Feynman diagram theory for multifrequency nonlinear acoustics

The Feynman diagram theory with the state-space formalism is adopted to study the multifrequency nonlinear acoustics effects. By establishing the relation between the strain magnitude corresponding to any final state S(m1,…,mn; x) and the number of paths from the initial state of the interactingphonons to the final state, not only the complete perturbation solutions but also the corresponding analytical expressions of the acoustic harmonics and intermodulation products have been obtained. For a few special cases, results of our theory is consistent with those obtained by conventional methods. While the general solution for any number of frequencies can easily be obtained by our theory, this is impossible by using conventional methods.

Nonlinear wave propagation in acoustic metamaterials with bilinear nonlinearity

Nonlinear phononic crystals have attracted great interest because of their unique properties absent in linear phononic crystals.However,few researches have considered the bilinear nonlinearity as well as its consequences in acoustic metamaterials.Hence,we introduce bilinear nonlinearity into acoustic metamaterials,and investigate the propagation behaviors of the fundamental and the second harmonic waves in the nonlinear acoustic metamaterials by discretization method,revealing the influence of the system parameters.Furthermore,we investigate the influence of partially periodic nonlinear acoustic metamaterials on the second harmonic wave propagation,and the results suggest that pass-band and band-gap can be transformed into each other under certain conditions.Our findings could be beneficial to the band gap control in nonlinear acoustic metamaterials.

The(1+1)-dimensional nonlinear ion acoustic waves in multicomponent plasma containing kappa electrons

Large amplitude (1+1)-dimensional nonlinear ion acoustic waves are theoretically studied in multicomponent plasma consisting of positively charged ions and negatively charged ions, ion beam, kappa-distributed electrons, and dust grains,respectively. By using the Sagdeev potential method, the dynamical system and the Sagdeev potential function are obtained.The important influences of system parameters on the phase diagram of this system are investigated. It is found that the linear waves, the nonlinear waves and the solitary waves are coexistent in the multicomponent plasma system. Meanwhile,the variations of Sagdeev potential with parameter can also be obtained. Finally, it seems that the propagating characteristics of (1+1)-dimensional nonlinear ion acoustic solitary waves and ion acoustic nonlinear shock wave can be influenced by different parameters of this system.

Cumulative solutions of nonlinear longitudinal vibration in isotropic solid bars

Based on the strain invariant relationship and taking the high-order elastic energy into account, a nonlinear wave equation is derived, in which the excitation, linear damping, and the other nonlinear terms are regarded as the first-order correction to the linear wave equation. To solve the equation, the biggest challenge is that the secular terms exist not only in the fundamental wave equation but also in the harmonic wave equation （unlike the Duffing oscillator, where they exist only in the fundamental wave equation）. In order to overcome this difficulty and to obtain a steady periodic solution by the perturbation technique, the following procedures are taken： （i） for the fundamental wave equation, the secular term is eliminated and therefore a frequency response equation is obtained; （ii） for the harmonics, the cumulative solutions are sought by the Lagrange variation parameter method. It is shown by the results obtained that the second- and higher-order harmonic waves exist in a vibrating bar, of which the amplitude increases linearly with the distance from the source when its length is much more than the wavelength; the shift of the resonant peak and the amplitudes of the harmonic waves depend closely on nonlinear coefficients; there are similarities to a certain extent among the amplitudes of the odd- （or even-） order harmonics, based on which the nonlinear coefficients can be determined by varying the strain and measuring the amplitudes of the harmonic waves in different locations.

Concrete damage diagnosed using the non-classical nonlinear acoustic method

It is known that the strength of concrete is seriously affected by damage and cracking. In this paper, six concrete samples under different damage levels are studied. The experimental results show a linear dependence of the resonance frequency shift on strain amplitude at the fundamental frequency, and approximate quadratic dependence of the am- plitudes of the second and third harmonics on strain amplitude at the fundamental frequency as well. In addition, the amplitude of the third harmonics is shown to increase with the increase of damage level, which is even higher than that of the second harmonics in samples with higher damage levels. These are three properties of non-classical nonlinear acoustics. The nonlinear parameters increase from 106 to 108 with damage level, and are more sensitive to the damage level of the concrete than the linear parameters obtained by using traditional acoustics methods. So, this method based on non-classical nonlinear acoustics may provide a better means of non-destructive testing （NDT） of concrete and other porous materials.

Multi-crack imaging using nonclassical nonlinear acoustic method

Solid materials with cracks exhibit the nonclassical nonlinear acoustical behavior. The micro-defects in solid materials can be detected by nonlinear elastic wave spectroscopy （NEWS） method with a time-reversal （TR） mirror. While defects lie in viscoelastic solid material with different distances from one another, the nonlinear and hysteretic stress-strain relation is established with Preisach-Mayergoyz （PM） model in crack zone. Pulse inversion （PI） and TR methods are used in numerical simulation and defect locations can be determined from images obtained by the maximum value. Since false-positive defects might appear and degrade the imaging when the defects are located quite closely, the maximum value imaging with a time window is introduced to analyze how defects affect each other and how the fake one occurs. Furthermore, NEWS-TR- NEWS method is put forward to improve NEWS-TR scheme, with another forward propagation （NEWS） added to the existing phases （NEWS and TR）. In the added phase, scanner locations are determined by locations of all defects imaged in previous phases, so that whether an imaged defect is real can be deduced. NEWS-TR-NEWS method is proved to be effective to distinguish real defects from the false-positive ones. Moreover, it is also helpful to detect the crack that is weaker than others during imaging procedure.

Receptivity of hypersonic boundary layer due to fast-slow acoustics interaction

The objective of receptivity is to investigate the mechanisms by which external disturbances generate unsta- ble waves. In hypersonic boundary layers, a new receptivity process is revealed, which is that fast and slow acoustics through nonlinear interaction can excite the second mode near the lower-branch of the second mode. They can generate a sum-frequency disturbance though nonlinear interaction, which can excite the second mode. This receptivity process is generated by the nonlinear interaction and the nonparal- lel nature of the boundary layer. The receptivity coefficient is sensitive to the wavenumber difference between the sumfrequency disturbance and the lower-branch second mode. When the wavenumber difference is zero, the receptivity coefficient is maximum. The receptivity coefficient decreases with the increase of the wavenumber difference. It is also found that the evolution of the sum-frequency disturbance grows linearly in the beginning. It indicates that the forced term generated by the sum-frequency disturbance resonates with the second mode.

Nonlinear acoustic waves in a collisional self-gravitating dusty plasma

Using the reductive perturbation method, we investigate the small amplitude nonlinear acoustic wave in a collisional self-gravitating dusty plasma. The result shows that the small amplitude dust acoustic wave can be expressed by a modified Korteweg-de Vries equation, and the nonlinear wave is instable because of the collisions between the neutral gas molecules and the charged particles.

Molecular structure dependence of acoustic nonlinearity parameter B/A for silicone oils

Exploring new acoustic parameters is essential to develop a noninvasive imaging technique for the surgery of silicone oil tamponades. In this study, the acoustic nonlinearity parameters B/A of varied silicone oil samples （e.g., linear or hyper-branched） are experimentally measured by using a modified thermodynamic method. The results show that： （i） when the concentration of the silicone oil with a molecular weight of 5 × 10^4 increases from 0.5 g/100 ml to 8 g/100 ml, the corresponding B/A value increases by about 18%, but the acoustic velocity only increases by about 0.1%; （ii） when the molecular weight of the hyper-branched silicone oil is enhanced from 2 × 10^5 to 1 × 10^6, the B/A value increases by about 22%, while the acoustic velocity is only raised by about 0.2%. This study suggests that the B/A parameter of the silicone oil is more sensitive to the change in its molecular structure than that of the acoustic velocity. Thus, the B/A parameter might be utilized as an effective index for the development and optimization of the noninvasive imaging of the surgery of silicone oil tamponades.

Microcrack localization using a collinear Lamb wave frequency-mixing technique in a thin plate

A novel Lamb wave frequency-mixing technique is proposed for locating microcracks in a thin plate,which does not require the resonance condition of Lamb wave mixing and can accurately locate the microcracks through only one-time sensing.Based on the bilinear stress-strain constitutive model,a two-dimensional finite element(FE)model is built to investigate the frequency-mixing response induced by the interaction between two primary Lamb waves and a microcrack.When two primary Lamb waves of A0 and S0 modes with different frequencies excited on the same side of the plate simultaneously impinge on the examined microcrack,under the modulation of the contact acoustic nonlinearity,the microcrack itself can be deemed as the secondary sound source and it will radiate the Lamb waves of new combined frequencies.Based on the time of flight of the generated A0 mode at difference frequency,an indicator named normalized amplitude index(NAI)is defined to directly locate the multi-microcracks in the given plate.It is found that the number and location of the microcracks can be intuitively visualized by using the NAI based frequency-mixing technique.It is also demonstrated that the proposed frequency mixing technique is a promising approach for the microcrack localization.

Ultrasonic study on organic liquid and binary organic liquid mixtures by using Schaaffs＇ collision factor theory

Based on Schaaff＇s collision factor theory （CFT） in liquids, the equations for nonlinear ultrasonic parameters in both organic liquid and binary organic liquid mixtures are deduced. The nonlinear ultrasonic parameters, including pressure coefficient, temperature coefficients of ultrasonic velocity, and nonlinear acoustic parameter B/A in both organic liquid and binary organic liquid mixtures, are evaluated for comparison with the measured results and data from other sources. The equations show that the coefficient of ultrasonic velocity and nonlinear acoustic parameter B/A are closely related to molecular interactions. These nonlinear ultrasonic parameters reflect some information of internal structure and outside status of the medium or mixtures. From the exponent of repulsive forces of the molecules, several thermodynamic parameters, pressure and temperature of the medium, the nonlinear ultrasonic parameters and ultrasonic nature of the medium can be evaluated. When evaluating and studying nonlinear acoustic parameter B/A of binary organic liquid mixtures, there is no need to know the nonlinear acoustic parameter B/A of the components. Obviously, the equation reveals the connection between the nonlinear ultrasonic nature and internal structure and outside status of the mixtures more directly and distinctly than traditional mixture law for B/A, e.g. Apfel＇s and Sehgal＇s laws for liquid binary mixtures.

A semi-analytical method to compute acoustic nonlinearity parameter of Cu,Ag and Au

In this paper,a semi-analytical method was proposed to evaluate the acoustic nonlinearity parameter for single crystals of Cu,Ag and Au.The acoustic nonlinearity parameter can be derived analytically by general expressions in terms of the interatomic potentials with the distances between each pair of atoms in these transition metals.To evaluate the acoustic nonlinearity parameter,one needs to conduct one step molecular static simulation and obtain the equilibrium positions of all the atoms.Further,based on this method,numerical experiments with molecular dynamic code LAMMPS were given to compute the acoustic nonlinearity parameter of Cu,Ag and Au.To illustrate the validity of these expressions,comparison was made between calculation results and data in the literature.Reasonable agreement is observed.Because of the analytical nature of this method,it provides a fundamental understanding of the nonlinear elastic behavior of these transition metals.

Modeling of the nonlinear acoustic field generated from a phased array using Gaussian superposition technique

The nonlinearity has significant effect on the ultrasonic therapy using phased ar- rays. A numerical approach is developed to calculate the nonlinear sound field generated from a phased array based on the Gaussian superposition technique. The parameters of the phased array elements are first estimated from the focal parameters using the inverse matrix algorithm; Then the elements are expressed as a set of Gaussian functions; Finally, the nonlinear sound field can be calculated using the Gaussian superposition technique. In the numerical simulation, a 64~ 1 phased array is used as the transmitter. In the linear case, the difference between the results of the Gaussian superposition technique and the Fresnel integral is less than 0.5%, which verifies the feasibility of the approach. In the nonlinear case, the nonlinear fields of single-focus modes and double-focus modes are calculated. The results reveal that the nonlinear effects can improve the focusing performance, and the nonlinear effects are related with the source pressures and the excitation frequencies.

Nonlinearity acoustic parameter B/A in organic liquids

Based on Jacobson's free length theory and the dependence of ultrasonic velocity on the free length in organic liquids, the equation of nonlinearity acoustic parameter B/A was given, and the calculated nonlinearity acoustic parameter B/A in some organic liquids are in good agreement with the measured results.

Acoustic Nonlinearity Parameters Due to Microstructural Defects

This study presents a general approach to derive the acoustic nonlinearity parameters induced by various types of dislocation configurations including dislocation strings （monopoles）, dislocation dipoles, dislocation pileups and extended dislocations. It is found that expressions of the acoustic nonlinearity parameter induced by such a variety of dislocation con- figurations share a common mathematical form. They are all scaled with （Lch/b）n, where Lch is a characteristic length of the dislocation configuration, b is the magnitude of the Burgers vector, and n is either 3 or 4. Semiquantitative analysis is presented to compare the magnitudes of the acoustic nonlinearity parameters among different types of dislocation configurations.

The influence of molecular structure of protein on the acoustic nonlinearity parameter B/A

In this paper, the influence of molecular structure of proteins on the acoustic non-linearity parameter B/A has been studied. By using biochemical technique, three proteins such as bovine serum albumin, bovine hemoglobin and pepsin were employed and their quarternary,tertiary and secondary protein structures were perturbed by the denaturing agent sodium do-decyl sulfate (SDS) solution, while their primary structures of protein were not changed. This means that only the structural features were altered and the chemical composition maintained unchanged. B/A has been measured by using improved thermodynamic method. The experi-mental results show that when the concentration of SDS solution increases, the alterations of the protein structure increase, and the contribution of protein to the B/A value decreases. Re-sults indicate that the B/A values can display the destruction of molecular structure of protein.Some explanation of these phenomena has also been made in this paper.

A numerical study of noise reduction in ducts with flow by anti-sound

Using the measures adopted in fluid mechanics, a numerical method of noise reduction in duct with flow by anti-sound is established, in which a mathematical anti-sound model is deduced strictly. Several numerical examples are given in the cascs of backward and forward sound propagation to illustrate the influence of anti-sound on sound field in duct and to discuss the effects of intensity and phase angle of anti-sound sources, and the effect of flow velocity.It is shown that noise reduction by anti-sound does have a bright prospect in engineering applications.