ACTIVE CONTROL OF SOUND RADIATED FROM
A BAFFLED PIPE OPENING
Jing Tian, Bilong Liu, Jie Pan* and Xiaodong Li
Institute of Acoustics, Chine Academy of Sciences,
P.O.Box 2712, Beijing 100080, P.R.China,
* School of Mechanical and Materials Engineering,
The University of Western Australia, Nelands,West.Aust.6907
E-mail address of lead author: tian@mail.ioa.ac
Abstract
When the coupling among the fluidic modes and structural modes cannot be neglected such as i n a water-filled pipe, the sound radiated from the pipe opening attached to a baffling panel is also compod of two parts from the opening and the panel parately. Therefore, active control of the so
und radiation from such an opening is critical to the contribution of each part. In this paper, the sound radiations from the two parts are calculated. Experimental verifications are also given, bad on which a simulation of active control system for such a pipe opening and the possible noi attenuation is conducted and discusd. The results show that, for a water-filled pipe, both of the fluidic and structural modes are important to the sound radiation. The two types of modes are more or less coupled in different frequency ranges. Tho imply that an effective active control system should be well designed in the positions and transducing mechanisms of the nsors and condary actuators.
INTRODUCTION
婴儿吃盐
The wave travelling characteristics in pipes received much attention recently. Harari1 and Fuller2studied wave propagation in cylindrical shells with structural discontinuity. Schlesinger3, Tso and Hann4 investigated the wave propagation through cylindrical/plate junction. The dispersion relations and energy distributions
for wave travelling in a fluid-filled elastic pipe were thoroughly analyzed by Fuller and Fahy 5.
In this paper, the exhaust pipe system is modeled as a water-filled pipe coupled with a finite plate at t
he pipe opening. The disturbance from the source end of the pipe is transmitted to the pipe opening as water-borne sound and to the attached plate as structural -borne sound radiated into the medium above the plate. The numerical results on the couplings of fluid and structure in the pipe and effects of fluid loading on radiation surface are given and discusd. A simple experiment on sound radiation into air in a mi-anechoic room from the system is also conducted to validate the theoretic model. Finally, bad on the understanding of vibro-acoustic characteristics of involved system, a simulation of active control system for such a pipe opening and the possible noi attenuation is prented and discusd.
SYSTEM SOLUTION AND NUMERIC RESULTS
The system model is shown in Figure.1, where (σ,θ, z) denote radial, circumferential and axial co-ordinates above the plate, ),,(w v u and (p p p w v u ,,) reprent displacements in the three orthogonal directions of the pipe wall and the plate. The thickness of the pipe and the plate i s h , the length and radius of the pipe are L and a respectively. The plate attached to the pipe opening has the radius of b and is clamped on a rigid baffle. A velocity source located at the bottom of the pipe is ud to generate sound and vibration.
Figure 1. System model and co-ordinates definition.
杀人如麻的意思Detailed theoretic solution could be en in reference 6, in which the traveling wave meth od is ud to deal with the part of water-filled pipe, and the coupling between the pipe wall and the fluid are come down to find dispersion curves in water-filled pipe. At the same time, method of extended mode shape function 7 is applied to describe vibration of the attached plate, and correspondingly the fluid loadings above the plate are ascribed to calculate mode radiation impedance.
澳大利亚阿德莱德Following example is ud to illustrate the sound radiation and associated mechanisms. The system is excited by a uniformly distributed velocity source located at the bottom of the pipe. Only the waves and sound radiation due to 0=n circumferential modes are considered here. The system parameters are: m L 5.1=,m a 1.0=, m b 4.0=,m h 005.0=, s m c L /5200=, 3/7800m kg s =ρ, 3/1000m kg f =ρ,s m c f /1500=, s m V i /000001.0=. In investigation, damping is ignored and the frequencies are limited to lower for the p rimary interest of active control. Furthermore, the transfer impedance level between the radiated sound pressure P and the input velocity i V is defined as:
(10log *10122i V P
T =
(1) Figure 2 gives a numerical result of 1T , in which P is the radiated sound
pressure at (0,0,10m) and the non -dimensional frequency is defined as L a ω=Ω(L c is extensional pha speed of pipe shell). The solid lines in Figure 2 correspond to the results of radiation into light fluid. In this ca , the fluid loading above the plate is ignored and effect of the fluid/pipe coupling on sound radiation could be investigated parately. The dashed lines are that of radiation into heavy fluid. The effect of fluid loading on the radiation surface is obrved. In the frequency range of intere
st, the fluid and structural waves are weakly coupled becau the characteristics of waves are similar to that of fluid plane wave in rigid-walled pipe and structural waves i n vacuo pipe respectively (e reference 9). The fluid and structural respon of the pipe is governed by the resonance of each wave type. The interaction between the fluid and structural waves can be approximately modeled by weakly coupled subsystems. For example, when the originally uncoupled resonance frequencies of the two subsystems are clo and the corresponding distributions of the mode shapes match spatially, some kinds of coupling would still h appen. In Figure 2(a), the resonance peaks are classified in terms of the number of antinodes in the distributed sound field in the pipe. Each index of the peak is attached with (f) to show that wave type in the pipe is dominated
by the fluid waves, and fluid wave radiation at the pipe opening contribute significantly to the total sound pressure radiated. Other peaks correspond to the large sound radiation from the plate and indexed by a number attached with (s). The number equals the antinodes in the plate vibration along the radial direction.
行李箱盖
Compared with the ca of light fluid assumption, the effects of fluid loading on vibrating surface will lead to lower values and deviations of resonance peaks which are ascribed to the effects of radiation resistance and reactance respectively (e dashed lines in Figure 2).
Figure 2 T1 as a function of non-dimensional frequency . (a) total sound radiation from the plate and pipe opening; (b) radiation from the plate and (c) radiation from pipe opening. Solid lines correspond to the results of omitting the fluid loading above the plate and dashed lines include effects of the fluid loading above the plate.
与蛇有关的成语EXPERIMENT
The theory and numerical results are validated experimentally. Figure 3 shows the experimental tup in a mi-anechoic room. The testing plate is clamped all around and a uniform velocity source located at the bottom of the pipe is ud to excite the system. The steel pipe is filled with water and the medium above the plate is air. The system parameters ud in the experimentation are m L 55.0=,m a 03.0=, m b 18.0=,m h 003.0=. The microphone was located at the position of (0,0,
0.35m), The experimental results are showed in Figure 4 where numeric results is also provided for comparison.
The experimental tup is bad on the model of sound radiation into the air and the measured impedance level 1T covers the frequency range of 7.047.0<Ω<which correspon ds to the transition region from weak couplings to strong couplings (e reference 9). As shown in Figure 4, the theoretical prediction agrees with the experimental result in terms of the general trend of resonance peak distribution and levels at the anti -resonance frequencies.
吴承恩的作品
Absorption
Air
Air
Figure 3 Schematics of experimental rig.
Figure 4 T1 as a function of non -dimensional frequency. Solid lines are experimental data and dashed lines are theoretic calculation.
SIMULATION OF ACTIVE CONTROL见此良人
Jing Tian 10 once investigated the energy mechanism in active noi reduction in a duct with a mon
opole source, and bad on the assumption of plane wave he concluded that the effect of condary sound source could be attributed to an impedance. )(6)(48[2ss ss ss ss ss kl A A i kl A A c Z +−≈ρ] (2)
in which ss l is the dimension of condary source,ss A and A correspond to the area of condary source and cross-ction of the pipe respectively, k is axial wave number
of plane wave in the fluid. Formula (2) shows that the mechanism of noi reduction is bad on reflecting sound energy to upstream. For a water-filled pipe, if we suppo the condary source only affects the i m pedance of fluid and so the effect of the condary source on structural impedance is omitted, then formula (2) could be ud to investigate the effects of active control in water-filled pipe.
Simulation results showed in Figure 6 in which system parameters ud in calculation are the same as ction 2 and the non -dimensional distance is defined as L L D sp /= (sp L is the distance between condary source and pipe opening). From Figure 5(c)(f)(i), it is easy to find that the sound radiation from the pipe opening reduces greatly after control, but that of the plate has not such impression (e Figure 6(b)(e)(h)). For the reflection effects of the condary source, the structure d
ominated resonance peaks are larger and keep no changes in position in comparison with that of before control. But the first fluid dominated resonance peaks after control is located higher than first anti -resonance peaks before control for the reason of decreasing distance of reflection surface (e Fi gure 6(a)).
Figure 5 Simulation results of active control where m l A A ss ss 1.0,1.0/== and in (a)(b)(c) D=0.1, (d)(e)(f) D=0.5, (g)(h)(i) D=0.9; (a)(d)(g) total sound radiation, (b)(e)(h) radiation from the plate and (c)(f)(i) radiation from the pipe opening; dashed lines are the results after control and solid lines are that of before control.
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