ESDU Engineer
Issue 9
Radiation of sound from orthotropic plates
As part of an on-going group of Items on Statistical Energy Analysis (SEA) in Volume 7 of the Vibration and Acoustic Fatigue Series, two Items have recently been issued on sound radiation from orthotropic rectangular plates, Item Nos 02009 and 02010. SEA is a method for predicting high frequency noise and vibration levels in complex structures. As the modes are numerous and close together at high frequencies, it is difficult to predict individual natural frequencies and modal shapes, hence a statistical approach may be desirable. SEA has found applications in predicting vibration levels in space vehicles, interior noise in aircraft and noise in automobile structures, amongst others. Complex structures have to be broken down into sub-units so that the energy flow can be studied.
In selecting an analysis method the Engineer will find that Item No. 97033 (Methods for Analysis of the Dynamic Response of Structures) gives useful guidance for the suitability and scope of the different methods available, including SEA. More details on SEA have been provided in Item No. 99009, An Introduction to Statistical Energy Analysis. This Item gives the Engineer information on many of the essential concepts in SEA, such as sub-systems, power balance equations, coupling loss factors and modal density, etc. Further Items in the Series look at energy flow in more detail, for example, energy transmitted between coupled plates is considered in Item No. 98020, which include computer programs for design purposes. There is also an Item on sound radiation from isotropic plates.
Item No. 02009 may be used to estimate the sound radiation efficiency of orthotropic plates. Radiation efficiency is a fundamental quantity and provides information on how effectively bodies produce sound. There is a radiation efficiency associated with each mode of vibration of the plate, but more importantly there is an average radiation efficiency that is an average of the radiation efficiencies of the modes in a frequency band. The method used in Item No. 02009 for the estimation of radiation efficiencies is based on an asymptotic approximation which has been extended to orthotropic plates.
There are few homogeneous and orthotropic materials that occur in practice. Wood is probably the best known example. However, sandwich panels made from layers of carbon fibres are important examples of orthotropic plates. Additionally, panels that can have orthotropic characteristics include honeycombs, ribbed plates and corrugated sheets, etc. Equivalent orthotropic plates can be formed from these structures and Item No. 02009 can be used to estimate their average radiation efficiencies. The bending stiffnesses for the equivalent plates are required and they can either be measured or estimated from formulae given in the Item. The method described is for simply-supported plates, although guidance is provided on how to deal with plates which are clamped or partially clamped at the edges. Orthotropic plates can be shown to have two coincidence frequencies. In the frequency range between the two frequencies the sound radiation efficiency is greater than that for a similar isotropic plate.
Estimation of the sound radiation efficiency for orthotropic plates may be implemented in two ways, firstly by using design curves provided in the Item and secondly by computer programs. The data required by the input program are the plate dimensions (length, width and thickness), the mean density of the plate and the bending stiffnesses (or, for a single layer, the material properties such as the Young’s moduli, shear modulus, etc). The main program A0209 calls the input program and computes the averaged sound radiation efficiencies in either one-third or one-sixth octave bands. An output file is created which holds both the input and output data. As the method used is a high frequency approximation, only results above a certain frequency are computed.
Since some of the results and methods of Item No. 02009 are new, a special effort was put into validation. A numerical study was commissioned from the Institute of Sound and Vibration Research, University of Southampton. Experimental data were provided by the Structures and Materials Centre, QinetiQ. Additional experimental data were found in the literature. Results produced by the method of Item No. 02009 agreed well with the numerical and experimental data. Details of the validation are given in Item No. 02010.
John Anderson is the Senior Engineer responsible for the Vibration and Acoustic Fatigue Series. He can be contacted at jand@esdu.com