Abstract
Statistical vibroacoustics, also called statistical energy analysis (SEA) in the field of engineering, is born from the application of statistical physics concepts to the study of random vibration in mechanical and acoustical systems. This article is a discussion on the thermodynamic foundation for that approach with particular emphasis devoted to the meaning of entropy, a concept missing in SEA. The theory focuses on vibration confined to the audio frequency range. In this frequency band, heat is defined as random vibration that is disordered vibration and temperature is the vibration energy per mode. Always in this frequency band, the concept of entropy is introduced and its meaning and role in vibroacoustics are enlightened, together with the related evolutionary equation. It is shown that statistical vibroacoustics is non-equilibrium thermodynamics applied to the audio range.
Highlights
Thermodynamics can be viewed as the theory of transformation of work, that is the mechanical energy with slowing varying forces to heat, that is vibration energy in thermal range while statistical vibroacoustics focuses on the only audio frequency range
The statistical approach applied to vibroacoustics is not fundamentally different from non-equilibrium thermodynamics
The concepts of vibrational temperature, vibrational heat and vibrational entropy and their relationships exactly match with the classical definitions and relationships in thermodynamics
Summary
Vibracoustics is the science of structural waves, acoustical waves and their interaction. Vibroacoustics is usually divided into the study of propagation of waves, natural modes, radiation of sound, sound transparency and structural response. This science is at the interface of acoustics and elastodynamics that is the theories of propagation of small perturbations in fluids. The major advance was to recognize that sound radiation is mainly due to edges, corners and other singularities With these two approaches, wave method for infinite or semi-infinite problems and modal decomposition for finite structures, almost all canonical problems of sound radiation and structural response have been solved either with exact or approximated solutions. This limit is not so high (Table 1) in regards to the audio frequency range 20 Hz–20 kHz
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