An eigen theory of waves in piezoelectric solids

Based on the standard spaces of the physical presentation, both the quasi-static mechanical approximation and the quasi-static electromagnetic approximation of piezoelectric solids are studied here. The complete set of uncoupled elastic wave and electromagnetic wave equations are deduced. The results show that the number and propagation speed of elastic waves and electromagnetic waves in anisotropic piezoelectric solids are determined by both the subspaces of electromagnetically anisotropic media and ones of mechanically anisotropic media. Based on these laws, we discuss the propagation behaviour of elastic waves and electromagnetic waves in the piezoelectric material of class 6 mm.

ANALYTICAL SOLUTION FOR MODE Ⅲ DYNAMIC RUPTURE OF STANDARD LINEAR VISCOELASTIC SOLID WITH NONLINEAR DAMPING

Introducing the nonlinear Rayleigh damping into the governing equation of the Mode Ⅲ dynamic rupture for standard viscoelastic solid, this equation is a partial differential and integral equation. First, eliminating the integral term, a PDE of third_order is obtained. Then, applying the small parameter expansion method, linearized asymptotic governing equation for each order of the small parameter is obtained. Dividing the third_order PDE into an elastic part with known solution, the rest part pertains to viscous effect which is neither a Mathieu equation nor a Hill one. The WKBJ method is still adopted to solve it analytically.

Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model

The weakly forced vibration of an axially moving viscoelastic beam is inves- tigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration are derived from the dynamical, constitutive, and geometrical relations. The method of multiple scales is used to determine the steady-state response. The modulation equation is derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response are derived from the modulation equation. The stability of non- trivial steady-state response is examined via the Routh-Hurwitz criterion.

THE NEW MODEL FOR CALCULATION OF STANDARD ENTROPIES OF SOLID COMPOUNDS Ⅲ CALCULATION FOR STANDARD ENTROPIES OF SOLID BINARY OXIDES

This paper establishes a new model for calculation of the standard entropies of solid binary oxides as follows: S_(29)=27.07×Φ_1+1.120×Φ_2+n_1×k×Φ, -22.19 e.u (R=0.9960) We have invesigated 103 binary oxides. and found good agreemenl between estimated and experimental entropies.

Time-dependent viscoelastic properties along rat small intestine

AIM： To measure the time-dependent （viscoelastic） behavior in the change of the small intestinal opening angle and to test how well the behavior could be described by the Kelvin model for a standard linear solid. METHODS： Segments from the duodenum, jejunum, and ileum were harvested from 10 female Wistar rats and the luminal diameter, wall thickness, and opening angle over time （θ（t）） were measured from rings cut from these segments. RESULTS： Morphometric variations were found along the small intestine with an increase in luminal area and a decrease in wall thickness from the duodenum to the ileum. The opening angle obtained after 60 rain was highest in the duodenum （220.8±12.9°）and decreased along the length of the intestine to 143.9±8.9° in the jejunum and 151.4±9.4° in the ileum. The change of opening angle as a function of time, fitted well to the Kelvin model using the equation θ（t）/θo = [1-ηexp （-λt）] after the ring was cut. The computed creep rate λ. did not differ between the segments. Compared to constant calculated from pig aorta and coronary artery, it showed that α agreed well （within 5%）, η was three times larger than that for vascular tissue, and λ ranged ±40% from the value of the pig coronary artery and was a third of the value of pig aorta. CONCLUSION： The change of opening angle over time for all the small intestine segments fits well to the standard linear spring-dashpot model. This viscoelastic constant of the rat small intestine is fairly homogenous along its length. The data obtained from this study add to a base set of biomechanical data on the small intestine and provide a reference state for comparison to other tissues,diseased intestinal tissue or intestinal tissue exposed to drugs or chemicals.

Transient vibration of thin viscoelastic orthotropic plates

This article deals with solutions of transient vibration of a rectangular viscoelastic orthotropic thin 2D plate for particular deformation models according to Flu¨gge and Timoshenko-Mindlin.The linear model,a general standard viscoelastic body,of the rheologic properties of a viscoelastic material was applied.The time and coordinate curves of the basic quantities displacement,rotation,velocity,stress and deformation are compared.The results obtained by an approximate analytic method are compared with numerical results for 3D plate generated by FEM application and with experimental investigation.

Viscosity Transient Phenomenon in Drop Impact Testing of Soft Material

The authors carried out drop impact tests for several soft materials under a flat frontal impact condition in which a drop hammer with a flat bottom surface strikes a plate-like soft material in the normal direction. The experimental results indicated that the impact force waveforms of soft materials consisted of a thorn-shaped waveform and a subsequent mountain-shaped waveform. The thorn-shaped waveform was strongly affected by the strain rate. In the present study, the occurrence mechanism of this distinctive waveform was discussed from the viewpoint of the viscosity transient phenomenon. A standard linear solid (SLS) model in which the viscosity transient phenomenon was considered was applied to the simulation. Some features of the impact force waveform of soft materials could be explained by the SLS model. Furthermore, the thorn-shape waveform could also be observed in the impact force waveforms of human skin and free-falling hollow balls.

The Effect of Strain Rate on Tensile Properties of Cotton Yarns

The effect of strain rate on tensile properties of cotton yarns is analyzed using the standard linear solid model. The tensile curve, breaking strength and work of rupture of the yarns under different strain rate are calculated. A good correlation exists between the experiment results and theoretical anticipations.

Experimental Study on Wave Propagation in One-Dimensional Viscoelastic Metamaterial

A locally resonant viscoelastic mass-spring cell is experimentally realized by a unit cell design fabricated by 3D printing.The standard linear solid model is introduced for the viscoelastic metamaterial.The complex band structures of both viscoelastic unit cell and elastic cases are presented to show the effect of viscoelasticity.Both the harmonic excitation and stochastic excitation are conducted on the finite viscoelastic metamaterial in experiments.Distinct wave attenuation is found in bandgap via sweep frequency response analysis under harmonic excitation.The experiments of the metamaterial under narrow-band noise excitation demonstrate good performance of wave attenuation in bandgap.Finally,the obtained bandgaps via numerical calculation are well consistent with the frequency ranges of wave attenuation from experiments,which confirm the effectiveness of the proposed viscoelastic model.

Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

We develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation.The material model is a super-imposition of N standard linear solid mechanisms,which commonly is used in seismology to model a material with constant quality factor Q.The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables,making it significantly more memory efficient than the commonly used first order velocitystress formulation.The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation[SIAM J.Numer.Anal.,45(2007),pp.1902–1936].Our main result is a proof that the proposed discretization is energy stable,even in the case of variable material properties.The proof relies on the summation-by-parts property of the discretization.The newscheme is implemented with grid refinement with hanging nodes on the interface.Numerical experiments verify the accuracy and stability of the new scheme.Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy.We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.