A nonlinear equation of state and the corresponding wave equation are derived in the framework of a rheological model suggested for elastic media containing defects with relaxation. The defects in the model are considered as highly compliant visco-elastic inclusions that exhibit a nonlinear
stress-strain dependence. For real solids, these inclusions may model, for example, cracks, intergrain contacts and other similar defects. The proposed model thus can be applied to a wide class of microinhomogeneous materials (Earth rocks, engineering materials, damaged metals, etc.), which
are also called "mesoscopic" solids. The derived equations consistently comprise the following material properties connected to the presence of the defects: (i) the microstructure-induced absorption (including near-constant Q-factor), (ii) the complementary dispersion of sound velocity,
(iii) increased magnitude of the "mesoscopic" elastic nonlinearity and (iv) frequency dependence of the nonlinearity. To illustrate the aforementioned manifestations of the material microstructure, a few basic nonlinear effects (second and difference-frequency harmonics generation, and self-demodulation
of high-frequency pulses) are analyzed in the framework of the derived equations. Main distinctions of the effects compared to the case of "classical" lattice (atomic) nonlinearity of homogeneous solids are pointed out.
Document Type: Research Article
Publication date: January 1, 2002
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Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.