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Research Papers

A Two-Stage Model for Energy Transmission and Radiation Analysis of Laminated Composite Double-Leaf Structures

[+] Author and Article Information
Atanu Sahu

Mem. ASME
Department of Civil Engineering,
Jadavpur University,
188, Raja S. C. Mallik Road,
Kolkata 700032, India
e-mail: atanush@gmail.com

Arup Guha Niyogi

Department of Civil Engineering,
Jadavpur University,
188, Raja S. C. Mallik Road,
Kolkata 700032, India
e-mail: agn_ju@yahoo.com

Michael Rose

Institute of Composite Structures and Adaptive Systems,
German Aerospace Center (DLR),
Lilienthalplatz 7,
Braunschweig 38108, Germany
e-mail: michael.rose@dlr.de

Partha Bhattacharya

Department of Civil Engineering,
Jadavpur University,
188, Raja S. C. Mallik Road,
Kolkata 700032, India
e-mail: p_bhatta@daad-alumni.de

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 20, 2016; final manuscript received March 17, 2017; published online May 30, 2017. Assoc. Editor: Ronald N. Miles.

J. Vib. Acoust 139(4), 041008 (May 30, 2017) (13 pages) Paper No: VIB-16-1404; doi: 10.1115/1.4036390 History: Received August 20, 2016; Revised March 17, 2017

A two-stage numerical model is developed to understand the energy transmission characteristics through a finite double-leaf structure placed in an infinite baffle subjected to an external excitation and subsequently the sound radiation behavior of the same into the semi-infinite receiving side. In the first stage, a mobility-based coupled finite element–boundary element (FE–BE) technique is implemented to model the energy transmission from the primary panel to the secondary panel through an air gap. In the second stage, a separate boundary element (BE)-based model is developed to estimate the sound power radiated by the radiating (secondary) panel into the receiving side which is assumed to be semi-infinite. The advantage of the proposed approach is that it is sufficient to mesh the structural panels alone, thereby reducing the problem dimensions and the difficulty in modeling. Moreover, the developed model can be easily implemented for structures made up of various constituent materials (isotropic or laminated composites) with complex boundary conditions and varying panel geometries. Numerical experiments are carried out for different material models by varying air-gap thicknesses and also by introducing alternate energy transmission path in terms of mechanical links and the obtained results are discussed.

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References

Figures

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Fig. 1

Schematic representation of the double leaf structure in an infinite baffle

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Fig. 2

An arbitrary shaped vibrating body enclosing a finite acoustic domain

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Fig. 3

Flowchart explaining the scheme of analysis

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Fig. 4

Averaged quadratic velocity spectra in decibels (reference: 2.5 × 10−15 m2 s−2) for panels for isotropic (aluminum) double-leaf structure with an air-gap thickness of 0.33 m

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Fig. 5

(a) Experimental setup: 1, frame; 2, aluminum panel (dimensions indicated) point supported at four corners, (b) schematic of the measurement setup, and (c) measurement of plate velocity with the vibrometer and measurement of sound intensity with the intensity probe

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Fig. 6

Comparison of the BE estimate of the radiated sound intensity (reference: 10−12 W/m2) with the experimental data

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Fig. 7

Radiated sound power from panel b in decibels (reference: 10−12 W) for case I (isotropic double-leaf structure with air gap of 0.33 m thick)

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Fig. 8

Schematic of the alignment of the fiber with respect to the global axis in a lamina

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Fig. 10

Averaged quadratic velocity spectra in decibels (reference: 2.5 × 10−15 m2 s−2) for uncoupled response of panel a only (made of aluminum and carbon-fiber-epoxy composite material)

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Fig. 9

Averaged quadratic velocity spectra in decibels (reference: 2.5 × 10−15 m2 s−2) for the orthotropic double-leaf structure with entrapped air gap of 0.33 m thick

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Fig. 11

Radiated sound power from panel b in decibels (reference: 10−12 W) for case II (laminated composite double-leaf structure with air gap of 0.33 m thick)

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Fig. 12

Averaged quadratic velocity plots in decibels (reference: 2.5 × 10−15 m2 s−2) for the orthotropic double-leaf structure (air gap = 0.1 m)

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Fig. 13

Radiated sound power from panel b in decibels (reference: 10−12 W) for the orthotropic double-leaf structure with air gap of 0.1 m thick (case III)

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Fig. 14

Radiated sound power in decibels (reference: 10−12 W) from the double-leaf structure when panel a is made of aluminum and panel b is made of orthotropic material with varying lamina sequences (case IV)

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Fig. 15

Comparison of the averaged quadratic velocity in decibels (reference: 2.5 × 10−15 m2 s−2) for a double-wall configuration, with link and without link

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Fig. 16

Comparison of the radiated sound power in decibels (reference: 10−12 W) from a double-wall structure, with link and without link

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Fig. 17

Kinetic energy ratios of the panels for different isotropic and orthotropic cases

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Fig. 18

ETI for different isotropic and orthotropic cases

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