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This work presents a vibroacoustic response model for a fluid-loaded, simply supported rectangular plate covered by a composite acoustic coating consisting of damping and decoupling layers. The model treated the damping layer and base plate as a unified whole under pure bending moments and the decoupling layer as a three-dimensional, isotropic, linear elastic solid. The validity of the model was verified by both numerical analysis and experiments and was shown to accurately extend previous studies that were limited to a plate covered by a single damping or decoupling layer with an evaluation confined solely to numerical analysis. The trends of the numerical and experimental results are generally consistent, with some differences due to the influences of water pressure and the frequency dependence of the material parameters, which are not taken into account by the numerical analysis. Both experimental and numerical results consistently show that the radiated noise reduction effect of the composite coating is superior to that of single-type coatings, which is attributed to the fact that the composite coating combines the merits of both the high vibration suppression performance of the damping layer and the superior vibration isolation performance of the decoupling layer.

As an effective noise reduction approach for resonant structures immersed in water, the addition of a composite acoustic coating consisting of both damping and decoupling layers is proposed herein as a new method to reduce the vibrations and radiated noise generated in the structure. Such a composite acoustic coating combines the high vibration suppression performance of a damping layer and the superior vibration isolation performance of a decoupling layer, which can dramatically reduce vibrations and radiated noise with negligible increase in the thickness or weight of the acoustic coating.

A damping coating suppresses structural vibrations and reduces radiated noise through the internal friction of a viscoelastic polymer chain. Numerous studies have been performed regarding the vibroacoustics of resonant structures covered by damping coatings. Alam and Asnani [

A decoupling coating lessens the sound radiation by reducing vibration transfer from the resonant structure to the fluid via vibration isolation. Three types of dynamic models have been applied to decoupling coatings. The first of model is based on the theory of wave propagation in a layered media [

From the above discussion, we see that previously published studies have been concerned with resonant structures covered with single-layer damping or decoupling coatings or multilayered coatings comprising only damping layers and have provided no experimental verification of their theoretical-based results. Therefore, the vibroacoustic response of a resonant structure covered by a composite acoustic coating comprising both damping and decoupling layers is fairly unknown.

This paper proposes an exact analytical model for a fluid-loaded, simply supported rectangular plate covered by a damping and decoupling composite acoustic coating. The model treats the damping layer and base plate as a unified whole under pure bending moments and employs 3D elasticity theory for the decoupling layer. The vibration suppression performance, decoupling performance, and radiated noise reduction effect of various composite coatings were studied theoretically and experimentally, and the results reveal the mechanisms of noise reduction and provide principles for appropriate materials selection for the composite coating. The experiments also validate the proposed analytical model.

As shown in Figure

Schematic illustration of the resonant structure system.

The equation of motion of the composite plate, consisting of the base plate and the damping layer, is given by

According to the pure bending moment theory, (

The decoupling layer is governed by the Navier-Cauchy equation:

Because the water media is considered ideal and nonviscous, the acoustic pressure

The simply supported boundary conditions at the edges of the base plate and the damping layer are

The boundary conditions at the damping-decoupling interface (

The boundary conditions on the lateral sides of the decoupling layer are [

The above boundary conditions physically show that the lateral sides of the decoupling layer are fixed in the

The boundary conditions at the decoupling-fluid interface (

The problem is entirely defined using (

The choices of such trigonometric functions are determined by the boundary conditions of (

Equations (

In this paper, three vibroacoustic indicators are introduced: the mean squared velocity of the base plate (

The proposed model treated the damping layer and base plate as a unified whole under pure bending moments, as described by (

Sound power radiated by the system, compared with [^{3},

To investigate the noise reduction mechanism of the damping and decoupling composite acoustic coating, numerical calculations were performed based on three specimens with different decoupling layer parameters, which represent a varying influence on the vibroacoustic behavior. The structural dimensions and material properties of the coating are tabulated in Table ^{3}, ^{3}, respectively. A point force is applied on the base plate at

Structural dimensions and material properties of the composite coating.

Symbol | Units | Composite coating | ||
---|---|---|---|---|

DC-001 | DC-002 | DC-003 | ||

| kg/m^{3} | 1350 | 1350 | 1350 |

| Pa | 101 × 10^{7} | 101 × 10^{7} | 101 × 10^{7} |

| — | 0.497 | 0.497 | 0.497 |

| m | 0.010 | 0.010 | 0.010 |

| kg/m^{3} | 1160 | 1180 | 100 |

| Pa | 1.34 × 10^{7} | 0.12 × 10^{7} | 1 × 10^{5} |

| — | 0.497 | 0.498 | 0.45 |

| m | 0.020 | 0.020 | 0.020 |

Because (

As shown in Figure

Mean squared velocity of the base plate (

Figure

Comparison of the mean squared velocities of the base plate and the outer surface (

As shown in Figure

Sound power radiated by the three specimens.

Figure

Schematic of the experimental test system.

Figure

Comparison of theoretical and experimental values of

Mean squared velocity of the base plate with and without water in the tank.

As shown in Figure

Comparison of theoretical and experimental values of

Comparison of theoretical and experimental sound fields.

This is demonstrated in Figure

Figures

Mean squared velocities of the base plates of two specimens.

Comparison of the mean squared velocities of base plates and outer decoupling layer surfaces.

Sound pressure radiated by the two specimens.

Figure

As shown in Figure

This work presented the vibroacoustic response of a fluid-loaded, simply supported rectangular plate covered by a damping and decoupling composite acoustic coating. The vibration suppression performance, decoupling performance, and sound radiation of various composite coatings were studied theoretically and experimentally. Based on the obtained results, the following conclusions can be drawn:

The trends of the theoretical and experimental results are consistent. Some differences are observed due to the influence of water pressure and the frequency dependence of material parameters, which the numerical analysis did not take into account.

The composite acoustic coating combines the merits of both the high vibration suppression performance of a damping coating and the superior vibration isolation performance of a decoupling coating. The radiation noise reduction effect is therefore significantly better than can be obtained using a single-type coating.

Only when the loss modulus of the damping layer is sufficiently high and the stiffness of the decoupling layer is sufficiently low can the system provide an excellent vibration isolation and noise reduction effect.

The authors declare that they have no competing interests.