板/壳—腔结构声振耦合分析及减振降噪优化研究
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摘要
结构噪声的研究与控制是学术界,工程界普遍关心的问题,结构与声腔耦合后的声振耦合特性及其声辐射特性的研究尤其受到重视。本文首先通过结构动力学方程建立弹性板-壳-声腔结构的耦合模型,并应用此模型分析一端固定一端封闭的弹性板-圆柱壳封闭结构的声振耦合特性,验证了模型的正确性。通过板-腔模型进一步利用模态叠加法分析板-腔结构的双边耦合特性;而后又针对多通域情况,利用Trefftz有限元方法以及无网格方法进行分析;减振降噪方面,根据分析目标的不同,本文分别采用了有源力控制以及阻尼减振降噪两种方法,并给出了适合工程上复杂结构的阻尼层近似拓扑优化方法。
本文的工作主要包括以下几部分:
第一章:综述了声振耦合以及噪声控制技术的分析方法以及研究现状,论述了目前应用于声学领域的主要研究方法,包括解析方法,数值方法,统计能量方法等。同时介绍了目前应用于噪声控制领域的方式有源噪声控制方法与无源噪声控制方法。并概述了目前声振耦合领域以及减振降噪方面的研究现状,最后给出了本论文的主要研究内容。
第二章:根据板壳原理,在弹性板与弹性壳之间施加假想的弹簧系统模拟不同的边界条件,同时考虑弹性板的面内振动,推导弹性板-壳-声腔的封闭系统的耦合方程,通过求解耦合方程探讨弹性板-圆柱壳-声腔结构的耦合特性。该模型同时考虑了弹性板与圆柱壳之间以及弹性板-圆柱壳与内声场之间的耦合,算例表明,弹性板-声腔结构的耦合具有明显的板控模态以及声控模态。
第三章:利用模态叠加方法,探讨双边耦合问题。分别研究了弹性板-声腔-弹性板双边耦合情况,以及声腔-弹性板-声腔双边耦合情况,得到耦合结构的声传递公式,在实际工程中经常会遇到双层板,或者带有隔板的腔体结构,这其实就是双边耦合问题,通过模态分析的方法得到声振耦合后声压的传递特性,为进行此类结构的声振耦合分析以及减振降噪提供理论依据。
第四章:分别利用Trefftz有限元方法和无网格方法分析多通域封闭声场的声响应情况,给出Trefftz单元位移插值,以及等效节点载荷,并给出带有孔洞的多通域Trefftz完整解系,求解内部带有孔洞的多通域封闭声腔的声响应。对于不规则的多通域,由于较难得到Trefftz完整解系,本章基于核重构的最小二乘法给出亥姆霍兹方程的最小二乘配点格式,分别计算一维以及二维多通域封闭声腔的声响应,将典型算例与解析解比较验证其准确性以及稳定性。
第五章:根据点源组合原则推导出弹性板以及圆柱壳振动所产生的声辐射在外场点的声压级公式,分析当外力单独作用于弹性板或者圆柱壳时外场点的声压级。研究表明,对外场点声压级起决定作用的是受到外载荷作用的弹性结构振动。分析外场点声压级计算公式,利用外载荷的模态力,可以方便的得到有源力控制的幅值。应用有源力控制的方式进行减振降噪简便易行。
第六章:应用拉氏变换对阻尼弹性板以及封闭声腔的有限元耦合模型进行求解,分析耦合结构的声振灵敏度。通过对结构以及声腔分别进行有限元描述,得到结构-声腔耦合结构的耦合方程。通过抑制影响声腔内指定点声压较大的板上特定节点位移的方法降低指定点声压。经matlab编程利用约束阻尼层板动力学性能的变密度优化方法对阻尼材料敷设位置予以优化,同时引入Sigmund提出的过滤公式有效的抑制了棋盘格现象,得到了约束阻尼层的最优拓扑构形。经验证敷贴约束阻尼层后约束点位置的声压明显减低,与均匀敷贴阻尼相比大大提高了阻尼材料的利用率。
第七章:基于能量思想建立阻尼层的快速拓扑优化方法,也就是在耗能最多的位置粘贴阻尼材料,只需要计算一次特征值问题就可以得到近似的阻尼层最优分布。利用商业有限元软件得到工程结构的有限元模型,编写matlab程序,读出结构节点信息以及刚度和质量矩阵。根据声传递向量找到影响场点声压的主要模态,对其进行控制可以有效的起到减振降噪的作用,同时利用过滤公式有效的抑制了棋盘格现象。本章方法简便易用工程应用,并适用于复杂曲板或者板-壳的组合结构。
第八章:对本文的工作予以总结,并对需要解决的问题进行探讨与展望。
Structure-borne noise control is a common academic and engineering concern. Structure-acoustic coupling characteristics and the sound radiation characteristics are given particular attention. Above all, analytical model was established through structural dynamic equation of elastic plate-shell-cavity coupling structure, and then structure-acoustic coupling characteristics were analyzed. Based on this model, bilateral -coupling between plate and cavity was further studied. Considering multi-domain, Trefftz finite method and meshless method were utilized. About vibration and noise reduction, active force controlling method and damping control method were given. Especially to complex structure, an approximation method of topological optimization was given, which was simple and suitable for engineering applications.
Better understand the structure-acoustic coupling theory,and realize optimal designing during the period of product design. This work includes the following sections:
Chapter I: Summary of the research on structural-acoustic coupling and noise control technology, discusses the current main research methods applied to this field, which include analytical methods, numerical methods, statistical energy methods, and so on. The current method used in the field of noise control --Active noise control method and passive noise control methods were introduced. An overview of the current field of acoustic coupling, vibration and noise reduction status were also illustrated. Finally, main contents of this paper were given.
Chapter II: According to the plate and shell theory, analytical method was used to derivate the coupling equation of the plate-shell-cavity structure. Spring system was exerted to simulate different hypothetical boundary conditions. Took into account the in-plane vibration and considered both the coupling between plate and shell and the coupling between structure and acoustics, a model was established. Examples show that the elastic plate- cavity coupling structure has clear structure-control modes and cavity-control modes.
Chapter III: Using the mode superposition method to discuss bilateral coupling between plate and cavity. The structure-acoustic coupling of plate-cavity-plate and cavity-plate-cavity was discussed. Acoustic transfer characteristics were obtained through modal analysis. In the real engineering project the two-layer board, or the chamber board structure which is in fact bilateral coupling system are usual. Bilateral coupling analysis provides a theoretical basis for vibration and noise reduction of this type of structure.
Chapter IV: About multi-domain problems, the key is to solve Helmholtz equation. Trefftz quadrilateral element of eight nodes formula is derived. Trefftz complete solution to Helmholtz equation within a multi-domain was derived. However considering more complex multi-domain, meshless method was more beneficial. In this paper, approximated functions were constructed based on the principle of reproducing kernel particle method and least-square collocation method. A least-square collocation formulation based on kernel reproducing particle method was established for solving multi-domain acoustic response. To verify the proposed method, several numerical examples of one and two-dimensional problems were analyzed. Examples show the results have good accuracy and convergence.
Chapter V: According to the principle of point sources combination, sound radiation generated by the cylindrical shell and plate are derived. Sound pressure level (SPL) was analysised. Results show the elastic structure force impact on directly is the role to SPL. Based on the SPL formulation, modal force can be calculated, and then amplitude of the active force can be got easily. Application of active force control approach to vibration and noise reduction is feasible.
Chapter VI: Laplace transform was utilized to solve the coupled equation of plate and acoustic cavity and analysis sensitivity of the vibro-acoustic system. Research on vibro-acoustic coupling system includes not only computation of the coupling frequencies, coupling modes and also sensitivities of the coupling system to design variables. Reducing displacement amplitude of the specified nodes on the plate is on the target of depressing sound pressure of the measured point. The sensitivity of the displacement amplitude with respect to size and shape design parameters for the coupled system is derived. The distribution of the damping material on the plate was then optimized by penalized density topology optimization theory. Filter method raised by Sigmund was developed to suppress the numerical instabilities such as checkerboards. Numerical example is given to show the validity and efficiency of the sensitivity analysis and design optimization method.
Chapter VII: Commercial finite element software was used to obtain the finite element model of complex engineering structures. Nodes information, stiffness and mass matrix were read out by matlab program. Acoustic transfer vector was utilized to find the main modes which affect the sound pressure most. Fast damping layer topology optimization method was established on the base of energy-consuming. Only one eigenvalue calculating can approximate the optimal distribution of the damping layer. At the same time filter formula used effectively inhibit the checkerboard phenomenon. The approximation topology optimization method is simple and suitable for complex engineering applications.
Chapter VIII: summarized the whole work and addressed some problems and prospects.
本文的工作主要包括以下几部分:
第一章:综述了声振耦合以及噪声控制技术的分析方法以及研究现状,论述了目前应用于声学领域的主要研究方法,包括解析方法,数值方法,统计能量方法等。同时介绍了目前应用于噪声控制领域的方式有源噪声控制方法与无源噪声控制方法。并概述了目前声振耦合领域以及减振降噪方面的研究现状,最后给出了本论文的主要研究内容。
第二章:根据板壳原理,在弹性板与弹性壳之间施加假想的弹簧系统模拟不同的边界条件,同时考虑弹性板的面内振动,推导弹性板-壳-声腔的封闭系统的耦合方程,通过求解耦合方程探讨弹性板-圆柱壳-声腔结构的耦合特性。该模型同时考虑了弹性板与圆柱壳之间以及弹性板-圆柱壳与内声场之间的耦合,算例表明,弹性板-声腔结构的耦合具有明显的板控模态以及声控模态。
第三章:利用模态叠加方法,探讨双边耦合问题。分别研究了弹性板-声腔-弹性板双边耦合情况,以及声腔-弹性板-声腔双边耦合情况,得到耦合结构的声传递公式,在实际工程中经常会遇到双层板,或者带有隔板的腔体结构,这其实就是双边耦合问题,通过模态分析的方法得到声振耦合后声压的传递特性,为进行此类结构的声振耦合分析以及减振降噪提供理论依据。
第四章:分别利用Trefftz有限元方法和无网格方法分析多通域封闭声场的声响应情况,给出Trefftz单元位移插值,以及等效节点载荷,并给出带有孔洞的多通域Trefftz完整解系,求解内部带有孔洞的多通域封闭声腔的声响应。对于不规则的多通域,由于较难得到Trefftz完整解系,本章基于核重构的最小二乘法给出亥姆霍兹方程的最小二乘配点格式,分别计算一维以及二维多通域封闭声腔的声响应,将典型算例与解析解比较验证其准确性以及稳定性。
第五章:根据点源组合原则推导出弹性板以及圆柱壳振动所产生的声辐射在外场点的声压级公式,分析当外力单独作用于弹性板或者圆柱壳时外场点的声压级。研究表明,对外场点声压级起决定作用的是受到外载荷作用的弹性结构振动。分析外场点声压级计算公式,利用外载荷的模态力,可以方便的得到有源力控制的幅值。应用有源力控制的方式进行减振降噪简便易行。
第六章:应用拉氏变换对阻尼弹性板以及封闭声腔的有限元耦合模型进行求解,分析耦合结构的声振灵敏度。通过对结构以及声腔分别进行有限元描述,得到结构-声腔耦合结构的耦合方程。通过抑制影响声腔内指定点声压较大的板上特定节点位移的方法降低指定点声压。经matlab编程利用约束阻尼层板动力学性能的变密度优化方法对阻尼材料敷设位置予以优化,同时引入Sigmund提出的过滤公式有效的抑制了棋盘格现象,得到了约束阻尼层的最优拓扑构形。经验证敷贴约束阻尼层后约束点位置的声压明显减低,与均匀敷贴阻尼相比大大提高了阻尼材料的利用率。
第七章:基于能量思想建立阻尼层的快速拓扑优化方法,也就是在耗能最多的位置粘贴阻尼材料,只需要计算一次特征值问题就可以得到近似的阻尼层最优分布。利用商业有限元软件得到工程结构的有限元模型,编写matlab程序,读出结构节点信息以及刚度和质量矩阵。根据声传递向量找到影响场点声压的主要模态,对其进行控制可以有效的起到减振降噪的作用,同时利用过滤公式有效的抑制了棋盘格现象。本章方法简便易用工程应用,并适用于复杂曲板或者板-壳的组合结构。
第八章:对本文的工作予以总结,并对需要解决的问题进行探讨与展望。
Structure-borne noise control is a common academic and engineering concern. Structure-acoustic coupling characteristics and the sound radiation characteristics are given particular attention. Above all, analytical model was established through structural dynamic equation of elastic plate-shell-cavity coupling structure, and then structure-acoustic coupling characteristics were analyzed. Based on this model, bilateral -coupling between plate and cavity was further studied. Considering multi-domain, Trefftz finite method and meshless method were utilized. About vibration and noise reduction, active force controlling method and damping control method were given. Especially to complex structure, an approximation method of topological optimization was given, which was simple and suitable for engineering applications.
Better understand the structure-acoustic coupling theory,and realize optimal designing during the period of product design. This work includes the following sections:
Chapter I: Summary of the research on structural-acoustic coupling and noise control technology, discusses the current main research methods applied to this field, which include analytical methods, numerical methods, statistical energy methods, and so on. The current method used in the field of noise control --Active noise control method and passive noise control methods were introduced. An overview of the current field of acoustic coupling, vibration and noise reduction status were also illustrated. Finally, main contents of this paper were given.
Chapter II: According to the plate and shell theory, analytical method was used to derivate the coupling equation of the plate-shell-cavity structure. Spring system was exerted to simulate different hypothetical boundary conditions. Took into account the in-plane vibration and considered both the coupling between plate and shell and the coupling between structure and acoustics, a model was established. Examples show that the elastic plate- cavity coupling structure has clear structure-control modes and cavity-control modes.
Chapter III: Using the mode superposition method to discuss bilateral coupling between plate and cavity. The structure-acoustic coupling of plate-cavity-plate and cavity-plate-cavity was discussed. Acoustic transfer characteristics were obtained through modal analysis. In the real engineering project the two-layer board, or the chamber board structure which is in fact bilateral coupling system are usual. Bilateral coupling analysis provides a theoretical basis for vibration and noise reduction of this type of structure.
Chapter IV: About multi-domain problems, the key is to solve Helmholtz equation. Trefftz quadrilateral element of eight nodes formula is derived. Trefftz complete solution to Helmholtz equation within a multi-domain was derived. However considering more complex multi-domain, meshless method was more beneficial. In this paper, approximated functions were constructed based on the principle of reproducing kernel particle method and least-square collocation method. A least-square collocation formulation based on kernel reproducing particle method was established for solving multi-domain acoustic response. To verify the proposed method, several numerical examples of one and two-dimensional problems were analyzed. Examples show the results have good accuracy and convergence.
Chapter V: According to the principle of point sources combination, sound radiation generated by the cylindrical shell and plate are derived. Sound pressure level (SPL) was analysised. Results show the elastic structure force impact on directly is the role to SPL. Based on the SPL formulation, modal force can be calculated, and then amplitude of the active force can be got easily. Application of active force control approach to vibration and noise reduction is feasible.
Chapter VI: Laplace transform was utilized to solve the coupled equation of plate and acoustic cavity and analysis sensitivity of the vibro-acoustic system. Research on vibro-acoustic coupling system includes not only computation of the coupling frequencies, coupling modes and also sensitivities of the coupling system to design variables. Reducing displacement amplitude of the specified nodes on the plate is on the target of depressing sound pressure of the measured point. The sensitivity of the displacement amplitude with respect to size and shape design parameters for the coupled system is derived. The distribution of the damping material on the plate was then optimized by penalized density topology optimization theory. Filter method raised by Sigmund was developed to suppress the numerical instabilities such as checkerboards. Numerical example is given to show the validity and efficiency of the sensitivity analysis and design optimization method.
Chapter VII: Commercial finite element software was used to obtain the finite element model of complex engineering structures. Nodes information, stiffness and mass matrix were read out by matlab program. Acoustic transfer vector was utilized to find the main modes which affect the sound pressure most. Fast damping layer topology optimization method was established on the base of energy-consuming. Only one eigenvalue calculating can approximate the optimal distribution of the damping layer. At the same time filter formula used effectively inhibit the checkerboard phenomenon. The approximation topology optimization method is simple and suitable for complex engineering applications.
Chapter VIII: summarized the whole work and addressed some problems and prospects.
引文
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