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EXISTENCE OF GLOBAL SMOOTH SOLUTION TO INITIAL BOUNDARY VALUE PROBLEM FOR A viscoelastic model WITH RELAXATION

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Acta Mathematica Scientia 2004年第2期24卷 265-274页

作者：阮立志朱长江 LaboratoryofNonlinearAnalysis Dept.ofMath.CentralChinaNormalUniversityWuhan430079China

This paper is concerned with the initial boundary value problem for a viscoelastic model with relaxation. Under the only assumption that the C^0-norm of the initial data is small, without smallness hypothesis for the C^1-norm, the existence of the global smooth solution to the corresponding initial boundary value problem is proved. The analysis is based on some a priori estimates obtained by the 'maximum principle' of first-order quasilinear hyperbolic system.

关键词： viscoelastic model relaxation a priori estimates maximum principle

Finite-difference modeling of Maxwell viscoelastic media developed from perfectly matched layer

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Petroleum Science 2023年第5期20卷 2759-2772页

作者： Ruo-Long Song College of Physics Jilin UniversityChangchun130012JilinChina

In numerical simulation of wave propagation,both viscoelastic materials and perfectly matched layers(PMLs)attenuate *** wave equations for both the viscoelastic model and the PML contain convolution ***,convolution operator is intractable in finite-difference time-domain(FDTD)method.A great deal of progress has been made in using time stepping instead of convolution in *** incorporate PML into viscoelastic media,more memory variables need to be introduced,which increases the code complexity and computation *** modifying the nonsplitting PML formulation,I propose a viscoelastic model,which can be used as a viscoelastic material and/or a PML just by adjusting the *** proposed viscoelastic model is essentially equivalent to a Maxwell *** with existing PML methods,the proposed method requires less memory and its implementation in existing finite-difference codes is much *** attenuation and phase velocity of P-and S-waves are frequency independent in the viscoelastic model if the related quality factors(Q)are greater than *** numerical examples show that the method is stable for materials with high absorption(Q=1),and for heterogeneous media with large contrast of acoustic impedance and large contrast of viscosity.

关键词： Finite difference viscoelastic model Nonsplitting perfectly matched layer

Experimental measurement and numerical analysis of fused taper shape for optical fiber coupler

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Journal of Central South University of Technology 2007年第2期14卷 251-254页

作者：帅词俊段吉安钟掘 School of Mechanical and Electrical Engineering Central South university

To find out the effect of the shape of fused taper region on the optical fiber coupler, the fiber couplers were fabricated at different drawing speeds with a six-axes fiber coupler machine. The results, which were obtained fi＇om the shape of fused taper region measured with microscope, show that there is a close correlation between the cone angle and optical performance of fiber coupler. High-performance fiber coupler cannot be obtained until rheological shape is controlled accurately. The numerical analysis model, which was built based on generalized Maxwell viscoelastic theory, is resolved with ANSYS software. The calculated results accord with the experimental data. It can apply a theoretic basis for forecasting the shape of fiber coupler fabricated under the conditions of different technological parameters.

关键词： optical fiber coupler fused biconical taper viscoelastic model rheological shape

TRANSVERSAL INERTIAL EFFECT ON RELAXATION/RETARDATION TIME OF CEMENT MORTAR UNDER HARMONIC WAVE

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Acta Mechanica Solida Sinica 2008年第1期21卷 44-50页

作者： Jue Zhu Yonghui Cao Jiankang Chen Mechanics and Materials Science Research Center Ningbo University Ningbo 315211 China

Under dynamic loading, the constitutive relation of the cement mortar will be significantly affected by the transversal inertial effect of specimens with large diameters. In this paper, one-dimensional theoretical analysis is carried out to determine the transversal inertial effect on the relaxation/retardation time of the cement mortar under the harmonic wave. Relaxation time or retardation time is obtained by means of the wave velocity, attenuation coefficient and the frequency of the harmonic wave. Thus, the transversal inertial effect on the relaxation time from Maxwell model, as well as on retardation time from Voigt model is analyzed. The results show that the transversal inertial effect may lead to the increase of the relaxation time, but induce the decrease of the retardation time. Those should be taken into account when eliminating the transversal inertial effect in applications.

关键词： cement mortar harmonic wave viscoelastic model relaxation/retardation time

Prediction of viscoelastic Behavior of Unidirectional Polymer Matrix Composites

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Journal of Wuhan University of Technology(Materials Science) 2016年第3期31卷 695-699页

作者：张小玉 HUANG Qianyu 陈建中 LI Zhuoqiu School of Science Wuhan University of TechnologyWuhan 430070China Wuhan Boiler Group Chaoshun Boiler Equipment Manufacture Co. LtdWuhan 430070China

To develop a novel method predicting the viscoelastic behavior of polymer matrix composites according to the viscoelasticity of the matrix, we used the viscoelastic model of the matrix to build new models for unidirectional composites in both 0° and 90° directions. viscoelastic parameters for both new models were derived, and the obtained equations shared the same form as the viscoelastic constitutive equation of matrix material. The viscoelastic behaviors of matrix material and unidirectional composites were also tested. Results showed that fitting parameters of creep compliance equation were close to the theoretical values of viscoelastic constitutive parameters of the unidirectional composites, proving the validity of the models. A new method was obtained to predict the viscoelastic property of the unidirectional composites based on the viscoelastic property of composite matrix and elastic property of the unidirectional composites. This method provides a theoretical basis for future studies on the viscoelasticity of composite laminates.

关键词： viscoelastic model polymer matrix composites creep microscopic-mechanical models long-term behavior

ON THE CALCULATION OF ENERGY RELEASE RATE FOR viscoelastic CRACKED LAMINATES

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Applied Mathematics and Mechanics(English Edition) 2003年第1期24卷 14-21页

作者：刘玉岚王彪王殿富 Research Center for Composite Materials Harbin Institute of Technology Harbin 150001 China

The energy release rate(ERR) of crack growth as the energy change at the same time t between the two states of the structure is redefined, one is with crack length a under the loading σ(t), the other is the state with crack length a+ Δ a under the same loading condition. Thus the defined energy release rate corresponds to the released energy when a crack grows from a to a+ Δ a in an infinitesimal time. It is found that under a given loading history, the ERR is a function of time, and its maximum value should correspond with the critical state for delamination to propagate. Following William’s work, the explicit expressions of ERR for DCB experimental configurations to measure the interfacial fracture toughness have been obtained through the classical beam assumption.

关键词： composite laminate viscoelastic model analysis delamination

Temperature Dependency of Dynamic Mechanical Properties of Cement Asphalt Paste by DMTA Method

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Journal of Wuhan University of Technology(Materials Science) 2017年第6期32卷 1379-1387页

作者：方雷 YUAN Qiang PAN Yunrui WANG Yong KHAYAT Kamal 邓德华 School of Civil Engineering National Engineering Laboratory for Construction of High Speed Railway Central South UniversityChangsha 410075 China Department of Civil Architectural and Environmental Engineering Missouri University of Science and Technology Rolla MO United States

We investigated the temperature dependency of the dynamic mechanical properties of cement asphalt paste by the dynamic mechanical thermal analysis（DMTA） method. The experimental results show that the dynamic mechanical properties of cement asphalt pastes are sensitive to temperature due to the inclusion of asphalt, and may go through different states within a temperature range of-40 ℃ to 60 ℃, which is different from that of pure cement and asphalt. As the temperature of the cement asphalt paste increases, a considerable change of dynamic mechanical properties, including storage modulus（E＇）, loss modulus（E＇＇） and loss factor（tand） is observed. Moreover, the influence of asphalt to cement（A/C） ratio on the temperature sensitivity of the dynamic mechanical properties of cement asphalt composites was investigated. The temperature dependency of cement asphalt composites is ascribed to the temperature dependency of the asphalt and its interaction with cement paste. A simple fractional model is proposed to describe the viscoelastic behavior of cement asphalt composites.

关键词： cement asphalt paste dynamic mechanical property dynamic mechanical thermal analysis viscoelastic model

ANALYSIS model ON GRADUAL CHANGE PRINCIPLE OF EFFECT ZONES OF LAYER FACE FOR ROLLED CONTROL CONCRETE DAM

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Applied Mathematics and Mechanics(English Edition) 2006年第11期27卷 1523-1529页

作者：顾冲时宋敬衖方海挺 College of Water Conservancy and Hydropower Engineering Hohai UniversityNanjing 210098P. R. China Zhejiang Design Institute of Water Conservancy & Hydro-electric Power Hangzhou 310002P. R. China

The effect zones of layer face for RCC （rolled control concrete） dam have gradual change characteristics. Based on the analysis thought of complex material, a model was built to analyze above principle of RCC dam by use of series-wound and shunt-wound connection. Some methods were proposed to determine the instantaneous Young＇s modulus, delayed Young＇s modulus and viscosity coefficient of effect zones of layer face. Above models and methods were used to mine the principle of gradual change of key calculation parameters which can response the characteristics of effect zones. The principle of gradual change was described. A model was established to analyze the threedimensional viscoelastic problem of RCC dam. Above programs were developed. The examples show that the proposed models and methods to determine the key calculation parameters of effect zones can reflect the status of RCC dam accurately.

关键词： (rolled control concrete dam) effect zones calculation parameter principle of gradual change viscoelastic model

Principal Resonance of Parametrically Excited Moving viscoelastic Belts with Geometrical Nonlinearity

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Tsinghua Science and Technology 2004年第3期9卷 331-337页

作者：侯之超祖武争 State Key Laboratory of Automotive Safety and Energy Department of Automotive Engineering Tsinghua University Beijing 100084 Department of Mechanical and Industrial Engineering University of Toronto Toronto Canada

Nonlinear dynamic analysis is performed on moving belts subjected to geometric nonlinearity and initial tension fluctuation. To incorporate more accurately the damping mechanism of belt material, linear viscoelastic models are adopted in a unified form of differential operators. To circumvent high-order differential vibration equation of time-varying coefficients and with gyroscopic and nonlinear terms, where analytical solution is almost impossible, a systematic approach is presented by reforming the motion equation and directly using the method of multiple scales. To exemplify the procedure, the solutions at principal resonance are obtained and their stability conditions are derived for employing a Kelvin-Voigt model to reflect the property of the belt material. The solutions and stability conditions successfully reduce to those for using Kelvin model and elastic model, which validate the present approaches. Numerical simulations highlight the effects of tension fluctuations and translating speeds on the stability of the belt vibration.

关键词： belt drive moving string viscoelastic model parametric excitation stability analytical solution