Rapidly Measuring Elastic Coefficients Of New Piezoelectric Materials Using Resonant Ultrasound Spectroscopy

The rapid and accurate characterization of elastic coefficients c_ij is not only significant to the traditional characterization of mechanical properties of materials,but also important for the development of materials and devices,which has important academic value in exploring the essence of some phenomena in materials.Compared with other material characterization methods,the resonant ultrasound spectroscopy(RUS)has the advantages of high precision,wide application range and no restriction on the shape and size of materials.In recent years,the RUS-based material c_ij characterization has become increasingly demanding for rapidity.In this paper,aiming at the key problems that affect the rapid characterization based on RUS,a corresponding optimization method is proposed,which realizes the c_ij fast-dynamic characterization based on RUS.For the forward problem of RUS,the resonance spectrum is usually calculated by the frequency domain response method based on finite element method(FEM),which includes the intrinsic frequency and amplitude of resonance pulses.However,the calculation takes too much of time,and the process of measuring elastic material constants is rather long.In order to further shorten the measurement time,only the eigenfrequency is calculated using FEM in this paper.In order to solve the problem of artificial matching of repeated measured resonance spectrum data in the backward derivation of RUS.This paper proposes a Bayesian formulation of repeated measurements which introduces probability distributions for each resonant peak.Firstly,the parametric modeling of resonant spectral signal is performed.Then,the posteriori probabilities are deduced from the priori probabilities of the parameters according to the Bayesian model theory.Using reversible jump Markov chain Monte Carlo(RJ-MCMC)algorithm to sample the posterior probabilities,the probability estimates of the resonant peak parameters(number,frequency and amplitude)of the single measurement are obtained.Finally,every estimation resonance spectra are weighted by the Akaike Information Criterion.The resonance spectrum data fusion is realized by a Bayesian formulation of the repeated measurements.For the backward problem of RUS,the frequency matching needs to be manually performed between the predicted frequency and the measured frequency.the pairing probability of predicted frequency and measured frequency,and a probabilistic matching method are proposed.The larger matching probability is,the greater of the degree between the two frequencies matches.In addition,a high-performance optimization algorithm combining particle swarm optimization with simulated annealing algorithm(PSO-SA)is proposed,which is applied to solve the inverse operation of anisotropic material constant.Finally,this paper realizes the sample excitation and the data acquisition of resonance spectrum by means of the conventional universal ultrasonic measuring instrument RAM-5000/SNAP equipping with the corresponding transducer.We have accomplished the positive calculation of the sample eigenfrequency and automatic mode analysis with the use of commercial finite element software COMSOL and Matlab interface program,which makes the measurement of the material constants of irregular,arbitrary shape samples come true.we measured the elastic constants and piezoelectric constants of the anisotropic piezoelectric material La₃Ga₅Si O₁₄(LGS)and CNA_0.5G_0.5S(CNAGS),which verifies the modal probability matching method proposed in this paper.