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Research Papers

Relation Between Structural Intensity-Based Scalars and Sound Radiation Using the Example of Plate-Rib Models

[+] Author and Article Information
Clarissa Schaal

System Reliability and Machine Acoustics SzM,
Department of Mechanical Engineering,
Technische Universität Darmstadt,
64289 Darmstadt, Germany
e-mail: schaal@szm.tu-darmstadt.de

Johannes Ebert

Structure-borne Sound and Vibrations,
Department of Structural Dynamics,
BMW Group,
80788 München, Germany
e-mail: johannes.ebert@bmw.de

Joachim Bös

System Reliability and Machine Acoustics SzM,
Department of Mechanical Engineering,
Technische Universität Darmstadt,
64289 Darmstadt, Germany
e-mail: boes@szm.tu-darmstadt.de

Tobias Melz

Professor
System Reliability and Machine Acoustics SzM,
Department of Mechanical Engineering,
Technische Universität Darmstadt,
64289 Darmstadt, Germany
e-mail: melz@szm.tu-darmstadt.de

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 16, 2014; final manuscript received March 29, 2016; published online May 25, 2016. Assoc. Editor: Lonny L. Thompson.

J. Vib. Acoust 138(4), 041011 (May 25, 2016) (9 pages) Paper No: VIB-14-1478; doi: 10.1115/1.4033339 History: Received December 16, 2014; Revised March 29, 2016

The ability of the structural intensity (STI) to predict changes in the sound radiation of structures due to geometric modifications is investigated using the academic example of plate-rib models. All models consist of the same plate and are modified by attaching a rib, whose position, orientation, and length are varied. Various scalar quantities are derived from the STI and quantitatively compared to the equivalent radiated sound power (ERP) for each model. Based on this comparison the relation between the STI-based scalars and the ERP is studied to determine an STI-based scalar that can serve as the objective function for numerical structural optimizations. The influence of the rib parameters on the most promising STI-based scalar is analyzed by means of a variance-based sensitivity analysis. The STI pattern of those models with very high and very low ERP values are additionally analyzed to describe the characteristics of STI. The results of this study indicate that the STI pattern of models with low ERP has paths and vortices that can be more clearly identified compared to those in models with high ERP. The angular orientation of the rib has by far the highest influence on changes in STI and ERP. The results reveal a correlation between the energy flow into a specific region of a structure, an STI-based scalar, and the ERP. Therefore, the vibrational energy flow can indeed serve as an objective function for numerical structural optimizations aiming at reducing the sound radiation.

Copyright © 2016 by ASME
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Figures

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Fig. 1

Definition of the section forces (a), section moments (b), and rotational angles (c)

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Fig. 2

Model of the plate with its parameters and geometry

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Fig. 3

Factor levels of the full factorial design. The crosses mark the center of the ribs.

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Fig. 4

ERP of part A plotted against the maximum of the flux density in part A for the first 15 modes

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Fig. 5

ERP of part A plotted against the maximum of the flux density in part A—summed up over the modes

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Fig. 6

ERP of part A plotted against the minimum of the flux density for the first 15 modes

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Fig. 7

ERP of part A plotted against the minimum of the flux density—summed up over the modes

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Fig. 8

ERP of part A plotted against the summed up flux density of part A for the first 15 modes

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Fig. 9

ERP of part A plotted against the summed up flux density of part A—summed up over the modes

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Fig. 10

ERP of part A plotted against the surface percentage of part A with a flux density equal to or higher than 1% of the maximum flux density of part A for the first 15 modes

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Fig. 11

ERP of part A plotted against the surface percentage of part A with a flux density equal to or higher than 1% of the maximum flux density of part A—summed up over the modes

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Fig. 12

ERP of part A plotted against the energy flow from part B to part A for the first 15 modes

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Fig. 13

ERP of part A plotted against the energy flow from part B to part A—summed up over the modes

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Fig. 14

Correlation coefficient between the ERP and the energy flow from part B to part A for summing up their values for an ascending number of modes

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Fig. 15

Plate-rib model with the lowest energy flow from part B to part A in mode 10 (axrib = 250 mm, ayrib = 260 mm, φrib=150 deg, lrib = 300 mm)

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Fig. 16

Plate-rib model with the highest energy flow from part B to part A in mode 10 (axrib = 220 mm, ayrib = 310 mm, φrib=30 deg, lrib = 300 mm)

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Fig. 17

Variance of the factors and the factor interactions on the energy flow from B to A—summed up over the frequencies

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