Article | REF: R6215 V2

Energetic statistic analysis of the vibroacoustic environment

Author: Gérard BORELLO

Publication date: June 10, 2012

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ABSTRACT

The computational simulation of vibratory and acoustic environment generated by machines and vehicles represents a number of major challenges starting with fatigue and vibratory resistance of equipment to acoustic comfort including controlling acoustic annoyance. Due to the wide spectral audio content, only the Statistical Energy Analysis (SEA) method currently allows for building numerical models which encompass it. The theoretical framework of SEA is introduced starting with simple cases which show that vibratory phenomena may be translated into energy-power balanced equations between the various components of the dynamic system. The derivation of exchange coefficients which link components is explained as well as basic underlying assumptions in proposed models. When frequency increases, the energy stored in the mechanical and acoustic vibrations in a finite medium, tends to diffuse due to the large number of resonant modes. This diffusion process combined with a statistics of vibrational modes generates fast and robust computational algorithms highlighting underlying physics of vibroacoustic environments and allowing the taking over of them thanks to scientific software. A part of these algorithms is based on infinite medium coupling and the duality infinite/finite of the representation of vibratory phenomena in the high frequency domain. This duality is brought to the forefront in practical modeling cases (acoustic multilayers, vibratory isolation) for simulating vibratory and acoustic treatments currently used in vehicles.

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AUTHOR

  • Gérard BORELLO: Doctorate in acoustics - Design engineer and Managing Director of InterAC

 INTRODUCTION

Statistical Energy Analysis (SEA) of dynamics problems between coupled vibratory subsystems was born in the early 1960s from the work of R.H. Lyon and G. Maïdanik. This work was in response to the need for predictive analytical tools to calculate the random vibrations of civil and military launchers, developed in parallel by the US Navy and the US Air Force in the troubled context of the Cold War. Indeed, launchers and their payloads are subjected to very high dynamic stresses at lift-off and during atmospheric flight (noise at lift-off, wind gusts, combustion instabilities, stage separation shocks), which can damage structures and equipment. Failure of the inertial control unit that guides the vehicle can result in loss of control and its destruction. In this pre-computer era, the availability of simple calculation formulas for vibration prediction was therefore a strategic objective, in order to avoid superfluous testing and establish robust specifications qualifying all on-board equipment.

Today, these objectives have become civilized and are still relevant today. It is preferable to predict the vibratory environment resulting from a machine's operating mode at the start of a project, rather than suffer unpredictable consequences requiring modifications after the event, which are always costly and often ineffective when the design is fixed. Vibro-acoustic predictive methodologies are now being developed in all areas of industry, and particularly in the transportation sector.

The stated aim is to control the vibration environment right from the design stage, in order to reduce prototyping stages and project duration. Finite element analysis (FEA) is the key tool in these developments, but despite the dazzling progress made by the computer industry over the last twenty years, the calculation of noise transmitted into the passenger compartment of an automobile cannot yet be resolved over the entire audible spectrum by this method alone.

Computing power is always limited by the size of the discretized problems. In addition, physical laws may evolve with frequency, necessitating complex and time-consuming finite element analyses. This is why SEA analysis, despite or thanks to its simplifying assumptions, has slowly but surely found its place in the acoustical engineer's panoply of calculation methods. SEA is particularly effective for reliable vibration diagnostics or for establishing acoustic environment specifications for a project. However, it is essential to master its assumptions and limitations, which are outlined in the following pages.

Nota

A table of symbols and abbreviations is given at the end of the article.

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Statistical energy analysis (SEA) of the vibroacoustic environment
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