Active control of radiated sound power of a smart cylindrical shell based on radiation modes

A new approach is proposed in this paper based on radiation modes to control the radiated sound pressure of a smart cylindrical shell equipped with piezoelectric sensor and actuators. The radiation modes determine the specific distribution of normal velocity of the shell that independently radiates sound to the surrounding space. In this study, the first radiation mode is controlled since it is the most effective mode in terms of the radiated power. The results indicate that most of the sound power is attenuated by controlling only this mode. The extended Hamilton’s principle, the Sanders shell theory and the assumed mode method are used to derive the equations of motion in a state space form that is suitable to design the controller. The radiated sound pressure is calculated using the simplified Kirchhoff-Helmholtz integral along with a Kalman filter to observe the system states, and a modified higher harmonic control (MHHC) is designed to attenuate the sound power. A numerical simulation demonstrated the effectiveness of the proposed approach compared to active vibration control (AVC) in attenuating the radiated sound in the low frequency domain.     

Active control of sound radiated by a submarine in bending vibration

This paper theoretically investigates the use of inertial actuators to reduce the sound radiated by a submarine hull in bending vibration under harmonic excitation from the propeller. The radial forces from the propeller are tonal at the blade passing frequency and are transmitted to the hull through the stern end cone. The hull is modelled as a fluid loaded cylindrical shell with ring stiffeners and two equally spaced bulkheads. The cylinder is closed by end-plates and conical end caps. The actuators are arranged in circumferential arrays and attached to the prow end cone. Both Active Vibration Control and Active Structural Acoustic Control are analysed. The inertial actuators can provide control forces with a magnitude large enough to reduce the sound radiated by the vibrations of the hull in some frequency ranges.     

Optimal locations and orientations of piezoelectric transducers on cylindrical shell based on gramians of contributed and undesired Rayleigh–Ritz modes using genetic algorithm

In this study, the active vibration control and configurational optimization of a cylindrical shell are analyzed by using piezoelectric transducers. The piezoelectric patches are attached to the surface of the cylindrical shell. The Rayleigh–Ritz method is used for deriving dynamic modeling of cylindrical shell and piezoelectric sensors and actuators based on the Donnel–Mushtari shell theory. The major goal of this study is to find the optimal locations and orientations of piezoelectric sensors and actuators on the cylindrical shell. The optimization procedure is designed based on desired controllability and observability of each contributed and undesired mode. Further, in order to limit spillover effects, the residual modes are taken into consideration. The optimization variables are the positions and orientations of piezoelectric patches. Genetic algorithm is utilized to evaluate the optimal configurations. In this article, for improving the maximum power and capacity of actuators for amplitude depreciation of negative velocity feedback strategy, we have proposed a new control strategy, called “Saturated Negative Velocity Feedback Rule (SNVF)”. The numerical results show that the optimization procedure is effective for vibration reduction, and specifically, by locating actuators and sensors in their optimal locations and orientations, the vibrations of cylindrical shell are suppressed more quickly.     

Theoretical and experimental study on active sound transmission control based on single structural mode actuation using point force actuators

This study deals with the feedforward active control of sound transmission through a simply supported rectangular panel using vibration actuators. The control effect largely depends on the excitation method, including the number and locations of actuators. In order to obtain a large control effect at low frequencies over a wide frequency, an active transmission control method based on single structural mode actuation is proposed. Then, with the goal of examining the feasibility of the proposed method, the (1, 3) mode is selected as the target mode and a modal actuation method in combination with six point force actuators is considered. Assuming that a single input single output feedforward control is used, sound transmission in the case minimizing the transmitted sound power is calculated for some actuation methods. Simulation results showed that the (1, 3) modal actuation is globally effective at reducing the sound transmission by more than 10?dB in the low-frequency range for both normal and oblique incidences. Finally, experimental results also showed that a large reduction could be achieved in the low-frequency range, which proves the validity and feasibility of the proposed method.     

Optimal design of PZT actuators in active structural acoustic control of a cylindrical shell with a floor partition

Genetic algorithms (GAs) are employed to optimize locations of PZT actuators in an active structural acoustic control (ASAC) system comprising a cylindrical shell with an internal floor partition. The effect of PZT actuators is simulated using a bending model and an in-plane force model, respectively. The characteristics of the optimal placements of both models are discussed and compared. Numerical simulations demonstrate that for the investigated structure, the in-plane force model has a better control performance than the bending model in the low-frequency range. The underlying physics of the control results are analyzed. Considering the practical applicability of optimally designed ASAC systems, the control performance of the optimal configuration obtained at a single frequency is assessed in the low-frequency range between 100 and 500 Hz, with results showing a significant sound attenuation in the whole range of interest.     

三弹性圆柱壳体多重耦合声辐射计算方法

为研究多圆柱壳组合结构的声辐射特性,采用模态叠加法建立了3个并排无限长弹性圆柱壳的振动声散射耦合物理模型,充分考虑了三圆柱壳的表面振动与散射声场的耦合,其中散射声场可分解为各圆柱壳刚性散射声场和弹性辐射声场的叠加,数学上将各壳间的声场耦合关系通过柱函数加法公式描述。利用该物理模型,分析了多重散射对稳态声场求解结果的影响,比较了三圆柱壳耦合系统与单个圆柱壳系统的辐射声场指向性、声压级及辐射声功率级的差异及其产生机理,结果表明:结构弹性耦合声辐射不仅在低频对总声场有显著影响,在高频范围也不可忽略;另外,针对本文设定参数的组合圆柱壳,在150 Hz以上频段,两旁圆柱壳对中间圆柱壳在正横方位产生了声辐射遮蔽效应,垂直方位则体现声泄漏作用。本文建立的方法可推广到三维空间任意多壳结构的声振耦合建模。      

Acoustic radiation from shear deformable stiffened laminated cylindrical shells

An analytical model of acoustic radiation from shear deformable laminated cylindrical shells with initial axial loadings and doubly periodic rings is presented. The shear deformation and rotary inertia of the rings are taken into account and the rings interact with the cylindrical shell only through the normal forces. The far-field sound pressure is found by using the Fourier wavenumber transform and stationary phase method. High frequency limitation issues of the first-order shear deformation theory are discussed and the effects of the second set of rings, axial initial loadings and multiple external loadings on the far-field acoustic radiation are explored. Further, the helical wave spectra of the radial displacement and sound pressure are used to study the vibrational and acoustic characteristics of the laminated shells. Above the ring frequency, the profile of the helical wave spectra of the far-field sound pressure induced by the cylindrical shell is an ellipse and the patterns of the helical wave spectra of the far-field sound pressure keep unchanged. Moreover, the ellipse distinguishes the supersonic wavenumbers and subsonic wavenumbers from the helical wave spectra of the radial displacement and surface sound pressure in the wavenumber domain. The bright spots and highlights of the helical wave spectra show that the corresponding waves are dominant.     

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.     

The measurement of structural mobilities of a circular cylindrical shell

Structural mobility is useful for the estimation of structural power flows in coupled systems. Although the methods of measuring structural mobilities are easily found for one-dimensional beam structures, few are available for cylindrical shells. In this paper, a new method is proposed for the measurement of the structural mobilities of a circular cylindrical shell. A point force excitation is used instead of circumferential modal forces which are difficult to implement in practice. This method utilizes the least squares technique to obtain the transfer function components of different circumferential modes from the measured data. Experiments were carried out on a circular cylindrical shell with different end conditions excited by a point force to verify the feasibility of this proposed method.     

Noise transmission from a curved panel into a cylindrical enclosure: analysis of structural acoustic coupling

Much of the research on sound transmission through the aircraft fuselage into the interior of aircraft has considered coupling of the entire cylinder to the acoustic modes of the enclosure. Yet, much of the work on structural acoustic control of sound radiation has focused on reducing sound radiation from individual panels into an acoustic space. Research by the authors seeks to bridge this gap by considering the transmission of sound from individual panels on the fuselage to the interior of the aircraft. As part of this research, an analytical model of a curved panel, with attached piezoelectric actuators, subjected to a static pressure load was previously developed. In the present work, the analytical model is extended to consider the coupling of a curved panel to the interior acoustics of a rigid-walled cylinder. Insight gained from an accurate analytical model of the dynamics of the noise transmission from the curved panels of the fuselage into the cylindrical enclosure of an aircraft is essential to the development of feedback control systems for the control of stochastic inputs, such as turbulent boundary layer excitation. The criteria for maximal structural acoustic coupling between the modes of the curved panel and the modes of the cylindrical enclosure are studied. For panels with aspect ratios typical of those found in aircraft, results indicate that predominately axial structural modes couple most efficiently to the acoustic modes of the enclosure. The effects of the position of the curved panel on the cylinder are also studied. Structural acoustic coupling is found to not be significantly affected by varying panel position. The impact of the findings of this study on structural acoustic control design is discussed.     

降低加肋双层圆柱壳辐射噪声线谱的结构声学设计

为降低双层圆柱壳辐射噪声线谱,从控制内壳振动响应和衰减壳间振动传递率进行结构声学设计。采用机械阻抗理论分析了环肋圆柱壳模态响应控制机理;由环肋振动方程推导分析了环肋径向机械阻抗特性;基于阻抗失配、波形转换原理提出一种阻抗加强环肋,分析了振动波阻抑特性;利用阻尼减振技术,综合考虑肋板的刚度、阻尼特性,设计了金属橡胶层叠肋板;结合数值计算实例,分析了设计双层壳模型的声辐射性能。结果表明:设计的双层加肋圆柱壳结构能有效降低辐射噪声线谱,在分析频段内辐射声压线谱平均降低约6.6 dB。研究结果对研制低噪声水下航行器具有良好的工程价值和应用前景。      

Active modal control simulation of vibro-acoustic response of a fluid-loaded plate

Active modal control simulation of vibro-acoustic response of a fluid-loaded plate is presented. The active modal control of the vibro-acoustic response is implemented using piezoelectric actuators/sensors. The active modal damping is added to the coupled system via negative velocity feedback. The feedback gain between the piezoelectric actuators/sensors for the modal control is obtained using the in-vacuo modal matrix and the incompressible fluid-loaded modal matrix. The modal control performance of structural vibration and acoustic radiation of a baffled plate is numerically studied. It is shown that the proposed method increases the modal damping ratio and achieves reduction in the mean square velocity and the sound power for given modes of the fluid-loaded plate.     

弯管对末端带弹性障板充液管路辐射声能量的影响

基于声固耦合有限元方法建立了末端带弹性障板的充液管路数值模型,重点分析了不同激励下弯管对管口辐射声能量的影响.结果表明:弯管引入的高阶周向模式耦合使结构振动和流体声传播都发生明显改变,以致系统辐射声能量及主要能量贡献源也发生转移,并随激励方式和频率而不同.对本文管路模型,平面波激励下弯管系统在低频的结构辐射声能量明显增...     

Characteristics of the vibrational power flow propagation in a submerged periodic ring-stiffened cylindrical shell

By using space-harmonic analysis method, the characteristics of the vibrational power flow propagation in an infinite periodic ring-stiffened cylindrical shell immersed in water are studied. The harmonic motion of the shell and the sound pressure field in the fluid are described by Flügge shell equations and Helmholtz equation, respectively, and four kinds of the rings’ forces and moments are considered. Along the shell axial direction, the propagation of the power flow carried by different internal forces (moments) of the shell wall can be obtained, thus the total power flow in the shell wall and the ratios of the component power flow carried by different shell internal forces (moments) to the total power flow are also studied. It is found that characteristics of the vibrational power flow propagation vary with different circumferential modes order and different frequencies. Moreover, the presence of the stiffeners and structural damping will greatly influence the results.     

Modeling of offshore pile driving noise using a semi-analytical variational formulation

Underwater noise radiated from offshore pile driving got much attention in recent years due to its threat to the marine environment. This study develops a three-dimensional semi-analytical method, in which the pile is modeled as an elastic thin cylindrical shell, to predict vibration and underwater acoustic radiation caused by hammer impact. The cylindrical shell, subject to the Reissner–Naghdi’s thin shell theory, is decomposed uniformly into shell segments whose motion is governed by a variational equation. The sound pressures in both exterior and interior fluid fields are expanded as analytical functions in frequency domain. The soil is modeled as uncoupled springs and dashpots distributed in three directions. The sound propagation characteristics are investigated based on the dispersion curves. The case study of a model subject to a non-axisymmetric force demonstrates that the radiated sound pressure has dependence on circumferential angle. The case study including an anvil shows that the presence of the anvil tends to lower the frequencies and the amplitudes of the peaks of sound pressure spectrum. A comparison to the measured data shows that the model is capable of predicting the pile driving noise quantitatively. This mechanical model can be used to predict underwater noise of piling and explore potential noise reduction measures to protect marine animals.     

On the contribution of circumferential resonance modes in acoustic radiation force experienced by cylindrical shells

A body insonified by a constant (time-varying) intensity sound field is known to experience a steady (oscillatory) force that is called the steady-state (dynamic) acoustic radiation force. Using the classical resonance scattering theorem (RST) which suggests the scattered field as a superposition of a resonance field and a background (non-resonance) component, we show that the radiation force acting on a cylindrical shell may be synthesized as a composition of three components: background part, resonance part and their interaction. The background component reveals the pure geometrical reflection effects and illustrates a regular behavior with respect to frequency, while the others demonstrate a singular behavior near the resonance frequencies. The results illustrate that the resonance effects associated to partial waves can be isolated by the subtraction of the background component from the total (steady-state or dynamic) radiation force function (i.e., residue component). In the case of steady-state radiation force, the components are exerted on the body as static forces. For the case of oscillatory amplitude excitation, the components are exerted at the modulation frequency with frequency-dependant phase shifts. The results demonstrate the dominant contribution of the non-resonance component of dynamic radiation force at high frequencies with respect to the residue component, which offers the potential application of ultrasound stimulated vibro-acoustic spectroscopy technique in low frequency resonance spectroscopy purposes. Furthermore, the proposed formulation may be useful essentially due to its intrinsic value in physical acoustics. In addition, it may unveil the contribution of resonance modes in the dynamic radiation force experienced by the cylindrical objects and its underlying physics.     

Active vibroacoustic control with multiple local feedback loops

When multiple actuators and sensors are used to control the vibration of a panel, or its sound radiation, they are usually positioned so that they couple into specific modes and are all connected together with a centralized control system. This paper investigates the physical effects of having a regular array of actuator and sensor pairs that are connected only by local feedback loops. An array of 4 x 4 force actuators and velocity sensors is first simulated, for which such a decentralized controller can be shown to be unconditionally stable. Significant reductions in both the kinetic energy of the panel and in its radiated sound power can be obtained for an optimal value of feedback gain, although higher values of feedback gain can induce extra resonances in the system and degrade the performance. A more practical transducer pair, consisting of a piezoelectric actuator and velocity sensor, is also investigated and the simulations suggest that a decentralized controller with this arrangement is also stable over a wide range of feedback gains. The resulting reductions in kinetic energy and sound power are not as great as with the force actuators, due to the extra resonances being more prominent and at lower frequencies, but are still worthwhile. This suggests that an array of independent modular systems, each of which included an actuator, a sensor, and a local feedback control loop, could be a simple and robust method of controlling broadband sound transmission when integrated into a panel.     

极点配置法弹性平板有源隔声系统优化

对混响声场中的弹性平板有源隔声系统进行优化。根据激励频率范围确定受控模态阶次,在模态空间中建立系统降阶方程,基于极点配置方法,采用分布式系统增加受控模态的阻尼,降低低频共振声传输。同时设计模态滤波器,为控制器提供所需的状态信息。为提高控制效能,本文对传感器和作动器布放位置进行优化,尝试不同极点配置方案,并对耦合控制与独立模态控制方法的隔声效果进行比较。仿真结果显示,极点配置法有源隔声可以有效降低共振声传输,优化布放和独立模态控制方式下,控制力明显降低。优化后的有源隔声系统效能有所提升。      

Sound pressure in cylindrical shells with regular orthogonal system of stiffeners excited by a random fields of forces

To identify deterministic and random vibrations of a closed cylindrical shell with a regular orthogonal system of stiffeners (stringers and frames) the effective prediction method was worked out. This method is a generalization of the known method of space-harmonic expansion based on the theorem of Bloch-Floquet for a two-dimensional case. The method permits considering correctly the stiffener discreteness and their interaction with the shell through all the components of displacement. On the basis of the method worked out the task of determining the sound field inside the cylindrical volume bounded by the shell excited by the deterministic and random fields of external forces is solved. The high efficiency of the method permits making the prediction of the shell vibrations and of the sound pressure levels inside the volume with account for sound-insulating layers over a wide frequency range. Examples of predicting the strengthened shell vibrations at large aircraft fuselage parameters are given as well as the sound pressure levels inside it under the point force excitation and under excitation by the random field of wall pressure fluctuations of the turbulent boundary layer (within the limits of one of the representation of the space correlation spectrum).     

Structure normal velocity reconstruction withsparse measurement points

To achieve normal velocity reconstruction of a vibrating surface with sparse measurement points, a reconstruction method is proposed by exploiting of acoustic radiation modes as expansion functions, which are capable of describing the geometric shape of a vibrating surface. Firstly, acoustic radiation modes of the vibrating surface are calculated and the relationship between normal velocity and acoustic radiation modes is built. Then actual measured normal velocity values are expressed by corresponding acoustic radiation modes and the expansion coefficients are calculated. Subsequently, all normal velocity values can be reconstructed by the obtained expansion coefficients. Experimental validations have been performed by a double-layer steel cylindrical shell with enclosed ends in.an anechoic water tank. Two cases with different wavenumber components distribution were designed by a vibration shaker and a rotor device respectively. Two experimental results both show that actual vibration distribution cannot be revealed exactly by the sparse measurement points, which corresponds to severe loss of vibration related wavenumber components. On the other hand, normal velocity and corresponding wavenumber components can be restored accurately in both two wavenumber components distribution cases according to the proposed method, which demonstrates obvious effectiveness of the proposed method.