Amplitude-dependent Losses Research Articles

INVERSE ANALYSIS OF THE AMPLITUDE-DEPENDENT DAMPING PROPERTIES OF EPOXY/GLASS FIBER LAMINATES

In this paper, we present the experimental results obtained and corresponding inverse analysis employed to determine the amplitude-dependent damping properties of laminates made of glass fiber reinforced plastic (GFRP). Free damped vibration tests of cantilever beams with different symmetric stacking sequences were performed. Logarithmic decrement analysis was used to evaluate the effective amplitude-dependent loss factor of the samples. Inverse analysis was used to find the single-ply dynamic properties based on the laminated beam theory and the complex moduli approach. It was found that the loss factors of GFRP laminates almost linearly depend on the maximum strain amplitude. The maximum value of the loss factor of unidirectional ply was realized in the transverse direction to the fibers and reached ~ 0.023 for strain amplitudes up to 0.1% in the frequency range of 20-60 Hz.

Nonlinear acoustic effects in polycrystalline solids with saturation of amplitude-dependent internal friction

Theoretical and numerical studies of nonlinear acoustic effects arising from the propagation of initially harmonic waves in polycrystalline solids with saturation of amplitude-dependent internal friction have been carried out. Two main types of hysteresis are considered: elastic and inelastic. A comparative analysis of the regularities of nonlinear effects is carried out and the characteristics of nonlinear quasi-harmonic waves in such media are determined: amplitude-dependent losses and changes in propagation velocity, as well as amplitudes of higher harmonics. A method for determining the type of polycrystal hysteresis based on the analysis of theoretical and experimentally established amplitude dependences of nonlinear effects is proposed. Keywords: elastic waves, amplitude-dependent internal friction.

Нелинейные акустические эффекты в поликристаллических твердых телах с насыщением амплитудно-зависимого внутреннего трения

Theoretical and numerical studies of nonlinear acoustic effects arising from the propagation of initially harmonic waves in polycrystalline solids with saturation of amplitude-dependent internal friction have been carried out. Two main types of hysteresis are considered: elastic and inelastic. A comparative analysis of the regularities of nonlinear effects is carried out and the characteristics of nonlinear quasi-harmonic waves in such media are determined: amplitude-dependent losses and changes in propagation velocity, as well as amplitudes of higher harmonics. A method for determining the type of polycrystal hysteresis based on the analysis of theoretical and experimentally established amplitude dependences of nonlinear effects is proposed.

Effect of Water-to-Cement Ratio on Acoustic Nonlinearity of a Hardened Mortar

We present the results of experimental and theoretical studies of nonlinear acoustic phenomena (amplitude-dependent losses, resonant frequency shifts, generation of the second and third harmonics of a low-frequency (LF) wave, and self-action of ultrasonic finite-amplitude pulses) in rod resonators made of cement and river sand with various values of water–cement ratios (w/cs; 0.5, 0.6 and 0.9). We have also provided an analytical description of the observed phenomena within the frameworks of the phenomenological equations of state that contain LF hysteretic and high-frequency elastic nonlinearities. By analyzing the experimental and theoretical amplitude dependences of the nonlinear phenomena we determined values of the nonlinearity parameters of test materials. Comparison of changes in the measured nonlinear acoustic and strength properties of these materials demonstrates that an increase in the w/c, which leads to a decrease in the strength of the resulting mortars, also leads to an increase in its acoustic nonlinearity.

Temperature-controlled power modulation compensates for heterogeneous nanoparticle distributions: a computational optimization analysis for magnetic hyperthermia

Purpose: To study, with computational models, the utility of power modulation to reduce tissue temperature heterogeneity for variable nanoparticle distributions in magnetic nanoparticle hyperthermia.Methods: Tumour and surrounding tissue were modeled by elliptical two- and three-dimensional computational phantoms having six different nanoparticle distributions. Nanoparticles were modeled as point heat sources having amplitude-dependent loss power. The total number of nanoparticles was fixed, and their spatial distribution and heat output were varied. Heat transfer was computed by solving the Pennes’ bioheat equation using finite element methods (FEM) with temperature-dependent blood perfusion. Local temperature was regulated using a proportional-integral-derivative (PID) controller. Tissue temperature, thermal dose and tissue damage were calculated. The required minimum thermal dose delivered to the tumor was kept constant, and heating power was adjusted for comparison of both the heating methods.Results: Modulated power heating produced lower and more homogeneous temperature distributions than did constant power heating for all studied nanoparticle distributions. For a concentrated nanoparticle distribution, located off-center within the tumor, the maximum temperatures inside the tumor were 16% lower for modulated power heating when compared to constant power heating. This resulted in less damage to surrounding normal tissue. Modulated power heating reached target thermal doses up to nine-fold more rapidly when compared to constant power heating.Conclusions: Controlling the temperature at the tumor-healthy tissue boundary by modulating the heating power of magnetic nanoparticles demonstrably compensates for a variable nanoparticle distribution to deliver effective treatment.

Nonlinear Acoustic Effects in Rod Resonators with Rigid Boundaries

We theoretically study nonlinear acoustic effects (amplitude-dependent loss, resonant-frequency shift, and the second-harmonic generation) and determine the thresholds of parametric generation of subharmonic oscillations at fractional frequencies in the rod resonators with rigid boundaries and various nonlinearity types (elastic, hysteretic, different-modulus, etc.).

Viscoelastic internal damping finite-difference model for musical instruments physical model sound production

A viscoelastic model for the internal damping of musical instrument parts, like membranes or plates is implemented within a Finite-Difference Time Domain (FDTD) method. Internal damping of wood, leather, nylon, mylar, glue, or varnish strongly change the timbre of musical instruments and the precise spectrum of this damping contributes strongly to the individual instrument character. The model assumes a complex, frequency-dependent and linear stiffness in the frequency domain, which is analytically transferred into the time-domain using a Laplace transform. The resulting mass-weighted restoring force integral of the respective membrane or plate differential equation is solved using a circular buffer accumulation method for each spatial node on the geometry, which is effective, as the model is implemented on a massive parallel Graphics Processing Unit (GPU). The model is able to reproduce arbitrarily shaped internal damping frequency responses with sharp bandwidth and fast response. The model is also able to reproduce other energy distribution problems, like energy loss or even energy supply by different parts of musical instruments through coupling, time-dependent energy loss and supply behavior, or nonlinear damping behavior, like amplitude-dependent loss strength. So also internal damping of metamaterials can be calculated with this model.

Nonlinear acoustic phenomena in a quartzite rod resonator

Here we have presented the results of experimental and theoretical studies of nonlinear acoustic effects (such as low-frequency amplitude-dependent losses, resonant frequency shifts, and high harmonic generation as well as a damping and carrier phase delay of weak ultrasonic pulses under powerful low-frequency pumping wave) in a rod resonator made of a crystalline rock – quartzite. Also, we have given an analytical description of the observed phenomena within the frameworks of the phenomenological equations of state that contain low-frequency hysteretic nonlinearity and both dissipative and reactive high-frequency nonlinearities. Comparison of experimental and analytical amplitude–frequency dependencies of the nonlinear phenomena allowed us to determine quartzite acoustic nonlinearities parameter values.

The Wave Processes in the Media Having Inelastic Hysteresis with Saturation of The Nonlinear Loss

We study theoretically the nonlinear wave processes during excitation of a longitudinal harmonic wave in an unbounded medium and the rod resonator with inelastic hysteresis and saturation of the amplitude-dependent loss. The nonlinear-wave characteristics in such systems, namely, the amplitude-dependent loss, variation in the wave-propagation velocity, the resonant-frequency shift, and the higher-harmonic amplitudes are determined. The results of the theoretical and experimental studies of nonlinear effects in the rod resonator of annealed polycrystalline copper are compared. The effective parameters of the hysteretic nonlinearity of this metal are evaluated.

Nonlinear acoustic effects in a resonator with saturation of hysteretic loss

Nonlinear wave processes in an acoustic rod resonator with hysteretic nonlinearity under harmonic excitation are studied. The characteristics of longitudinal nonlinear modes of the resonator with hard and soft boundaries (amplitude-dependent loss, shifts of resonance frequencies, and amplitudes of the second and third harmonics) are determined. The comparison of the theoretical and experimental dependences of nonlinear acoustic effects in a resonator that is made of annealed polycrystalline copper is used to determine the parameters of the hysteretic nonlinearity.

Amplitude-Dependent Internal Friction and Harmonic Generation in Media with Hysteresis Nonlinearity and Linear Dissipation

Based on generalization and integration of models for dislocation mechanisms of the hysteresis nonlinearity, we propose a hysteresis equation of state of polycrystalline solids with saturated amplitude-dependent losses. Using the perturbation method, we study, both theoretically and numerically, the nonlinear effects during propagation of acoustic waves in the media with hysteresis nonlinearity and linear viscous dissipation. Nonlinear damping rate and propagation velocity of the wave at the fundamental frequency, as well as regularities for the amplitudes and phase velocities at its second and third harmonics, are determined. It is shown that the media described by such hysteresis equations of state have a nonlinear dispersion, which leads to a nonmonotonic rise and amplitude beats of the higher harmonics as the wave amplitude increases at the fundamental frequency.

Low- and high-frequency nonlinear acoustic phenomena in a magnesite

The results of experimental and theoretical studies of nonlinear acoustic phenomena (amplitude-dependent losses, resonant frequency shifts, damping of weak ultrasonic pulses and their carrier frequency phase delay under action of a powerful low-frequency pumping wave as well as amplitude-phase self-action of the finite-amplitude ultrasonic pulses) in a magnesite rod are presented. Analytical description of the observed phenomena was carried out within the frameworks of the phenomenological state equations that contain low-frequency hysteretic nonlinearity and both high-frequency dissipative and elastic nonlinearity. From comparison of experimental and analytical amplitude–frequency dependences of nonlinear phenomena, the values of magnesite acoustic nonlinearity parameters were determined. The frequency dependences have been discovered for hysteretic (in a range 3.6–17.2kHz) as well as dissipative and elastic nonlinearity (in a range 50–370kHz).

Calibration of a Quasi-Adiabatic Magneto-Thermal Calorimeter Used to Characterize Magnetic Nanoparticle Heating

To assess and validate temperature measurement and data analysis techniques for a quasi-adiabatic calorimeter used to measure amplitude-dependent loss power of magnetic nanoparticles exposed to an alternating magnetic field (AMF) at radiofrequencies (160 ± 5 kHz). The data collected and methods developed were used to measure the specific loss power (SLP) for two magnetic iron oxide nanoparticles (IONPs) suspensions, developed for magnetic nanoparticle hyperthermia. Calibration was performed by comparing measured against calculated values of specific absorption rate (SAR) of a copper wire subjected to AMF. Rate of temperature rise from induced eddy currents was measured (n = 4) for a copper wire of radius 0.99 mm and length of 3.38 mm in an AMF at amplitudes (H) of 16, 20, 24, and 28 kA/m. The AMF was generated by applying an alternating current using an 80-kW induction power supply to a capacitance network containing a 13.5-cm vertical solenoid that held the calorimeter. Samples were taped to an optical fiber temperature probe and inserted into a standard (polystyrene, 5 ml) test tube which was suspended in the calorimeter. The sample was subjected to the AMF for 30 s or until the temperature of the sample, increased by 30 °C, recorded at 0.3-s intervals. The SAR of the sample was normalized by H2f1/2, averaged, and compared to theoretical values. Iron (Fe) normalized SLPs of two IONPs (JHU-MION and bionized-nanoferrite (BNF) particles (Micromod Partikeltechnologie, GmbH)) in aqueous suspension were measured in the same setup. We report experimental SAR values for the copper of 2.4 ± 0.1, 4.3 ± 0.2, 6.2 ± 0.1, and 8.5 ± 0.1 W/g compared to theoretical values 3.1 ± 0.1, 4.5 ± 0.2, 6.5 ± 0.1, and 9.2 ± 0.2 W/g at AMF amplitudes of 16 ± 0.1, 20 ± 0.2, 24 ± 0.1, and 28 ± 0.1 kA/m, respectively. Normalized experimental data followed a linear trend approximately parallel to theoretical values with an R2-value of 0.99. The measured SLPs of the JHU particles are higher than BNF particles within the tested AMF amplitude range of 15 kA/m to 45 kA/m. We demonstrated that copper can be used to calibrate magneto-thermal calorimetric systems used for SLP measurements of magnetic nanoparticles for a field range of 15–28 kA/m at 160 ± 5 kHz. We also note that the electrical conductivity, diameter of copper sample and accuracy, and response time of thermometry constrain calibration to lower amplitudes, highlighting the need for development of standard reference materials for such applications.

Amplitude-dependent internal friction, hysteretic nonlinearity, and nonlinear oscillations in a magnesite resonator

The results of experimental and theoretical studies of low-frequency nonlinear acoustics phenomena (amplitude-dependent loss, resonance frequency shifts, and a generation of second and third harmonics) in a magnesite rod resonator are presented. Acceleration and velocity oscillograms of vibrations of the free boundary of the resonator caused by harmonic excitations were measured and analyzed. A theoretical description of the observed amplitude dependences was carried out within the framework of the phenomenological state equations that contain either of the two types of hysteretic nonlinearity (elastic and inelastic). The type of hysteresis and parameters of acoustic nonlinearity of magnesite were established from comparing the experimental measurements with the theoretical dependences. The values of the parameters were anomalously high even when compared to those of other strongly nonlinear polycrystalline materials such as granite, marble, limestone, sandstone, etc.

Self-modulation of acoustic waves in resonant bars

Observations of the induced transparency in the oscillations of a glass bar containing an “artificial crack” in the form of a saw-cut with a tightly inserted small metal plate are reported. In such a configuration, the increase of the resonator quality factor with increasing wave amplitude (denoting a decrease of dissipation which will be referred to as self-induced transparency) has been observed indicating an important role of the amplitude-dependent losses introduced by the inter-surface contacts. The self-induced transparency manifests itself also by the discontinuities (jumps) in the acoustic wave amplitude measured as a function of sweeping excitation frequency around the sample eigenfrequencies and by a self-modulation instability of the primary acoustic wave. This instability leads to the generation of side-lobes in the wave spectrum near the fundamental excitation frequency. The developed theoretical model confirms that all these observations can be self-consistently attributed to nonlinearity of the sound dissipation process. Possible physical mechanisms of the nonlinear dissipation are discussed. Although self-modulation has already been observed in nonlinear acoustical systems, to the knowledge of the authors, the reported data constitute the first observation of the instabilities due to essentially dissipative system behaviour that requires neither nonlinear elasticity nor multimode interaction.

Relation between the tidal modulation of seismic noise and the amplitude-dependent loss in rock

Geological materials and many other microinhomogeneous media exhibit pronounced nonlinear properties under very small strains, when one may expect an almost linear behavior of the material. These properties are conventionally described on the basis of elastically nonlinear or hysteretic models. The present paper discusses the amplitude-dependent dissipation that is unrelated to hysteretic nonlinearity but is also a universal property of microinhomogeneous media. This property allows the explanation of the effect of correlation between the tidal strains of the Earth’s crust (on the order of 10−8) and the unexpectedly strong (on the order of 10−2–10−1) variations of seismic noise intensity, which has been observed for more than 25 years without being given any adequate interpretation.

Experimental study of nonlinear acoustical effects in limestone

Results of an experimental and theoretical study of nonlinear acoustic effects (amplitude-dependent loss, resonance frequency shift, second and third harmonic generation, and sound by sound damping) in a limestone bar resonator are reported. The observed effects are analytically described in the framework of phenomenological equations of state with allowance for the low-frequency hysteretic nonlinearity and the high-frequency dissipative nonlinearity. Experimental and analytical dependences of nonlinear effects are compared to find the parameters of the hysteretic and dissipative nonlinearities of the limestone sample studied.

Amplitude-dependent losses in ultrasound exposure measurement

Energy losses resulting from the nonlinear propagation of ultrasonic pulses in water have been measured using a polyvinylidene difluoride membrane hydrophone and a radiation-force balance. The focused ultrasonic transducers used were of low focal gain operating at source intensities and frequencies typical of those used in medical diagnostic applications. Energy transfer into harmonic components has been quantified by hydrophone measurements at the focus. At values of shock parameter sigma>pi/2, total loss of intensity was observed, with the greatest loss reaching 2.75 dB of the intensity predicted by linear extrapolation from low-amplitude measurements. A similar but smaller-magnitude reduction in the radiation force measured by a force balance was observed. These results are related to ranges of acoustic parameters obtained from surveys on clinical equipment. It is concluded that a significant majority of contemporary clinical scanners can generate ultrasonic pulses which will lose energy during transmission through water due to amplitude-dependent nonlinear losses, and that it is necessary to consider these, and other nonlinear phenomena, when predicting exposure conditions in vivo.

Nonlinear acoustics of micro-inhomogeneous media

Acoustic waves can interact in micro-inhomogeneous media much more intensively than in homogeneous media. This has been repeatedly observed in experiments with ground species, marine sediments, porous materials and metals. This paper considers two models of such media which seem to be applicable to the description of these results. One of them is based on the consideration of nonlinear sound scattering by separate spherical cavities in liquids and solids. The second model is based on the phenomenological stress-deformation relation in solids with microplasticity which often has hysteresis (heritage) properties associated with the micro-inhomogeneities. In metals, for example, it is caused by the movement of dislocations. Different nonlinear effects in such media (harmonic and combination frequency generation, nonlinear, variations of resonance frequency amplitude-dependent losses) are considered. Some results of experiments with metallic resonators supporting the theory developed here are also presented. These mechanisms may determine the nonlinear properties of real soils and rocks summarized in a table given in the paper.

A 310 mmφ torsional type antenna for gravitational experiments at low temperature

A torsional type antenna with a diameter of 310 mm, which is the maximum size of an extruded aluminium alloy bar commercially available, is developed for gravitational experiments at low temperature. The antenna shows a very long relaxation time of an externally excited oscillation; τ = 1.78 × 10 5 s corresponding to Q = 3.30 × 10 7 at liquid helium temperature. The decay characteristic is studied over a few relaxation periods to confirm a single exponential decay at small oscillation amplitude. An amplitude dependent loss is observed above a certain oscillation level at low temperature. The dynamic character of the antenna is studied between room temperature and liquid helium temperature.