We have investigated the temperature dependence of elastic modulus for various ferroelectric ceramics in the temperature range of 20–90 °C. The Na0.5Bi0.5TiO3 (NBT) ceramics has a phase transition at 200 °C, thus exhibits minimal change in elastic modulus up to 90 °C, while the elastic modulus of the BaZr0.07Ti0.93O3 (BZT-7) shows 12.5 % change at the phase transition temperature of 70 °C and that of the BaZr0.15Ti0.85O3 (BZT-15) ceramics shows 34.6 % change at the phase transition temperature of 60 °C. The variations of elastic modulus will affect the temperature stability of devices made by these lead-free ferroelectric ceramics.

High order nonlinear behaviors in Pb(Zr1−x,Tix)O3 (PZT) ceramics were studied using the harmonic generation technique, both before and after poling. It was found that the amplitude of the third harmonic is smaller than that of the second harmonic before poling, but the situation is reversed after poling with a substantial increase of the third harmonic amplitude. Noticeable time dependence of nonlinearities were observed in poled ceramics, which gradually decreased and saturated after about two days. These facts confirmed the generation of microcracks during poling.Highlights► The 2nd and 3rd order nonlinearities have been studied in PZT ceramics. ► Before poling the 2nd harmonic of PZT is larger than that of the 3rd harmonic. ► After poling the nonlinear behavior becomes mixed classic and non-classic type. ► The nonlinear phenomena in PZT change with time initially but saturate after two days.

•Harmonics and modulated wave filtering were used to show the retrofocal quality.•We testify the feasibility of the NEWS–TR method for microdamage imaging of defects.•The influence of frequency on the prediction of the defects was discussed.In non-classical nonlinear media, much characteristic information is contained in their dynamic elastic responses. A method combining nonlinear elastic wave spectroscopy (NEWS) with a time-reversal (TR) process is used in this numerical study, in which the presence of one defect and two defects acting with non-classical nonlinearity in an attenuating medium is simulated. Nonlinear defect behavior is introduced using a modified Preisach–Mayergoyz (PM) model. Two methods are used to determine retrofocal quality: harmonic filtering and modulated wave filtering. In the simulation, the nonlinear signal is filtered from the received continuous wave, then reversed and re-sent; a crack image can be obtained from the nonlinear signal in a lossy solid. By comparison with the actual defect, the image can reflect the distribution of one or two flaws, which show the feasibility and value of the NEWS–TR methodology for microdamage imaging of two defects. These results also show that images obtained with different harmonic and modulated frequencies can reflect the presence of defects. With increasing frequency, the crack positions obtained from the image change due to the influence of solid loss and interaction with sound waves.

High order nonlinear behaviors in Pb(Zr1−x,Tix)O3 (PZT) ceramics were studied using the harmonic generation technique, both before and after poling. It was found that the amplitude of the third harmonic is smaller than that of the second harmonic before poling, but the situation is reversed after poling with a substantial increase of the third harmonic amplitude. Noticeable time dependence of nonlinearities were observed in poled ceramics, which gradually decreased and saturated after about two days. These facts confirmed the generation of microcracks during poling.Highlights► The 2nd and 3rd order nonlinearities have been studied in PZT ceramics. ► Before poling the 2nd harmonic of PZT is larger than that of the 3rd harmonic. ► After poling the nonlinear behavior becomes mixed classic and non-classic type. ► The nonlinear phenomena in PZT change with time initially but saturate after two days.

•The beam coefficients of the zero-order quasi-Bessel-Gauss beam are proposed.•The quasi-Bessel-Gauss beam can perform negative axial radiation forces.•Beam width significantly influences the radiation force on sphere of bigger radius for quasi-Bessel-Gauss beam.By means of series expansion theory, the incident quasi-Bessel-Gauss beam is expanded using spherical harmonic functions, and the beam coefficients of the quasi-Bessel-Gauss beam are calculated. According to the theory, the acoustic radiation force function, which is the radiation force per unit energy on a unit cross-sectional surface on a sphere made of diverse materials and immersed in an ideal fluid along the propagation axis of zero-order quasi-Bessel-Gauss progressive and standing beams, is investigated. The acoustic radiation force function is calculated as a function of the spherical radius parameter ka and the half-cone angle β with different beam widths in a progressive and standing zero-order Bessel-Gauss beam. Simulation results indicate that the acoustic radiation forces with different waist radii demonstrate remarkably different features from those found in previous studies. The results are expected to be useful in potential applications such as acoustic tweezers.

•The Gaussian quasi-standing waves are expressed in terms of spherical wave functions.•The radiation force on a sphere in Gaussian quasi-standing waves is expressed.•The radiation force is computed when the sphere is translated axially.•The feasibility of a Gaussian standing wave trapping is demonstrated theoretically.Based on the finite series method, the Gaussian standing or quasi-standing beam is expressed in terms of spherical wave functions and a weighting parameter, which describe the beam shape and location relative to the particle. An expression is derived for the radiation force on a sphere centered on the axis of a Gaussian standing or quasi-standing wave propagating in an ideal fluid. Rigid, fluid, elastic, and viscoelastic spheres immersed in water are treated as examples. In addition, a method is proposed to compute the axial acoustic radiation force when the sphere is translated axially. Results indicate the capability of the proposed method to manipulate and separate spheres based on their mechanical and acoustical properties. The interaction of a Gaussian quasi-standing beam with a sphere can result in periodic axial force under specific operating conditions. The results presented here may provide a theoretical basis for the development of acoustical tweezers in a Gaussian standing beam, which would be useful in micro-fluidic lab-on-chip applications.

The third-order nonlinearity parameter C/A for biological media is studied theoretically and experimentally. Based on the theory of fluid dynamics, the generalized Burgers equation is extended to the third order for biological media. A perturbation solution of the equation is carried out and the formula for C/A for biological media is derived. The sound pressure of the third harmonics changing with distance in water is measured and compared with the theoretical results. An experimental set-up is established for measurement of C/A for biological media and the values of the acoustic nonlinearity parameter C/A are measured for several porcine samples. The results show that the values of C/A for the measured biological tissues are in the range of 60.0–120.0 while the values B/A for the measured biological tissues are in the range 6.5–11.0. The maximum relative deviation for C/A among the measured biological tissues is 81.2% while it is only 66.2% for B/A. Therefore, C/A may be more appropriate for tissue characterization compared with B/A.