bush单元的组合来模拟阻抗矩阵的公式。算例表明:在Nastran中采用该方法可以从数值上模拟阻抗矩阵。利用该方法求得的模拟胶接结合部的bush参数将用于下一章的动力学计算。
(7)基座动力学特性的实验研究与仿真计算——通过实验和有限元计算两种方法研究了加肋圆柱壳中安装复合结构基座或钢基座的动力学特性,比较了两者的减振和隔振效果。结果表明:复合结构基座的有限元建模方法是合理的。复合结构基座比钢基座具有更好的减振效果。无论采用加速度振级落差还是功率流传递率作为评价指标,复合结构基座都比钢基座具有更好的隔振效果。隔振效果的具体数值与激励位置和激励频率有关。
(8)总结与展望——总结了本文的研究内容和成果,并对下一步的研究内容进行了展望。
本文创新性的工作主要体现在:
(1)为了提高机械隔振效率,提出了以不同材料组成的复合结构基座替代钢基座的新思路。
(2)提出了一种复合材料腹板与钢质阻振质块相结合的新型机械设备振动隔离基座形式。
(3)基于波动理论,采用与频率相关的形函数,推导了梁、杆结构的四端参数矩阵,结合数值算例编制了计算程序,该程序与常规有限元程序的计算结果基本相同,但计算量较小。对于简化的基座理论模型,应用已推导的梁、杆、刚体和质量等的四端参数矩阵,导出了带有阻振质量的基座的系统方程,为设计阻振质量基座提供了简便的工具。
(4)基于计算机—实验辅助建模思想,提出了复合结构基座的动力学建模方法。对非胶接部分的部件采用常规有限元程序模拟;针对胶接结合部的动力学特性难以建模的困难,采用非线性拟合方法对阻抗测试平台上测得的频域实验数据进行了参数识别,得到杆和T型接头试件的系统方程,从中提取出胶接部分的阻抗矩阵,并用有限元程序Nastran中的3个bush单元的组合从数值上模拟了该阻抗矩阵。
(5)对于复合结构基座和钢基座进行了实验研究和有限元计算,结果表明复合结构基座的建模方法是合理的,且与钢基座相比,经过精心设计的复合结构基座的隔振效果十分明显。
The prediction and control of noise and vibration is a very important field in ship engineering. The research and application of related technology in this field is very significant to improve the quality and safety of merchant ship, or battle effectiveness and survival capability of military ship. The research on the control of ship vibration and sound radiation in the water caused by mechanical excitation has a long history and a lot of results all over the world. In order to improve the effect of vibration and noise reduction, it is very attractive to develop new vibration isolation technology based on composite structures dynamic characteristics.
Marine mechanical equipment foundation is the most important mechanical vibration transferring route to ship hull structures. In order to improve the effect of foundation on vibration and noise reduction, the composite foundation, which is different from traditional steel foundation, is designed in this paper. And its vibration properties are studied by theoretical and experimental methods. The paper consists of the following aspects:
(1) A literature review of the related researches—The whole frame of mechanical noise control are given based on acoustic concepts. The theories of flexible vibration isolation systems are presented based on mechanical design concepts. The theories of structure-borne sound propagation are also presented based on structure design concepts. Finally, the researches on damping of fiber reinforced polymer composite are reviewed.
(2) Investigation on dynamic characteristics of two pole elements by matrix description approach—Relationships between input state vectors and output state vectors of continuous elements (Euler-Bernoulli beam, rod) and discrete elements (mass, spring, damper, rigid body) are deduced respectively in element coordinating system. Analytical formulae of forward transfer matrix, reverse transfer matrix, impedance matrix and mobility matrix are derived separately when the positive definition of state vectors are assumed the same. The characteristics of the four matrices are studied. Analytical formulae of the four matrices of a general beam are given by combining the corresponding formulae of Euler-Bernoulli beam with those of the rod. Numerical examples show that the results respectively by the present method and those of the finite element method are nearly the same. When frequency is close to zero, the relationship between the displacement impedance matrix and the static stiffness matrix are established. The relationship between dynamic matrix description method and static matrix description method is discussed.
(3) The impedance synthesis method of built-up structures—The basic and generalized definitions of mechanical impedance are given. The four poles parameters matrices and algorithm of passive linear vibration mechanical systems are also given. The impedance synthesis method is introduced. The analytical formulae of simple model are deduced by transfer matrix method. The longitudinal vibration equations of the anti-vibration foundation are achieved both by transfer matrix method and mobility matrix method. The analytical formula for the longitudinal force transmissibility is given. Two approaches yields similar results, but the process of transfer matrix method is simpler. The transverse vibration equations of the anti-vibration foundation are also deduced using transfer matrix method. The analytical formula for the transverse force transmissibility is consequently given. It is showed that matrix description methods facilitate solving dynamic questions using computer programming. Analytical formulae in this paper can be applied in dynamic design of the anti-vibration foundation to achieve good precision with less computation.
(4) Dynamic experiment and analysis of a composite rod—The formulae of driving point impedance and transfer impedance of the rod under different boundary conditions are deduced. The influences of damping and material parameters to the impedance are analyzed. The composite rod is tested on an impedance platform facility with single point excitation and the mechanical impedance data are obtained. It shows that theoretical results agree with the experimental data when excitation frequency is higher than 100Hz, which also validate the measurement method. The initial modal parameters are then identified with the experiment method, analytical method and hybrid method. After these, the optimal modal parameters are identified by two nonlinear least square methods called Levenberg-Marquardt and Trust region algorithms respectively. Research work show that the mechanical impedance data, which are calculated from the discrete system modal with single degree of freedom and based on optimal modal parameters, coincide well with the experimental result, and this modal can describe the dynamic properties of the composite rod within testing frequency range very well.
(5) Dynamic experiment and analysis of a composite T joint—The typical marine T joint is designed. The T joint is tested on the impedance platform facility with the help of special designed tools and the positive and negative mechanical impedance data are obtained. The discrete system mathematical modal of T joint is obtained using the method developed in the fourth chapter.
(6) Dynamic properties of the adhesive joint—The linear dynamic properties of the adhesive joint in normal direction are studied with theoretical and experimental compound method. The impedance matrix can be numerically simulated using the combination of three“bush”elements based on viscoelastic theory. Numerical example shows that the results from FEM method coincide with those from transfer matrix method. The parameters of“bush”elements are used in the seventh chapter.
(7) Experimental and simulation researches on dynamic properties of the composite foundation—The dynamic properties of two systems, that is, the composite foundation installed in a framed cylinder, and equivalent steel foundation installed the same cylinder, are studied respectively with experimental and FEM method. Results show that the computer and test aided modeling method of the composite foundation are reasonable. The vibration isolation effect of the composite foundation is better than that of the equivalent steel foundation.
(8) Summary and forecast—The research contents in the dissertation are summarized. The future research contents of related fields are proposed.
The innovation research works in the dissertation are primarily as follows:
(1) To improve the efficiency of mechanical vibration isolation, a new idea of using composite foundation in place of steel foundation is presented.
(2) The composite mechanical equipment vibration isolation foundation, which is a combination of composite web plate and steel anti-vibration mass, is presented.
(3) Based on the wave theory, the four poles parameters matrices of the Euler-Bernoulli beam and rod are deduced using the shape functions related to frequency. The computer programs are made to calculate special numerical examples. The results of the programs are almost the same with those of ordinary FE programs. For the simplified theoretical model, with the deduced four poles parameters matrices of the Euler-Bernoulli beam, rod, rigid body and mass, the system formulae of anti-vibration foundation are deduced, which provide simple tools for the design of anti-vibration foundation.
(4) Based on the computer and test aided modeling idea, the dynamic modeling method of the composite foundation is presented. The ordinary FE programs are used to model non adhesive parts. The experimental data in frequency domain are obtained from an impedance platform facility. Then two nonlinear least square methods called Levenberg-Marquardt and Trust region algorithms are used to carry out parameter identification. The reasonable system formulae of specimen are achieved. The impedance matrixes of the adhesive parts, which are obtained from the system formulae of rod and T joint, are numerically simulated using a combination of three“bush”elements in Nastran program.
(5) The composite foundation and steel foundation are researched using experimental and FEM methods. The results show that the dynamic modeling method of the composite foundation is reasonable. Compared with steel foundation, the vibration isolation effect of the composite foundation is very good.
机械设备的基座结构是设备振动传递到船体结构的最重要通道。为更好地发挥该通道在减振降噪中的作用,本文突破了船舶机械设备钢质基座的传统形式,设计了复合结构基座,并从理论和实验两方面研究了其隔振效果。本文的结构及主要研究内容如下:
(1)课题相关研究领域的综述——从声学的角度,分析了机械噪声控制的整体框架和思路。在该框架内,从轮机设计的角度,综述了船舶柔性隔振系统的研究方法;从结构设计的角度,综述了船体基座及船体结构中声传递的研究方法;最后,综述了纤维增强树脂基复合材料阻尼的研究进展。
(2)基本元件动力学特性的矩阵描述法——在元件坐标系下,分别推导了连续元件(欧拉—伯努利梁、杆)和离散元件(质量、弹簧、阻尼、刚体)输入端状态向量与输出端状态向量之间的关系。在状态向量正方向的定义相同时,给出了向前传递矩阵、向后传递矩阵、阻抗矩阵和导纳矩阵的解析公式,研究了四种矩阵的特性。结合欧拉梁和杆的相关公式,得到了一般二维梁的传递矩阵和广义阻抗矩阵的解析公式。数值算例表明:在激励频率较低时,本文方法与有限元法的结果基本相同。当激振频率趋近于零时,获得了位移阻抗矩阵和静力学有限元刚度矩阵之间的关系。讨论了动力学中的矩阵描述法(阻抗矩阵法、导纳矩阵法和传递矩阵法)与静力学中的矩阵描述法(位移法、力法和混合法)的对应关系。
(3)组合结构动力学特性的阻抗综合法——给出了机械阻抗的基本定义和广义定义。给出了无源线性振动系统的四端参数矩阵的一般形式,给出了四端系统的串联和并联运算法则。介绍了阻抗综合法的基本原理,采用传递矩阵法推导了单层隔振模型的振动方程。本文分别采用传递矩阵法和导纳矩阵法推导了加固型阻振基座的纵向振动方程,得到了纵向力传递率的解析公式,两种方法得到的结果相同,但传递矩阵法的推导过程更简洁。本文还采用传递矩阵法推导了悬臂型阻振基座的横向振动方程,得到了横向力传递率的解析公式。矩阵描述法有利于利用计算机编程计算动力学问题,本文所导得的公式可用于指导阻振基座的动力学设计,计算工作量不大且精度较高。
(4)复合材料杆件动力学实验及分析——推导了杆在不同边界下原点阻抗和传递阻抗的公式,分析了阻尼和材料对杆阻抗数值的影响。在机械阻抗测试平台上,采用常用的单点激振法进行实验,得到频域内复合材料杆件的机械阻抗数据,频率高于100Hz时,理论预测值和实验值基本吻合,证明了该实验方法的正确性。用实验方法、解析方法和混合方法进行了模态参数的初步识别,并用非线性最小二乘方法中的Levenberg-Marquardt和Trust region算法分别求得了模态参数的最优值,比较了两种算法的结果。由采用优化参数的单自由度离散模型求得的机械阻抗值与实验值吻合良好,该模型可以较好地描述复合材料试件的动力学特性。
(5)复合材料T型胶接接头动力学实验及分析——设计了典型的船用T型胶接接头,利用前一章的实验及分析方法,借助设计的夹具,在阻抗测试平台上测得了正装和反装的机械阻抗数据,获得了T型接头的离散系统数学模型。
(6)胶接元件的动力学特性——采用理论结合实验的方法研究了T型接头的胶接结合部在法线方向上的线性动力学特性。根据粘弹性力学原理,推导了由3个bush单元的组合来模拟阻抗矩阵的公式。算例表明:在Nastran中采用该方法可以从数值上模拟阻抗矩阵。利用该方法求得的模拟胶接结合部的bush参数将用于下一章的动力学计算。
(7)基座动力学特性的实验研究与仿真计算——通过实验和有限元计算两种方法研究了加肋圆柱壳中安装复合结构基座或钢基座的动力学特性,比较了两者的减振和隔振效果。结果表明:复合结构基座的有限元建模方法是合理的。复合结构基座比钢基座具有更好的减振效果。无论采用加速度振级落差还是功率流传递率作为评价指标,复合结构基座都比钢基座具有更好的隔振效果。隔振效果的具体数值与激励位置和激励频率有关。
(8)总结与展望——总结了本文的研究内容和成果,并对下一步的研究内容进行了展望。
本文创新性的工作主要体现在:
(1)为了提高机械隔振效率,提出了以不同材料组成的复合结构基座替代钢基座的新思路。
(2)提出了一种复合材料腹板与钢质阻振质块相结合的新型机械设备振动隔离基座形式。
(3)基于波动理论,采用与频率相关的形函数,推导了梁、杆结构的四端参数矩阵,结合数值算例编制了计算程序,该程序与常规有限元程序的计算结果基本相同,但计算量较小。对于简化的基座理论模型,应用已推导的梁、杆、刚体和质量等的四端参数矩阵,导出了带有阻振质量的基座的系统方程,为设计阻振质量基座提供了简便的工具。
(4)基于计算机—实验辅助建模思想,提出了复合结构基座的动力学建模方法。对非胶接部分的部件采用常规有限元程序模拟;针对胶接结合部的动力学特性难以建模的困难,采用非线性拟合方法对阻抗测试平台上测得的频域实验数据进行了参数识别,得到杆和T型接头试件的系统方程,从中提取出胶接部分的阻抗矩阵,并用有限元程序Nastran中的3个bush单元的组合从数值上模拟了该阻抗矩阵。
(5)对于复合结构基座和钢基座进行了实验研究和有限元计算,结果表明复合结构基座的建模方法是合理的,且与钢基座相比,经过精心设计的复合结构基座的隔振效果十分明显。
The prediction and control of noise and vibration is a very important field in ship engineering. The research and application of related technology in this field is very significant to improve the quality and safety of merchant ship, or battle effectiveness and survival capability of military ship. The research on the control of ship vibration and sound radiation in the water caused by mechanical excitation has a long history and a lot of results all over the world. In order to improve the effect of vibration and noise reduction, it is very attractive to develop new vibration isolation technology based on composite structures dynamic characteristics.
Marine mechanical equipment foundation is the most important mechanical vibration transferring route to ship hull structures. In order to improve the effect of foundation on vibration and noise reduction, the composite foundation, which is different from traditional steel foundation, is designed in this paper. And its vibration properties are studied by theoretical and experimental methods. The paper consists of the following aspects:
(1) A literature review of the related researches—The whole frame of mechanical noise control are given based on acoustic concepts. The theories of flexible vibration isolation systems are presented based on mechanical design concepts. The theories of structure-borne sound propagation are also presented based on structure design concepts. Finally, the researches on damping of fiber reinforced polymer composite are reviewed.
(2) Investigation on dynamic characteristics of two pole elements by matrix description approach—Relationships between input state vectors and output state vectors of continuous elements (Euler-Bernoulli beam, rod) and discrete elements (mass, spring, damper, rigid body) are deduced respectively in element coordinating system. Analytical formulae of forward transfer matrix, reverse transfer matrix, impedance matrix and mobility matrix are derived separately when the positive definition of state vectors are assumed the same. The characteristics of the four matrices are studied. Analytical formulae of the four matrices of a general beam are given by combining the corresponding formulae of Euler-Bernoulli beam with those of the rod. Numerical examples show that the results respectively by the present method and those of the finite element method are nearly the same. When frequency is close to zero, the relationship between the displacement impedance matrix and the static stiffness matrix are established. The relationship between dynamic matrix description method and static matrix description method is discussed.
(3) The impedance synthesis method of built-up structures—The basic and generalized definitions of mechanical impedance are given. The four poles parameters matrices and algorithm of passive linear vibration mechanical systems are also given. The impedance synthesis method is introduced. The analytical formulae of simple model are deduced by transfer matrix method. The longitudinal vibration equations of the anti-vibration foundation are achieved both by transfer matrix method and mobility matrix method. The analytical formula for the longitudinal force transmissibility is given. Two approaches yields similar results, but the process of transfer matrix method is simpler. The transverse vibration equations of the anti-vibration foundation are also deduced using transfer matrix method. The analytical formula for the transverse force transmissibility is consequently given. It is showed that matrix description methods facilitate solving dynamic questions using computer programming. Analytical formulae in this paper can be applied in dynamic design of the anti-vibration foundation to achieve good precision with less computation.
(4) Dynamic experiment and analysis of a composite rod—The formulae of driving point impedance and transfer impedance of the rod under different boundary conditions are deduced. The influences of damping and material parameters to the impedance are analyzed. The composite rod is tested on an impedance platform facility with single point excitation and the mechanical impedance data are obtained. It shows that theoretical results agree with the experimental data when excitation frequency is higher than 100Hz, which also validate the measurement method. The initial modal parameters are then identified with the experiment method, analytical method and hybrid method. After these, the optimal modal parameters are identified by two nonlinear least square methods called Levenberg-Marquardt and Trust region algorithms respectively. Research work show that the mechanical impedance data, which are calculated from the discrete system modal with single degree of freedom and based on optimal modal parameters, coincide well with the experimental result, and this modal can describe the dynamic properties of the composite rod within testing frequency range very well.
(5) Dynamic experiment and analysis of a composite T joint—The typical marine T joint is designed. The T joint is tested on the impedance platform facility with the help of special designed tools and the positive and negative mechanical impedance data are obtained. The discrete system mathematical modal of T joint is obtained using the method developed in the fourth chapter.
(6) Dynamic properties of the adhesive joint—The linear dynamic properties of the adhesive joint in normal direction are studied with theoretical and experimental compound method. The impedance matrix can be numerically simulated using the combination of three“bush”elements based on viscoelastic theory. Numerical example shows that the results from FEM method coincide with those from transfer matrix method. The parameters of“bush”elements are used in the seventh chapter.
(7) Experimental and simulation researches on dynamic properties of the composite foundation—The dynamic properties of two systems, that is, the composite foundation installed in a framed cylinder, and equivalent steel foundation installed the same cylinder, are studied respectively with experimental and FEM method. Results show that the computer and test aided modeling method of the composite foundation are reasonable. The vibration isolation effect of the composite foundation is better than that of the equivalent steel foundation.
(8) Summary and forecast—The research contents in the dissertation are summarized. The future research contents of related fields are proposed.
The innovation research works in the dissertation are primarily as follows:
(1) To improve the efficiency of mechanical vibration isolation, a new idea of using composite foundation in place of steel foundation is presented.
(2) The composite mechanical equipment vibration isolation foundation, which is a combination of composite web plate and steel anti-vibration mass, is presented.
(3) Based on the wave theory, the four poles parameters matrices of the Euler-Bernoulli beam and rod are deduced using the shape functions related to frequency. The computer programs are made to calculate special numerical examples. The results of the programs are almost the same with those of ordinary FE programs. For the simplified theoretical model, with the deduced four poles parameters matrices of the Euler-Bernoulli beam, rod, rigid body and mass, the system formulae of anti-vibration foundation are deduced, which provide simple tools for the design of anti-vibration foundation.
(4) Based on the computer and test aided modeling idea, the dynamic modeling method of the composite foundation is presented. The ordinary FE programs are used to model non adhesive parts. The experimental data in frequency domain are obtained from an impedance platform facility. Then two nonlinear least square methods called Levenberg-Marquardt and Trust region algorithms are used to carry out parameter identification. The reasonable system formulae of specimen are achieved. The impedance matrixes of the adhesive parts, which are obtained from the system formulae of rod and T joint, are numerically simulated using a combination of three“bush”elements in Nastran program.
(5) The composite foundation and steel foundation are researched using experimental and FEM methods. The results show that the dynamic modeling method of the composite foundation is reasonable. Compared with steel foundation, the vibration isolation effect of the composite foundation is very good.
引文
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