The vibroacoustic response and sound absorption performance of multilayer,microperforated rib-stiffened plates

The vibroacoustic response and sound absorption performance of a structure composed of multilayer plates and one rigid back wall are theoretically analyzed. In this structure, all plates are two-dimensional, microperforated, and periodically rib-stiffened. To investigate such a structural system, semianalytical models of one-layer and multilayer plate structures considering the vibration effects are first developed. Then approaches of the space harmonic method and Fourier transforms are applied to a one-layer plate, and finally the cascade connection method is utilized for a multilayer plate structure. Based on fundamental acoustic formulas,the vibroacoustic responses of microperforated stiffened plates are expressed as functions of a series of harmonic amplitudes of plate displacement, which are then solved by employing the numerical truncation method. Applying the inverse Fourier transform, wave propagation, and linear addition properties, the equations of the sound pressures and absorption coefficients for the one-layer and multilayer stiffened plates in physical space are finally derived. Using numerical examples, the effects of the most important physical parameters—for example, the perforation ratio of the plate, sound incident angles, and periodical rib spacing—on sound absorption performance are examined. Numerical results indicate that the sound absorption performance of the studied structure is effectively enhanced by the flexural vibration of the plate in water.Finally,the proposed approaches are validated by comparing the results of stiffened plates of the present work with solutions from previous studies.     

双周期加筋微穿孔板的振动响应及声透射的研究

本文主要研究了水下无穷大双周期加筋微穿孔薄板,在平面声波斜入射下的振动响应和声透射,并提出了一种半解析半数值的计算方法。利用微穿孔板的声阻抗以及薄板表面的振速边界条件,建立了加筋穿孔薄板的振动方程,并根据傅立叶变换及空间波数法将振动位移表达为波数分量的迭加形式。采用数值计算的方法对波数分量进行求解并通过傅里叶逆变换,最终得到了双周期加筋穿孔薄板的振动响应及透射系数。通过与Takahashi穿孔板声压结果的对比,证明了本方法的正确性。在算例中,分析了加强筋及穿孔率对薄板结构的振动和声透射的影响。     

无穷大周期加筋微穿孔板结构振动响应及吸声特性

研究在平面声波斜入射情况下,无穷大双周期加筋的微穿孔薄板结构的振动响应及吸声性能.首先在马大猷和Takahashi微穿孔板声学理论基础上,建立了微穿孔加筋薄板结构振动的半解析模型;然后应用傅里叶变换及空间波数分析方法,将周期加筋微穿孔薄板的振动位移及辐射声压表示为频域内波数的分量迭加形式;最后通过对波数分量进行求解,并利用傅里叶逆变换得到双周期加筋的微穿孔薄板的振动响应及吸声系数表达式.计算结果表明,薄板的弯曲振动在水中对吸声的影响较大,空气中仅对轻质穿孔板的低频吸声效果有一定影响;同时微穿孔率对周期加筋薄板吸声系数的影响明显,通过改变穿孔率和加筋周期等可有效地提高水中微穿孔薄板结构的吸声性能.     

流固耦合的周期加强板的振动及声辐射研究

研究了流体负载下的无穷大双周期加强板, 在周期谐振力作用下的振动响应和声辐射,并提出了一种基于有限元和空间波数法的半解析半数值方法. 首先利用有限元的方法对周期结构进行单元离散, 并将结构对薄板的作用力等效为节点力的作用. 然后通过周期结构的振动方程, 结合薄板与结构的位移边界条件, 建立了节点力与薄板节点位移的函数方程. 最后应用空间波数法和傅里叶变换, 并采用数值计算的方法求解出薄板的节点位移, 得到了周期加强板关于离散节点位移的振动和辐射声压方程. 在数值算例中, 对该方法的正确性进行了验证, 并且分析了周期结构对薄板的振动和声辐射的影响.     

A SEMI-ANALYTICAL METHOD FOR THE VIBRATION OF AND SOUND RADIATION FROM A TWO-DIMENTIONAL BEAM-STIFFENED PLATE

A semi-analytical method based on space harmonics to investigate the vibration of and sound radiation from an infinite,fluid-loaded plate is presented.The plate is reinforced with two sets of orthogonally and equally spaced beam stiffeners,which are assumed to be line forces.The response of the stiffened plate to a convected harmonic pressure in the wave-number space is obtained by adopting the Green’s function and Fourier transform methods.Using the boundary conditions and space harmonic method,we establish the relationship between the stiffener forces and the vibration displacement of the plate.In this paper,the stiffener forces are expressed in terms of harmonic amplitudes of the plate displacement,which are calculated by using a numerical reduction technique.Finally,the Fourier inverse transform is employed to find expressions of the vibration and sound radiation in physical space.Agreements with existing results prove the validity of this approach and more numerical results are presented to show that this method converges rapidly.     

Experimental investigation of sound absorption in a composite absorber

A composite absorber made of a polyurethane sponge and multi-layer micro-perforated plates is presented in this study. Results from an acoustic impedance tube test show that the polyurethane sponge can exhibits higher low-frequency sound absorption in front of the micro-perforated plate, while sound absorption at medium and high-frequencies remains low. The physical mechanism behind this is that the micro-perforated plate increases the denpth cavity. If the polyurethane sponge is placed behind the micro-perforated plate, the amplitude of the original absorption peak will remain constant, but the absorption peaks will shift to lower frequencies. The reason for this phenomenon is that porous materials with low flow resistance can be approximately equivalent to fluid, which not only does not affect the resonance absorption coefficient of micro-perforated plate, but also makes the peaks move to low frequency. This study has the potential applications in the sound absorption design of composite structure.     

VIBRATION AND SOUND RADIATION OF AN ASYMMETRIC LAMINATED PLATE IN THERMAL ENVIRONMENTS

Analytical studies on the vibration and sound radiation characteristics of an asymmetric laminated rectangular plate are carried out in this paper. Theoretical formulations, in which the effects of thermal environments are taken into account, are derived for the vibration and sound radiation based on both first-order shear deformation plate theory and Rayleigh integral. It is found that the natural frequencies, the resonant amplitudes of vibration response and the sound pressure level decrease with the temperature rising. The natural frequencies of asymmetric plates are smaller than those of symmetric plates and the velocity responses of asymmetric plates are larger than those of symmetric plates.     

Discrete material optimization of vibrating laminated composite plates for minimum sound radiation

This paper deals with vibro-acoustic optimization of laminated composite plates. The vibration of the laminated plate is excited by time-harmonic external mechanical loading with prescribed frequency and amplitude, and the design objective is to minimize the total sound power radiated from the surface of the laminated plate to the surrounding acoustic medium. Instead of solving the Helmholtz equation for evaluation of the sound power, advantage is taken of the fact that the surface of the laminated plate is flat, which implies that Rayleigh’s integral approximation can be used to evaluate the sound power radiated from the surface of the plate. The novel Discrete Material Optimization (DMO) formulation has been applied to achieve the design optimization of fiber angles, stacking sequence and selection of material for laminated composite plates. Several numerical examples are presented in order to illustrate this approach.     

敷去耦层有限加筋板声辐射近似解析解

本文主要研究了流体负载下敷设去耦阻尼层的加筋板,在外界激励力作用下的振动和声辐射,推导出了敷设去耦层有限长加筋板的振动响应和水下辐射噪声近似解析解。采用弹性理论来描述去耦层,并采用模态迭加理论构造响应函数,将加强筋等效为线力的作用,以复模量形式计及去耦阻尼层损耗因子,建立了敷设去耦阻尼层加筋板的理论解析模型,结合加筋板与去耦层变形连续条件、结构与流体连续性条件组成了声-流体-结构的耦合方程,结合数值计算方法,得到了有限长加筋板结构的振动位移及水下辐射噪声。开展相应数值算例与模型试验结果吻合较好,验证本文方法的正确性。     

Nonlinear dynamic response of a stiffened plate with four edges clamped under primary resonance excitation

An approach is presented to study the nonlinear forced vibration of a stiffened plate. The stiffened plate is divided into one plate and some stiffeners, with the plate considered to be geometrically nonlinear, and the stiffeners taken as geometrically nonlinear Euler beams. Assuming the displacement of the stiffened plate, Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to energy of the system. A stiffened plate with four clamped edges subjected to harmonic excitation is studied by means of the method of multiple scales; the first approximation solutions of the double-modal motion of the system are obtained. Numerical examples for different stiffened plates are presented to discuss the steady response of the primary resonance and the amplitude?Cfrequency relationship; and some nonlinear forced vibration characteristics of the stiffened plate are obtained, which are useful for engineering design.     

曲线加筋Kirchhoff-Mindlin板自由振动分析

相比传统加筋板,曲线加筋板能够更充分地发挥材料力学性能.在加筋板力学分析中,厚板通常采用Reissner-Mindlin理论,然而当板厚较薄时易出现剪切自锁,离散的Kirchhoff-Mindlin理论采用假设剪切应变场可避免该问题.针对曲线加筋Kirchhoff-Mindlin板自由振动分析,采用离散的Kirchhoff-Mindlin三角形单元和Timoshenko曲梁单元分别模拟板和加强筋,根据板的位移插值函数及筋板交界面的位移协调条件,建立基于板单元位移自由度的有限元方程.为了验证方法的有效性和准确性,采用直线加筋薄板、曲线加筋薄板和厚板3种模型进行算例研究,通过收敛性和精度分析来选择合理的有限元网格密度.直线加筋薄板前20阶固有频率均与文献结果吻合良好;曲线加筋板算例中,本文方法满足收敛条件的板单元数目为2469,Nastran模型板单元数目为6243;本文所得曲线加筋板固有频率与Nastran计算结果最大误差为3.4%.研究结果表明,本文方法无需筋板单元共节点,可使用较少的有限元网格数量,并能够保证计算精度;在离散Kirchhoff-Mindlin三角形板单元基础上构造Timoshenko梁单元可同时适用于曲线加筋薄板与厚板自由振动分析.     

截锥型薄壁结构声振耦合动力特性分析

采用大型通用软件ANSYS,建立截锥型薄壁结构的实体有限元动力学模型,通过与相关实验数据的对比验证了模型合理性。据此,利用无限元模拟自由声场边界,建立声场-截锥型薄壁结构的直接耦合有限元动力学模型。通过数值仿真分析研究了声场中截锥壳结构的振动特性,并讨论了声振动对结构动力特性的影响。研究结果表明:数值仿真结果和截锥壳声振实验数据比较一致。在考虑声场影响后发现:结构位移共振频率值大多有所降低,结构位移共振频率数量显著增多;在低频下,结构位移响应峰值在声场的影响下明显增大;在高频下则明显减小。     

加筋板弹性大挠度的冲击响应分析

用半解析的方法分析了横向冲击载荷下加筋板的非线性瞬态响应。考虑膜力的存在 ,忽略筋截面上的剪切应力 ,引入板的应力函数 ,采用离散加筋板模型 ,运用能量原理建立加筋板的动响应控制方程。假设挠度为双级数形式 ,运用迦辽金法 ,将加筋板的动响应方程转化为一个多自由度的动力系统 ,采用数值方法来求解。最后给出了几个模型的计算结果。     

Dynamic buckling of stiffened plates under fluid-solid impact load

A simple solution of the dynamic buckling of stiffened plates under fluid-solid impact loading is presented. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stresses of stiffeners and in-plane displacement are neglected. Applying the Hamilton‘ s principle, the motion equations of stiffened plates are obtained. The deflection of the plate is taken as Fourier series, and using Galerkin method, the discrete equations can be deduced, which can be solved easily by Runge-Kutta method. The dynamic buckling loads of the stiffened plates are obtained from Budiansky-Roth ( B-R ) curves.     

受面内冲击载荷下加筋板的非线性动态屈曲

分析了受面内冲击载荷下加筋板的非线性弹性动态屈曲．考虑板与筋的膜力，忽略面内位移，运用Hamilton变分原理，得出非线性控制方程，采用双级数形式的挠度假设，由Galerkin方法得到离散方程组，根据B-R准则，判断加筋板的动态屈曲．     

四边固定加劲板的非线性自由振动

针对工程中常用的加劲板, 研究了非线性振动的求解方法与振动特性. 将加劲板分为板与加劲肋两个部分考虑, 其中板视为考虑几何非线性的大挠度板, 加劲肋视为Euler梁. 假定加劲板的位移, 利用Lagrange方程结合系统能量和振型叠加推导了加劲板的动力平衡方程. 运用椭圆函数及摄动法计算加劲板非线性振动的单模态解, 多模态解则通过增量迭代法进行求解. 最后, 结合有限元软件ANSYS对一个四边固定且不可移动的加劲板进行分析, 讨论解的收敛性, 并分析两个方向设置不同数量加劲肋的情况下非线性自振频率与振幅的关系, 得到了一些加劲板非线性振动特性.      

爆炸载荷作用下加筋板的失效模式分析及结构优化设计

通过对爆炸载荷下具有1根加强筋的固支矩形加筋板的有限元模拟，探讨了抗爆加筋板结构优化设计方法，分析了加筋板的失效模式以及加强筋相对刚度和冲击载荷强度对加筋板失效模式的影响，指出了失效模式Ⅰ下的3种变形模态以及失效模式Ⅱ下的2种子失效模式，得到了失效模式Ⅰ下加强筋和加筋板最大挠度的近似计算公式，提出了单根加筋板的两种失效模式的判别条件，并对具有1根加强筋的固支矩形加筋板抗爆结构进行了优化设计。结果表明，通过数值模拟或模型实验可以求得任意加筋板结构由发生塑性大变形到发生破损的临界条件，从而确定抗爆性能最强时加筋板的质量与加强筋横截面尺寸及间距间的关系，实现对抗爆加筋板结构的优化设计。     

智能板模态传感与控制的数值分析

智能结构技术对空间大型柔性结构 振动控制问题具有重要意义,采用独立模态空间控制技术对压电智能板进行主动振动控制是一种常用方法,以前对这一问题的研究仅限于解析的方法,本文采用有限单元法,设计了新的压电模态传感器与致动器,该方法能够适用于形状及边界条件较为复杂的智能板,算例分析证明了该方法的正确性。     

基于边光滑有限元法的加筋板静力和自由振动分析

运用边光滑有限元法,研究分析了加筋板结构的静力和自由振动问题。在边光滑有限元法中,将基于边的应变光滑技术用于对原来的应变场进行光滑操作;由于应变光滑技术能够适当地软化原来过刚的有限元模型,从而能够得到更加接近于系统准确刚度的光滑有限元模型;鉴于三角形单元良好的适用性,选用三角形单元对模型进行网格划分;同时,为了解决低阶Reissner-Mindlin板单元弯曲过程中的横向剪切自锁问题,采用了一种新型的离散剪切间隙技术。算例的数值计算结果表明,与传统的有限元法相比,边光滑有限元法能够得到精度更高的计算结果,且收敛更快,计算效率更佳。     

含有分层损伤的复合材料加筋层合板的屈曲性态研究

基于Ｍｉｎｄｉｎ假定推导了考虑剪切的复合材料加筋层板的有限元列式,并在此基础上计算出筋间基板含嵌入分层以及筋与基板连接处含穿透分层的加筋层合板在受压缩载荷情况下的屈曲模式和临界力。本文所给出的有限元方法及结论对从事复合材料结构设计的工程人员具有参考价值。