Optimized finite difference iterative scheme based on POD technique for 2D viscoelastic wave equation

This study develops an optimized finite difference iterative （OFDI） scheme for the two-dimensional （2D） viscoelastic wave equation. The OFDI scheme is obtained using a proper orthogonal decomposition （POD） method. It has sufficiently high accuracy with very few unknowns for the 2D viscoelastic wave equation. Existence, stability, and convergence of the OFDI solutions are analyzed. Numerical simulations verify efficiency and feasibility of the proposed scheme.

Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave Equations with Degenerate Nonlocal Damping and Source Terms

This paper is concerned with a system of nonlinear viscoelastic wave equations with degenerate nonlocal damping and memory terms.We will prove that the energy associated to the system is unbounded.In fact,it will be proved that the energy will grow up as an exponential function as time goes to infinity,provided that the initial data are positive initial energy.

HIGH ACCURACY ANALYSIS OF THE FINITE ELEMENT METHOD FOR NONLINEAR VISCOELASTIC WAVE EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

The standard finite elements of degree p over the rectangular meshes are applied to solve a kind of nonlinear viscoelastic wave equations with nonlinear boundary conditions, and the superclose property of the continuous Galerkin approximation is derived without using the nonclassical elliptic projection of the exact solution of the model problem. The global superconvergence of one order higher than the traditional error estimate is also obtained through the postprocessing technique.

GENERAL DECAY RATE ESTIMATES FOR VISCOELASTIC WAVE EQUATION WITH VARIABLE COEFFICIENTS

The authors study decay properties of solutions for a viscoelastic wave equation with variable coefficients and a nonlinear boundary damping by the differential geometric approach.

Error Estimates of H^1-Galerkin Mixed Methods for the Viscoelasticity Wave Equation

H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.

On the Fundamental Mode Love Wave in Devices Incorporating Thick Viscoelastic Layers

A detailed investigation is presented for Love waves （LWs） with thick viscoelastic guiding layers. A theoretical calculation and an experiment are carried out for LW devices incorporating an SU-8 guiding layer, an ST-90° X quartz substrate and two 28-μm periodic interdigital transducers. Both the calculated and the measured results show an increase in propagation velocity when h / λ〉0.05. The measured insertion loss of LWs is consistent with the calculated propagation loss. The insertion loss of bulk waves is also measured and is compared with that of LWs.

EXPONENTIAL DECAY FOR A NONLINEAR VISCOELASTIC EQUATION WITH SINGULAR KERNELS

The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, for a class of kernels 9 which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.

Workflow to numerically reproduce laboratory ultrasonic datasets

The risks and uncertainties related to the storage of high-level radioactive waste （HLRW） can be reducedthanks to focused studies and investigations. HLRWs are going to be placed in deep geological repositories,enveloped in an engineered bentonite barrier, whose physical conditions are subjected tochange throughout the lifespan of the infrastructure. Seismic tomography can be employed to monitor itsphysical state and integrity. The design of the seismic monitoring system can be optimized via conductingand analyzing numerical simulations of wave propagation in representative repository geometry.However, the quality of the numerical results relies on their initial calibration. The main aim of this paperis to provide a workflow to calibrate numerical tools employing laboratory ultrasonic datasets. The finitedifference code SOFI2D was employed to model ultrasonic waves propagating through a laboratorysample. Specifically, the input velocity model was calibrated to achieve a best match between experimentaland numerical ultrasonic traces. Likely due to the imperfections of the contact surfaces, theresultant velocities of P- and S-wave propagation tend to be noticeably lower than those a prioriassigned. Then, the calibrated model was employed to estimate the attenuation in a montmorillonitesample. The obtained low quality factors （Q） suggest that pronounced inelastic behavior of the clay has tobe taken into account in geophysical modeling and analysis. Consequently, this contribution should beconsidered as a first step towards the creation of a numerical tool to evaluate wave propagation innuclear waste repositories. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Splitting positive definite mixed element method for viscoelasticity wave equation

A splitting positive definite mixed finite element method is proposed for second-order viscoelasticity wave equation. The proposed procedure can be split into three independent symmetric positive definite integro-differential sub-system and does not need to solve a coupled system of equations. Error estimates are derived for both semidiscrete and fully discrete schemes. The existence and uniqueness for semidiscrete scheme are proved. Finally, a numerical example is provided to illustrate the efficiency of the method.

Propagation characteristics of laser-generated like-Rayleigh waves in viscoelastic adhesive coating/substrate structures

The propagation characteristics of laser-generated like-Rayleigh waves in viscoelastic adhesive coating/substrate structures were studied.Considering the viscoelasticity of the coating and substrate,we have established the finite element models in frequency domain for the laser-generated like-Rayleigh waves in the epoxy coating/aluminum substrate,epoxy coating/brass substrate,and epoxy coating/foam substrate structures,respectively.In addition,we have investigated the waveform and propagation characteristics of the like-Rayleigh waves and studied the influences of the coating transparency,coating thickness,coating viscoelasticity,and substrate viscoelasticity on the propagation characteristics of the like-Rayleigh waves.Moreover,we have verified the results by the theoretical phase velocity and attenuation curves.The results show that the coating viscoelasticity induces the attenuation characteristics of the higher frequencies of the like-Rayleigh waves,but has little effect on the lower frequencies,and the substrate viscoelasticity has the influences on both the higher and lower frequencies of the like-Rayleigh waves,especially the lower frequencies.Furthermore,the mode and dispersive characteristics of the like-Rayleigh waves are closely related to the substrates.This study provides a useful theoretical basis for inverting mechanical parameters and evaluating the adhesive quality of the viscoelastic adhesive coating/substrate structures.