Dissipative and hysteresis loops as images of irreversible processes in nonlinear acoustic fields

Abstract

Irreversible processes taking place during nonlinear acoustic wave propagation are considered using a representation by loops in a thermodynamic parameter space. For viscous and heat conducting media, the loops are constructed for quasi-harmonic and sawtooth waves and the descriptive equations are formulated. The linear and nonlinear absorptions are compared. For relaxing media, the processes are frequency-dependent. The loops broadens, narrows, and bends. The linear and nonlinear relaxation losses of wave energy are shown. Residual stresses and irreversible strains appear for hysteretic media, and here, a generalization of Rayleigh loops is pictured which takes into account the nonlinearly frequency-dependent hereditary properties. These describe the dynamic behavior, for which new equations are derived.

Hysteresis curves and loops for harmonic and impulse perturbations in some non-equilibrium gases

“…In a thermoconducting gas, loops of the curve ρ ( ) may form over the domains, where pressure decreases with time. Generally, hysteresis curves do not longer start from the point (0 0) [17]. A difference in the hysteresis curves between two considered examples of gases with relaxation is caused by a difference in acoustic sources of the thermal mode.…”

“…Ultrasonic relaxation makes it possible to heat or to cool a medium remotely. First authors who have attracted attention to the pressurevolume diagrams, hysteresis curves and loops, and physical distinction between different irreversible processes accompanying nonlinear propagation of intense sound in fluids, were Rudenko, Hedberg [17]. They have outlined an analogy and difference between hysteresis in Newtonian fluids and solids.…”

“…(12), is also valid in the quasi-planar geometry of slowly divergent sound beams. The hysteresis curves in the plane of thermodynamic states may be useful in reconstruction of dispersive and viscous properties of a medium [1,17], including these anomalous and in evaluation of a degree of disequilibrium. equals the inverse time The analogous problems in optics are usually solved by laser spectroscopy [27].…”

“…They have outlined an analogy and difference between hysteresis in Newtonian fluids and solids. The study [17] considers loops in the plane of acoustic perturbations for periodic harmonic and saw-tooth sound in a Newtonian fluid and in a fluid with relaxation which is described by some kernel in integral link between acoustic pressure and excess acoustic density. It includes important conclusions about dissipative and hysteresis processes in linear and nonlinear acoustic fields in fluids.…”

“…The thermodynamic cycles in a strain-stress diagrams for solid materials with hysteresis nonlinearity are usually represented by loops [15,16]. Less pronounced, but similar loops are typical in Newtonian thermoconducting fluids [17]. Hedberg, Rudenko were the first who have attracted attention to hysteresis in Newtonian and relaxing fluids.…”