Complex Elastic Coefficients Research Articles

Engineering nonreciprocal wave dispersion in a nonlocal micropolar metabeam

Active metamaterials with electronic control schemes can exhibit nonreciprocal and/or complex elastic coefficients that result in non-Hermitian wave phenomena. Here, we investigate theoretically and experimentally a non-Hermitian micropolar metabeam with piezoelectric elements and electronic nonlocal feed-forward control. Since the nonlocal feed-forward control breaks spatial reciprocity, the proposed metabeam supports nonreciprocal flexural wave propagation, featuring unidirectional amplification/attenuation and non-Hermitian skin effect. Theoretical homogenization modeling is developed to consider the nonlocal effect into an effective complex bending stiffness. The unidirectional wave amplification/attenuation is attributed to the energy conversion between electrical power and mechanical work. The non-Hermitian skin effect, characterized by a winding number, is the manifestation of the flexural nonreciprocity and admits an extensive number of localized bulk eigenmodes on open boundaries. The nonlocal metabeam is also employed to engineer the anomalous wave dispersion such as tunable roton-like dispersion and band tilting. The nonlocal micropolar metabeam could pave the ways for designing non-Hermitian topological mechanical metamaterials featuring programmable nonreciprocal wave transmission and engineering roton-like wave dispersion relations under ambient environments.

Propagation of seismic waves in patchy‐saturated porous media: double‐porosity representation

ABSTRACTPropagation of harmonic plane waves is studied in a patchy‐saturated porous medium. Patchy distribution of the two immiscible fluids is considered in a porous frame with uniform skeletal properties. A composition of two types of patches, connected through continuous paths, constitutes a double‐porosity medium. Different compressibilities of pore‐fluids in two porous phases facilitate the wave‐induced fluid‐flow in this composite material. Constitutive relations are considered with frequency‐dependent complex elastic coefficients, which define the dissipative behaviour of porous aggregate due to the flow of viscous fluid in connected patches. Relevant equations of motion are solved to explain the propagation of three compressional waves and one shear wave in patchy‐saturated porous solids. A numerical example is solved to illustrate dispersion in phase velocity and quality factor of attenuated waves in patchy‐saturated porous materials. Role of fluid–solid inertial coupling in Darcy's law is emphasized to keep a check on the dispersion of wave velocities in the porous composite. Effects of patchy saturation on phase velocities and quality factors of attenuation are analysed using the double‐porosity formulation as well as the reduced single‐porosity equivalents.

Complex elastic coefficient and mechanical losses for piezoelectric resonators under transversal and thickness modes

ABSTRACTThe performance of piezoelectric transducers depends upon a set of physical parameters. Among them, losses are one of the most important. Mechanical losses in piezoelectric devices are studied using complex numbers in the elastic coefficients of the models. Usually, numerical methods are employed to obtain the loss parameters through the minimization of an error function. We insert mechanical losses dependent on frequency in Mason's model to evaluate how this dependency affects the electrical impedance curve. The results show that a better curve fitting is achieved when the mechanical loss is a first order function of frequency.

Complex Elastic Properties and Piezoelectric Activity in Stoichiometric and Congruent LiNbO3 Single Crystals

Piezoelectric effect has been measured for stoichiometric (Li/Li + Nb = 50 mole%) and congruent (Li/Li + Nb = 48.6 mole%) lithium niobate crystals. Observations of the piezoelectric resonance allowed to investigate the temperature dependence of the complex elastic coefficient s*11. Distinct local maxima on the s″11(T) dependencies have been found.

Accurate determination of complex materials coefficients of piezoelectric resonators.

This paper presents a method of accurately determining the complex piezoelectric and elastic coefficients of piezoelectric ceramic resonators from the measurement of the normalized electric admittance, Y, which is electric admittance Y of piezoelectric resonator normalized by the angular frequency omega. The coefficients are derived from the measurements near three special frequency points that correspond to the maximum and the minimum normalized susceptance (B) and the maximum normalized conductance (G). The complex elastic coefficient is determined from the frequencies at these points, and the real and imaginary parts of the piezoelectric coefficient are related to the derivative of the susceptance with respect to the frequency and the asymmetry of the conductance, respectively, near the maximum conductance point. The measurements for some lead zirconate titanate (PZT) based ceramics are used as examples to demonstrate the calculation and experimental procedures and the comparisons with the standard methods.

Determination of the Elastic Properties of a Li 2 B 4 O 7 Single Crystal from the Piezoelectric Resonance

For materials with piezoelectric activity the application of forced harmonic oscillator model with complex amplitude gives the possibility to determine the complex elastic coefficient s = s - is . Temperature dependence of the complex elastic coefficient s E 11 has been investigated for a Li 2 B 4 O 7 single crystal in the temperature range 20-200 °C. It was shown that the imaginary part s " E 11 is more sensitive to abnormal behaviour of physical properties than the real part s ' E 11 . Distinct maximum of s " E 11 was observed at 68°C and 93°C. Between these temperature points the piezoelectric response splits into two resonances. Clear anomalies simultaneously on s ' E 11 ( T ) and s " E 11 ( T ) dependencies accompany a phase transition at 155°C.

A study of loss in piezoelectric ceramic resonators

Piezoelectric resonators and filters are important components in many military and commercial communication systems. Standard piezoelectric materials such as quartz have low coupling values and are quite expensive to fabricate. Newer materials like piezoceramics have been developed that are cheaper, have higher values of coupling constant, but can be considerably more lossy than single-crystal materials. The purpose of this work is to explore loss mechanisms through the use of complex elastic coefficients in the piezoelectric constitutive relations and the differential equations for a simple one-dimensional (1-D) resonator. Results will be presented that show how the complex elastic coefficients modify the acoustic wave velocity, the coupling constant, and the resonant frequencies of the resonator. An equivalent circuit model of a resonator will also be presented with and without loss to compare with the calculated results. An experiment has been designed to better characterize loss in devices by applying an exponentially decaying sine wave. In theory this type of signal should be able to excite the complex resonance of the device. Results will be presented for thickness-excited PZT resonators, and the results will be compared to the circuit models and the 1-D calculations.

The Simulation of Solid-Borne Noise in Buildings

Solid-borne noise in a building was calculated by a large computer. The building was modeled as assemblies of two dimensional beams. Bending displacements and elongations of beams with complex elastic coefficients were calculated

Temperature dependence of the electromechanical properties of ceramic polymer composite materials for hydrophone applications

The real and imaginary parts of the complex elastic, dielectric, and piezoelectric properties of two types of commercial piezoelectric composite materials were studied as a function of temperature from − 70°C to + 50°C using an electrical resonance technique described previously [J. Acoust. Soc. Am. Suppl. 1 82, S101 (1987)]. These materials consist of ceramic particles embedded in a polymer material and possess improved hydrostatic sensitivity as well as mechanical flexibility in comparison with conventional piezoelectric ceramics. Measurements of the temperature dependence of the hydrostatic piezoelectric coefficients have also been performed. The interrelationship of the properties is complicated by the presence of the glass transition of the elastomeric phase of the composite material where sharp changes in the electmechanical transition causes typical relaxation behavior in the complex elastic coefficients and a peak in the dielectric properties. The transition was studied further by the use of differential scanning calorimetry in order to corroborate the results of the resonance measurements. The results demonstrate some difficulties in using these particular materials and indicate that other polymeric materials should be investigated for use in these composite materials. [Work supported by ONR.]

Synthetic seismograms and the response of an anisotropic attenuating medium : Can J Earth Sci, V14, N5, May 1977, P1062–1076

The Haskell–Thomson matrix formulation has been modified to yield synthetic seismograms and theoretical spectral ratios in a system of parallel anisotropic lossy layers. Transfer function matrices are derived for the case of transverse isotropy with a unique vertical axis. Attenuation is included in the analysis through the use of complex elastic coefficients. Short period spectral ratios and time syntheses are found to be significantly affected by the presence of uniaxial anisotropy for a typical continental crustal model while long period spectral ratios are shown to be sensitive to anisotropy in the upper mantle. Normal values of Q for the crust produce almost no change in teleseismic spectral ratios at useful frequencies. Synthetic seismograms for a continental crust indicate that crustal reverberations of teleseismic impulses are attenuated within 5 s of onset

Synthetic seismograms and the response of an anisotropic attenuating medium

The Haskell–Thomson matrix formulation has been modified to yield synthetic seismograms and theoretical spectral ratios in a system of parallel anisotropic lossy layers. Transfer function matrices are derived for the case of transverse isotropy with a unique vertical axis. Attenuation is included in the analysis through the use of complex elastic coefficients. Short period spectral ratios and time syntheses are found to be significantly affected by the presence of uniaxial anisotropy for a typical continental crustal model while long period spectral ratios are shown to be sensitive to anisotropy in the upper mantle. Normal values of Q for the crust produce almost no change in teleseismic spectral ratios at useful frequencies. Synthetic seismograms for a continental crust indicate that crustal reverberations of teleseismic impulses are attenuated within 5 s of onset