Energetic statistic analysis of the vibroacoustic environment

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.