Analysis of structural-acoustic coupling problems by a two-level boundary integral equations method: Part 2: vibrations of a cylindrical shell of finite length in an acoustic medium

In Part 1 a method was proposed to evaluate the contact acoustic pressure and displacements of the surface of a composite thin-walled structure vibrating in an acoustic medium. Here the full formulation of a problem and its numerical aspect are examined in some detail. As an example, the method is applied to the analysis of vibrations of a reinforced cylindrical shell of finite length.     

Analytical research on structural-acoustic coupling of a cavity surrounded by flexible panel

The structural-acoustic coupling characteristics, mechanisms, effect of structural-acoustic coupling on natural mode and natural frequencies of the system are analyzed theoretically and numerically. Formulae for the natural frequencies of the coupled system are derived. Some new conclusions are obtained. Analytical results demonstrate that the strongly coupled system indicates obvious closed-loop feedback characteristics, whereas the weakly coupled system indicates obvious feedforward characteristics, and it is because of the presence of the feedback loop that the natural characteristics and natural frequencies are changed. Cluster coupling characteristic between the structural and acoustic modes for the regular cavity and panel system is found, which determines the coupling interaction between the flexible panel and cavity. Any mode in one mode cluster only interferes the modes and the modal natural frequencies in the same cluster independently. The modal cluster coupling changes not only the natural frequencies of the system but also the modal order and structural mode shape.     

弹性板结构封闭声腔的结构-声耦合特性分析

对弹性板封闭声腔结构-声耦合机制、耦合特性、耦合作用对系统固有频率和模态的影响以及影响结构-声耦合程度的系统物理参数进行了深入的理论与数值仿真分析,并导出了耦合系统固有频率估计式。结果表明:强耦合系统具有较强的闭环反馈系统特征,弱耦合系统具有较强的前馈系统特征;正是由于反馈环节的存在,改变了结构、声腔系统的固有特性和固有频率;发现了规则结构-声腔模态簇耦合的特性;并且发现模态间的簇耦合机制决定了整个结构-声腔系统的耦合作用;任何一簇的结构或声模态仅独立影响其同一簇的声或结构模态以及其耦合后的模态固有频率,而对其它簇的模态没有影响;模态间的簇耦合作用不仅能改变系统固有频率,还会改变耦合系统模态次序和板奇奇模态的模态形状。     

部分浸没圆柱壳声固耦合计算的半解析法研究

部分浸没圆柱壳-流场耦合系统的声振分析是一种典型的半空间域内声固耦合问题,其振动及声学计算目前主要依赖于数值方法求解,但无论从检验数值法还是从机理上揭示其声固耦合特性,解析或半解析方法的发展都是不可或缺的.本文提出了一种半解析方法,先将声场坐标系建立在自由液面上,采用正弦三角级数来满足自由液面上的声压释放边界条件;接着基于二维Flügge薄壳理论建立了以圆柱圆心为坐标原点的壳-液耦合系统的控制方程;然后再利用Galerkin法处理声固耦合界面的速度连续条件,推导得到声压幅值与壳体位移幅值之间的关系矩阵并求解该耦合系统的振动和水下声辐射.与有限元软件Comsol进行了耦合系统自由、受迫振动和水下辐射噪声计算结的对比分析,表明本文方法准确可靠.本文的研究为解析求解弹性结构与声场部分耦合的声振问题提供了新的思路.     

Active vibration control for structural-acoustic coupling system of a 3-D vehicle cabin model

This paper presents an active vibration control system for use with structural-acoustic coupling system using piezoelectric actuators and piezoelectric sensors. For modelling a complicated 3-D vehicle cabin model, the structural-acoustic coupling system is analyzed by combining the structural data from modal testing with the acoustic data from the finite element method. Through the structural-acoustic analysis program, the control plate and the control modes are selected, which are most effective for attenuating its noise. A robust LQG controller with two sensor signal filters is designed to remove the experimental problems such as the spillover effect due to uncontrolled modes. The robust LQG controller for the structural-acoustic coupling system can reduce the interior noise of the cavity as well as the structural vibration of the cabin.     

Scattering model of a cylindrical shell with internal axisymmetric frames by using the Circumferential Admittance Approach

A numerical model is proposed for predicting scattering pressure by a fluid-loaded cylindrical shell stiffened by axisymmetric internal frames and impacted by an acoustic plane wave. The proposed developments are based on the Circumferential Admittance Approach (CAA) which allows us assembling a numerical model of the fluid loaded shell with finite element models of the internal frames. The scattering pressure model deduced with the CAA can then take into account: (a) internal frames having a cross section with a complex geometry and thickness variations (like T-shaped stiffeners, bulkheads, and hemispherical end caps); (b) variations of frame spacings; and (c) frame-shell coupling in the three translational directions and tangential rotation. Comparison with the numerical and experimental results of the literature for a periodic stiffened shell shows that the scattering from Bragg, Bloch–Floquet, and Helical waves is correctly predicted. The effects on the backscattering pressure of axial and tangential coupling forces are highlighted. Finally, an example of a non-periodically stiffened shell is presented to highlight the versatility of the approach proposed.     

Study on sound transmission characteristics of a cylindrical shell using analytical and experimental models

A circular cylindrical cavity enclosed by a thin elastic shell is found in many practical devices such as expansion volume mufflers, hermetic compressors and aircraft cabins. Analytical and experimental studies are conducted in this work to understand the characteristics of sound transmission through the cylindrical wall of such a system. Using an infinitely long circular cylindrical shell subjected to a plane incident wave, an exact solution is obtained by solving the classical shell vibration equations and the acoustic wave equations simultaneously. Transmission losses obtained from the solution are compared to the transmission losses that are measured for a cylindrical shell of finite length and the same cross-sectional dimensions. The comparison suggests that the theoretical model can be used as an effective design tool despite considerable simplifications involved.     

Electromagnetic Casimir densities for a wedge with a coaxial cylindrical shell

Vacuum expectation values of the field square and the energy-momentum tensor for the electromagnetic field are investigated for the geometry of a wedge with a coaxial cylindrical boundary. All boundaries are assumed to be perfectly conducting, and both regions inside and outside the shell are considered. By using the generalized Abel–Plana formula, the vacuum expectation values are presented in the form of the sum of two terms. The first one corresponds to the geometry of the wedge without the cylindrical shell, and the second term is induced by the presence of the shell. The vacuum energy density induced by the shell is negative for the interior region and positive for the exterior region. The asymptotic behavior of the vacuum expectation values are investigated in various limiting cases. It is shown that the vacuum forces acting on the wedge sides due to the presence of the cylindrical boundary are always attractive. PACS 03.70.+k     

Dynamic behaviour of a cylindrical shell with a cutout

This paper presents the results of analytical and experimental investigations connected with the dynamic behaviour of a cylindrical shell with a rectangular cutout. The finite element method is used to predict the vibration frequencies and mode shapes. The resulting eigenvalue problems are solved by using a simultaneous iteration technique. The analytical study shows the influence of the cutout on the natural frequencies and mode shapes of the shell. The subtended angle of the cutout ranges from 40° to 120°. Experimental verification was performed on a machined mild steel shell having welded end rings bolted on to sturdy supports. A reasonably good agreement is obtained, with the discrepancies of the order of less than 10 %. The cutout is found to have very little influence on the natural frequencies.     

Free localized vibrations of a semi-infinite cylindrical shell

Free vibrations of a semi-infinite cylindrical shell, localized near the edge of the shell are investigated. The dynamic equations in the Kirchhoff-Love theory of shells are subjected to asymptotic analysis. Three types of localized vibrations, associated with bending, extensional, and super-low-frequency semi-membrane motions, are determined. A link between localized vibrations and Rayleigh-type bending and extensional waves, propagating along the edge, is established. Different boundary conditions on the edge are considered. It is shown that for bending and super-low-frequency vibrations the natural frequencies are real while for extensional vibrations they have asymptotically small imaginary parts. The latter corresponds to the radiation to infinity caused by coupling between extensional and bending modes.     

不同边界条件下的封闭矩形声腔的结构-声耦合分析

分析了由2块四边弹性支承的弹性板及4块刚性板构成的封闭矩形声腔的结构-声耦合特性。通过在弹性板边界施加假想的连续分布弹簧系统模拟板的不同边界和连接条件,利用汉密尔顿函数和瑞利-李兹方法,充分考虑了两弹性板之间以及弹性板与腔体内声场之间的耦合。腔体内的声压响应和弹性板的振动速度与Kim的实验结果能较好的吻合,验证了本文理论推导的正确性。最后,通过对耦合声场的分析计算,表明两弹性板之间为弱耦合,耦合声场主要由受到外激励的结构所决定;支承板的线弹簧的刚度变化对耦合声场的影响较旋转弹簧大。     

Three methods for analyzing forced vibration of a fluid-filled cylindrical shell

The forced vibration of an infinite elastic circular cylindrical shell filled with fluid is studied. Three methods are employed to analyze the forced vibration problem of this shell-fluid coupled system, that is, wave propagation approach (wave mode superposition), theorem of residues and a numerical integral method. In order to explain these methods more explicitly, before being used to investigate the vibration of an infinite fluid-filled elastic circular cylindrical shell, all these three methods are employed firstly to analyze the forced vibration problem of an infinite beam and an infinite elastic circular cylindrical shell in vacuo. Advantage and disadvantage of these three methods are discussed and their interesting relationship is revealed. That is, to any circumferential wavenumber and frequency of the external force, there is an unchangeable relationship between the general coordinates of various waves in the wave propagation approach and the residuals in the theorem of residues.     

Coupled vibration of a cylindrical shell for radiating high intensity ultrasound

The coupled vibrations of a cylindrical shell were analysed by a new method that we called ‘the apparent-elasticity method’. Several types of radiators using cylindrical shells were designed on the basis of analytical results and several acoustical characteristics were measured. In consequence, the analytical results were in good agreement with the experimental data, and the practicability of high intensity ultrasonic radiators using cylindrical shells was demonstrated.     

Linear dispersion and solitons in a liquid-filled cylindrical shell

The case of linear dispersion is investigated and a soliton solution is constructed for the problem of wave propagation in a system consisting of a liquid-filled elastic cylindrical shell. The dependence of the solution on the parameter characterizing the mutual influence of the shell and the liquid inside it is studied.     

Circumferential waves for a cylindrical shell in smooth contact with a continuum

Dispersion relations are determined for circumferential waves propagating in a layered, circular cylinder by using shell equations to approximate the behavior of the outer layer. These equations include the effects of transverse shear deformation and rotatory inertia. The cylinder consists of an elastic core in smooth contact with a hollow, circular cylinder of distinctly different elastic properties. Two distinct modes exist as the shell thickness reduces to zero. One mode is recognized to be surface waves on the convex cylindrical surface of the core; the second mode is associated with long longitudinal waves in the shell. The approximate dispersion curves for these modes are compared with curves obtained by employing elasticity equations for the layer. As the curvature increases, the agreement of the two theories becomes progressively poorer whether or not any disagreement exists for the case of no curvature. The agreement of the two theories is better when the layer is relatively stiff than when the layer is relatively soft. The shell equations simplify the calculations necessary to produce the dispersion curves.     

Reduction of sound transmission into a circular cylindrical shell using distributed vibration absorbers and Helmholtz resonators

A modal expansion method is used to model a cylindrical enclosure excited by an external plane wave. A set of distributed vibration absorbers (DVAs) and Helmholtz resonators (HRs) are applied to the structure to control the interior acoustic levels. Using an impedance matching method, the structure, the acoustic cavity, and the noise reduction devices are fully coupled to yield an analytical formulation of the structural kinetic energy and acoustic potential energy of a treated cylindrical cavity. Lightweight DVAs and small HRs tuned to the natural frequencies of the targeted structural and acoustic modes, respectively, result in significant acoustic and structural attenuation when the devices are optimally damped. Simulations show that significant interior noise reduction can only be achieved by adding damping to both structural and acoustic modes, which are resonant in the frequency bandwidth of interest. In order to be independent of the azimuth angle of the excitation and to avoid unwanted modal interactions, the devices are distributed evenly around the cylinder in rings. This treatment can only achieve good performance if the structure and the acoustic cavity are lightly damped.     

Diffraction of point-source-generated sound by an elastic cylindrical shell

The three-dimensional problem of the scattering of a harmonic sound wave by an elastic cylindrical shell is solved using Debye potentials. All potentials are represented in the form of integrals depending on the axial component of the wave vector.