夹层结构振动声辐射特性研究
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摘要
目前,由于军用、民用舰船均朝着高速、轻量化发展,比强度大、比重量轻的复合材料层合结构开始受到关注。但在国内的船舶与海洋工程领域,层合结构的各方面研究还不深入,与国际先进水平还存在着一定的差距;层合结构在船舶与海洋结构物上的应用方面亦相当薄弱。此外,振动和噪声大大破坏了舰船的隐蔽性和舒适性,结构振动和噪声预报及其控制研究对民船和军船都是一项十分重要的研究课题。本文主要采用有限元和声学边界元方法,对层合结构中的夹层结构振动和声辐射特性进行数值分析,完成的主要工作和创新性成果如下:
现有的夹层板理论大多仅考虑了芯板的垂向剪切应变和应力,很少考虑芯板的垂向正应变和正应力。而实际工程中,夹层板的芯板与面板相比其厚度要大得多,其弹性模量则要小很多,在变形过程中很容易产生垂向压缩或拉伸变形。因此忽略芯层垂向正应力和正应变的夹层板理论是不尽合理的。同时,对于夹层板结构,结构在低频时主要以弯曲振动的形式向外辐射噪声,当结构受到高频激励时,结构会以压缩波的形式向外辐射噪声。以往的夹层板理论由于忽略了芯层的垂向正应变,将不能体现结构的垂向压缩振动模式,即夹层板对称模态,这与结构的实际变形是不相符合的。为了消除上述不足,本文构造了一个新的考虑芯板压缩变形影响的夹层板单元。将上下面板分别采用基于一阶剪切理论的Mindlin板进行模拟,采用选择积分技术,消除了计算时的剪切闭锁问题;芯板位移和挠度沿厚度方向非线性变化,并用面板位移表示。该单元不仅考虑了芯板和面板的垂向剪切变形,还计及了芯板的垂向压缩变形的影响。推导了相应的位移应变关系,根据Halmiton原理建立了动力有限元方程,由能量守恒定律推导了夹层板的阻尼矩阵。数值计算结果表明本文所提出的夹层板位移模式是正确有效的;对于具有厚、软芯板的夹层板的自由振动和动力特性研究,考虑芯板的横向压缩变形的影响是合理的,并且夹层板的芯板厚度相对越大,弹性模量相对越小,芯板横向压缩变形的影响就越大。
耦合损耗因子是统计能量分析重要参数之一,通常只能在模态密度足够大的高频领域通过传统的波动方法求得。本文在前人工作的基础上给出了一种夹层板间耦合损耗因子表达式,它可以由耦合夹层板的模态信息完全表示,且无需计算夹层板的响应,能够在低频领域计算夹层板的耦合损耗因子。计算结果表明本文方法是正确有效的,且简便易行,不仅为统计能量分析在低频域应用提供了可能,也给出了一种表征夹层板间能量传输损耗大小的简单参数。
在夹层板有限元分析的基础上,应用声学边界元法对夹层板在空气中的声辐射特性进行研究,计算了不同物理和几何芯板参数下夹层板的声辐射特性,探讨了夹层板芯板参数对其声辐射特性的影响。
在本文夹层板有限元分析工作的基础上建立了一种考虑芯板垂向压缩变形影响的夹层加筋板有限元模型,其中加强筋采用Timoshenko梁模型模拟,给出了夹层加筋板的动能和势能,根据Hamilton原理推导了其控制微分方程,求解了夹层加筋板的固有频率和响应。
推导了考虑芯层垂向压缩变形影响的夹层梁的动态刚度矩阵。为动态刚度矩阵方法提供了一种新的单元类型。首先给出了一种考虑夹层梁芯层垂向压缩变形影响的夹层梁位移模式,推导了相应的夹层梁动能和势能,根据Hamilton原理推导了其控制微分方程,然后按照动态刚度矩阵的一般推导过程推导了考虑芯层垂向压缩变形影响的夹层梁动态刚度矩阵。计算结果证明本文推导的夹层梁动态刚度矩阵是正确可靠的。在夹层梁的动态刚度矩阵推导和高频计算中考虑芯层垂向压缩变形是合理的。
Sandwich structures have been used in aerospace applications for more than 50 years due to their high stiffness-to-weight and strength-to-weight ratios. Recently, with the development of civil ships and naval vessels in high speed and lightweight direction, new attention is focusing on using of sandwich structures in marine applications. Reduction of vibration and acoustic noise of marine structures is an important issue to designers. So it's very crucial to study sandwich structures' characteristics of vibration and radiation. This dissertation addresses an intensive study on numerical analysis of vibration and radiation of sandwich structures. The major contributions and conclusions are as follows.
Most of the sandwich plate theories developed in the past did not take account of the effect of transverse normal deformation of the core. When such sandwich plate theories are applied to analyze thick core, sandwich plates or to analyze high frequency vibration of sandwich plates, reasonable results could not be obtained due to ignoring of transvers normal deformation of the core. In this paper, a new composite sandwich plate (shell) element is developed which includes the transverse normal deformation in addition to the transverse shear deformation in the core. The two face layers are considered as Mindlin plates with shear and bending resistance. Nonlinear variation of displacements through the thickness of the core is assumed based on thick plates theory. The displacements of the core are expressed in terms of the displacements of two face plates. The governing equation of the sandwich plate system is derived based on Hamilton principle and is expressed in terms of the face plates' displacements. Numerical results show that the presented model is valid and the consideration of transverse normal deformation in the core is necessary and reasonable for dynamical response analysis.
Traditionally, CLF can only be calculated in high frequency band because of the need of high model density and modal overlap. In this paper, a theoretical study of CLF for two L-shaped sandwich plates which can make accurate results in low frequency band, is presented using finite element method (FEM) model characteristics. The numerical results are compared with those of the commercial software AUTOSEA, and it exhibits a good agreement between them.
The acoustic radiation power of the sandwich plate is calculated by boundary element method based on the finite element method results. The necessity of the consideration of transverse normal deformation as well as the effect of geometry and material parameters for the core in the analysis is discussed.
A finite element model is presented for the vibration of stiffened sandwich plates with moderately thick viscoelastic cores. The two face layers are considered as Mindlin plates with shear and bending resistance. Nonlinear variation of displacements through the thickness of the core is assumed based on thick plate theory. Meanwhile, the effect of transverse normal deformation of the core is taken into account. The stiffeners are modeled by Timoshenko beam. The displacements of the core and stiffeners are expressed in terms of the displacements of two face plates. The governing equation of the stiffened sandwich plate system is derived based on Hamilton principle and is expressed in terms of the face plates' displacements. Numerical results indicate the validation of presented model and show that the consideration of transverse normal deformation in the core is necessary for the vibration analysis of stiffened sandwich plate.
An accurate dynamic stiffness model for a three-layered sandwich beam of unequal thicknesses is developed and subsequently used to investigate its free vibration characteristics. Each face layer of the beam is idealized by the Timoshenko beam theory. Linear variation of displacements through the thickness of the core is assumed, so that the transverse normal deformation is taken into account. The combined system is reduced to a twelfth-order system using symbolic computation. An exact dynamic stiffness matrix is then developed by relating amplitudes of harmonically varying loads to those of the responses. The resulting dynamic stiffness matrix is used with particular reference to the Wittrick-Williams algorithm to carry out the free vibration analysis of a few illustrative examples.
现有的夹层板理论大多仅考虑了芯板的垂向剪切应变和应力,很少考虑芯板的垂向正应变和正应力。而实际工程中,夹层板的芯板与面板相比其厚度要大得多,其弹性模量则要小很多,在变形过程中很容易产生垂向压缩或拉伸变形。因此忽略芯层垂向正应力和正应变的夹层板理论是不尽合理的。同时,对于夹层板结构,结构在低频时主要以弯曲振动的形式向外辐射噪声,当结构受到高频激励时,结构会以压缩波的形式向外辐射噪声。以往的夹层板理论由于忽略了芯层的垂向正应变,将不能体现结构的垂向压缩振动模式,即夹层板对称模态,这与结构的实际变形是不相符合的。为了消除上述不足,本文构造了一个新的考虑芯板压缩变形影响的夹层板单元。将上下面板分别采用基于一阶剪切理论的Mindlin板进行模拟,采用选择积分技术,消除了计算时的剪切闭锁问题;芯板位移和挠度沿厚度方向非线性变化,并用面板位移表示。该单元不仅考虑了芯板和面板的垂向剪切变形,还计及了芯板的垂向压缩变形的影响。推导了相应的位移应变关系,根据Halmiton原理建立了动力有限元方程,由能量守恒定律推导了夹层板的阻尼矩阵。数值计算结果表明本文所提出的夹层板位移模式是正确有效的;对于具有厚、软芯板的夹层板的自由振动和动力特性研究,考虑芯板的横向压缩变形的影响是合理的,并且夹层板的芯板厚度相对越大,弹性模量相对越小,芯板横向压缩变形的影响就越大。
耦合损耗因子是统计能量分析重要参数之一,通常只能在模态密度足够大的高频领域通过传统的波动方法求得。本文在前人工作的基础上给出了一种夹层板间耦合损耗因子表达式,它可以由耦合夹层板的模态信息完全表示,且无需计算夹层板的响应,能够在低频领域计算夹层板的耦合损耗因子。计算结果表明本文方法是正确有效的,且简便易行,不仅为统计能量分析在低频域应用提供了可能,也给出了一种表征夹层板间能量传输损耗大小的简单参数。
在夹层板有限元分析的基础上,应用声学边界元法对夹层板在空气中的声辐射特性进行研究,计算了不同物理和几何芯板参数下夹层板的声辐射特性,探讨了夹层板芯板参数对其声辐射特性的影响。
在本文夹层板有限元分析工作的基础上建立了一种考虑芯板垂向压缩变形影响的夹层加筋板有限元模型,其中加强筋采用Timoshenko梁模型模拟,给出了夹层加筋板的动能和势能,根据Hamilton原理推导了其控制微分方程,求解了夹层加筋板的固有频率和响应。
推导了考虑芯层垂向压缩变形影响的夹层梁的动态刚度矩阵。为动态刚度矩阵方法提供了一种新的单元类型。首先给出了一种考虑夹层梁芯层垂向压缩变形影响的夹层梁位移模式,推导了相应的夹层梁动能和势能,根据Hamilton原理推导了其控制微分方程,然后按照动态刚度矩阵的一般推导过程推导了考虑芯层垂向压缩变形影响的夹层梁动态刚度矩阵。计算结果证明本文推导的夹层梁动态刚度矩阵是正确可靠的。在夹层梁的动态刚度矩阵推导和高频计算中考虑芯层垂向压缩变形是合理的。
Sandwich structures have been used in aerospace applications for more than 50 years due to their high stiffness-to-weight and strength-to-weight ratios. Recently, with the development of civil ships and naval vessels in high speed and lightweight direction, new attention is focusing on using of sandwich structures in marine applications. Reduction of vibration and acoustic noise of marine structures is an important issue to designers. So it's very crucial to study sandwich structures' characteristics of vibration and radiation. This dissertation addresses an intensive study on numerical analysis of vibration and radiation of sandwich structures. The major contributions and conclusions are as follows.
Most of the sandwich plate theories developed in the past did not take account of the effect of transverse normal deformation of the core. When such sandwich plate theories are applied to analyze thick core, sandwich plates or to analyze high frequency vibration of sandwich plates, reasonable results could not be obtained due to ignoring of transvers normal deformation of the core. In this paper, a new composite sandwich plate (shell) element is developed which includes the transverse normal deformation in addition to the transverse shear deformation in the core. The two face layers are considered as Mindlin plates with shear and bending resistance. Nonlinear variation of displacements through the thickness of the core is assumed based on thick plates theory. The displacements of the core are expressed in terms of the displacements of two face plates. The governing equation of the sandwich plate system is derived based on Hamilton principle and is expressed in terms of the face plates' displacements. Numerical results show that the presented model is valid and the consideration of transverse normal deformation in the core is necessary and reasonable for dynamical response analysis.
Traditionally, CLF can only be calculated in high frequency band because of the need of high model density and modal overlap. In this paper, a theoretical study of CLF for two L-shaped sandwich plates which can make accurate results in low frequency band, is presented using finite element method (FEM) model characteristics. The numerical results are compared with those of the commercial software AUTOSEA, and it exhibits a good agreement between them.
The acoustic radiation power of the sandwich plate is calculated by boundary element method based on the finite element method results. The necessity of the consideration of transverse normal deformation as well as the effect of geometry and material parameters for the core in the analysis is discussed.
A finite element model is presented for the vibration of stiffened sandwich plates with moderately thick viscoelastic cores. The two face layers are considered as Mindlin plates with shear and bending resistance. Nonlinear variation of displacements through the thickness of the core is assumed based on thick plate theory. Meanwhile, the effect of transverse normal deformation of the core is taken into account. The stiffeners are modeled by Timoshenko beam. The displacements of the core and stiffeners are expressed in terms of the displacements of two face plates. The governing equation of the stiffened sandwich plate system is derived based on Hamilton principle and is expressed in terms of the face plates' displacements. Numerical results indicate the validation of presented model and show that the consideration of transverse normal deformation in the core is necessary for the vibration analysis of stiffened sandwich plate.
An accurate dynamic stiffness model for a three-layered sandwich beam of unequal thicknesses is developed and subsequently used to investigate its free vibration characteristics. Each face layer of the beam is idealized by the Timoshenko beam theory. Linear variation of displacements through the thickness of the core is assumed, so that the transverse normal deformation is taken into account. The combined system is reduced to a twelfth-order system using symbolic computation. An exact dynamic stiffness matrix is then developed by relating amplitudes of harmonically varying loads to those of the responses. The resulting dynamic stiffness matrix is used with particular reference to the Wittrick-Williams algorithm to carry out the free vibration analysis of a few illustrative examples.
引文
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