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Dynamic Response of Fractional-Order Viscoelastic High-Order Shear Beam Based on Nonlocal Strain Gradient Elasticity

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Acta Mechanica Solida Sinica 2023年第6期36卷 875-883页

作者： Yuqian Xu peijun wei Department of Applied Mechanics University of Science and Technology BeijingBeijing 100083China

The dynamic behavior of a viscoelastic high-order shear microbeam is studied based on a new constitutive model which incorporates size effects and viscoelasticity *** size effects are modeled by the nonlocal gradient elasticity,while viscoelastic effects are modeled by fractional-order *** constitutive relation and the equations of motion are both differential equations with fractional-order *** on the Laplace transform and inverse transform,the analytical solution of the dynamic response under a step load is obtained in terms of the Mittag–Leffler *** order to verify the reliability of the analytical solution,a comparison with the numerical solution is also *** on the numerical results,the effects of the nonlocal parameter,strain gradient parameter,fractional-order parameter,and viscosity coefficient on the dynamic response of the viscoelastic microbeam are *** is found that the influences of the fractional order and the coefficient of viscosity on the dynamic response of the microbeam are very different,although both are related to the viscoelastic behavior.

关键词： Nonlocal strain gradient Higher-order beam Fractional-order derivatives Viscoelasticity Laplace transform Mittag–Leffler function

Influences of interphase on dynamic effective properties of composites reinforced by dispersed spherical particles

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维普期刊数据库

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Journal of University of Science and Technology Beijing 2006年第3期13卷 256-262页

作者： peijun wei Lili Gu Applied Sciences School University of Sciences and Technology Beijing Beijing 100083 China Tangshan Iron ＆ Steel Group Co. Ltd Tangshan 063016 China

The influences of interphase on dynamic effective properties of composites reinforced by randomly dispersed spherical particles were studied. A thin homogeneous elastic interphase with different shear and bulk moduli, located between the reinforced particle and the host matrix, was introduced to model the interfacial bonding state. The effects of such an interphase on the coherent plane waves were studied numerically. Numerical simulations were carried out for SiC-Al composites with four typical cases of interphase. It was found that the property of interphase has significant influences on the effective propagation constants of coherent waves and the dynamic effective elastic moduli of the composites. The influences on the coherent longitudinal wave and the coherent shear waves were different and dependent upon the frequency range. Moreover, several imperfect interface models, i.e., the spring model, mass model, and spring-mass model, were studied numerically and compared with the interphase model, It was found that the spring model is a more suitable model than the mass model for the light and weak interphase whereas the mass model is a more suitable model than the spring model for the heavy and strong interphase.

关键词： composites effective property coherent wave interface model interphase multiple scattering

Propagation of Thermo-Elastic Waves at Several Typical Interfaces Based on the Theory of Dipolar Gradient Elasticity

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Acta Mechanica Solida Sinica 2018年第2期31卷 229-242页

作者： Yueqiu Li peijun wei Department of Mathematics Qiqihar University Department of Applied Mechanics University of Science and Technology Beijing

The reflection and transmission properties of thermo-elastic waves at five possible interfaces between two different strain gradient thermo-elastic solids are investigated based on the generalized thermo-elastic theory without energy dissipation （the GN theory）. First, the function of free energy density is postulated and the constitutive relations are defined. Then, the temperature field and the displacement field are obtained from the motion equation in the form of displacement and the thermal transport equation without energy dissipation in the strain gradient thermo-elastic solid. Finally, the five types of thermo-elastic interracial conditions are used to calculate the amplitude ratios of the reflection and transmission waves with respect to the incident wave. Further, the reflection and transmission coefficients in terms of energy flux ratio are calculated and the numerical results are validated by the energy conservation along the normal direction. It is found that there are five types of dispersive waves, namely the coupled longitudinal wave （the CP wave）, the coupled thermal wave （the CT wave）, the shear wave, and two evanescent waves （the coupled SP wave and SS wave）, that become the surface waves at an interface. The mechanical interfacial conditions mainly influence the coupled CP waves, SV waves, and surface waves, while the thermal interracial conditions mainly influence the coupled CT waves.

关键词： Gradient elasticity Thermo-elasticity Interfacial condition Reflection Transmission

THE DIRECTION DEPENDENCE OF SURFACE WAVE SPEED AT THE SURFACE OF MAGNETO-ELECTRO-ELASTIC HALF-SPACE

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Acta Mechanica Solida Sinica 2015年第1期28卷 102-110页

作者： Li Li peijun wei Department of Applied Mechanics University of Sciences and Technology Beijing

The direction dependence of surface wave speed and the influence of electrically and magnetically short/open circuit are investigated in this paper. First, the elastic, piezoelectric and piezomagnetic coefficients in the considered ordinate system are obtained by Bonde transformation from those in the crystal axis ordinate system. Then, the secular equation of surface wave is derived from the free traction condition on the surface of half space with consideration of short/open circuit case. Some numerical examples are given. The direction dependence of surface wave speed and the influences of short/open circuit are shown graphically and discussed based on the numerical results.

关键词： surface wave piezoelectric and piezomagnetic short and open circuit Bonde trans-formation piezoelectric enhanced effects

Reflection and transmission of elastic waves at five types of possible interfaces between two dipolar gradient elastic half-spaces

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Acta Mechanica Sinica 2017年第1期33卷 173-188页

作者： Yueqiu Li peijun wei Department of Mathematics Qiqihar University Department of Applied Mechanics University of Sciences and Technology Beijing

Reflection and transmission of an incident plane wave at five types of possible interfaces between two dipolar gradient elastic solids are studied in this paper. First, the explicit expressions of monopolar tractions and dipolar tractions are derived from the postulated function of strain energy density. Then, the displacements, the normal derivative of displacements, monopolar tractions, and dipolar tractions are used to create the nontraditional interface conditions. There are five types of possible interfaces based on all possible combinations of the displacements and the normal derivative of displacements. These interfacial conditions with consideration of microstructure effects are used to determine the amplitude ratio of the reflection and transmission waves with respect to the incident wave. Further, the energy ratios of the reflection and transmission waves with respect to the incident wave are calculated. Some numerical results of the reflection and transmission coefficients are given in terms of energy flux ratio for five types of possible interfaces. The influences of the five types of possible interfaces on the energy partition between the refection waves and the transmission waves are discussed, and the concept of double channels of energy transfer is first proposed to explain the different influences of five types of interfaces.

关键词： Gradient elasticity Interfacial condition Energy flux ratio Amplitude ratio Dipolar traction

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分数阶粘弹性地基上裂纹梁的自由振动

力学季刊 2024年第3期45卷 877-886页

作者：张骏魏培君周小利王刚河北工程大学土木工程学院河北邯郸056038 北京科技大学应用力学系北京100083 河北工程大学计算力学与工程应用研究中心河北邯郸056038

本文研究了分数阶粘弹性Pasternak地基上含多裂纹Euler梁的自由振动问题.首先,引入分数阶导数概念,建立粘弹性Pasternak地基模型,推导出地基应力-应变本构的复模量以及地基反力.其次,将裂纹等效成无质量扭转弹簧,借助于裂纹能量释放率... 详细信息

本文研究了分数阶粘弹性Pasternak地基上含多裂纹Euler梁的自由振动问题.首先,引入分数阶导数概念,建立粘弹性Pasternak地基模型,推导出地基应力-应变本构的复模量以及地基反力.其次,将裂纹等效成无质量扭转弹簧,借助于裂纹能量释放率和应力强度因子的关系,推导出梁的局部柔度.然后,基于传递矩阵方法,建立含多裂纹梁的分段传递矩阵进而得到总体传递矩阵.最后,基于梁的边界条件,建立求解裂纹梁的复固有频率及振型的线性代数方程组,数值求解得到含多裂纹梁的固有频率及振型.以含双裂纹的两端简支Euler梁为例,数值计算了复固有频率和振型.并基于曲率模态分析裂纹位置对复固有频率和振型的影响.数值结果揭示了粘弹性地基的分数阶系数、粘性系数以及裂纹位置和裂纹深度对复固频率和振型的影响规律.

关键词：裂纹梁分数阶导数粘弹性地基复固有频率局部柔度法传递矩阵法

Free vibration of thermo-elastic microplate based on spatiotemporal fractional-order derivatives with nonlocal characteristic length and time

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Applied Mathematics and Mechanics(English Edition) 2023年第1期44卷 109-124页

作者： Lingkang ZHAO peijun wei Yueqiu LI Department of Applied Mechanics University of Science and Technology BeijingBeijing 100083China Department of Mathematics Qiqihar UniversityQiqihar 161006Heilongjiang ProvinceChina

A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear *** nonlocal strain gradient theory is modified with the introduction of the fractional-order derivatives and the nonlocal characteristic *** Fourier heat conduction is replaced by the non-Fourier heat conduction with the introduction of the fractional order and the memory characteristic *** calculations are performed to analyze the effects of the nonlocal strain gradient parameters,the spatiotemporal fractional order,the nonlocal characteristic length,and the memory characteristic time on the natural frequencies,the vibration attenuation,and the phase shift between the temperature field and the displacement *** numerical results show that the new thermo-elastic model with the spatiotemporal fractional order can provide more exquisite descriptions of the thermo-elastic behavior at a small scale.

关键词： orthotropic higher-order plate nonlocal strain gradient thermo-elastic coupling fractional-order derivative free vibration

Influences of interfacial damage on the effective wave velocity in composites with reinforced particles

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Science China(Physics,Mechanics & Astronomy) 2008年第8期51卷 1126-1133页

作者： LIU XiQiang wei peijun Department of Mathematics&Mechanics University of Science and Technology BeijingBeijing 100083China

The scattering of elastic waves by a spherical particle with imperfect interface and the multiple scattering by many spherical particles with imperfect interface are studied in this paper. First,the scattering of elastic waves by a spherical particle with imperfect interface,i.e. spring interface model,is studied. Then,the multiple scattering by random distributed particles with interfacial damage in a composite material is investigated. The equations to evaluate velocity and attenuation of effective waves defined by statistic averaging are given. Furthermore,based on the established relation between the effective velocity and interfacial constants,a method to evaluate the interfacial damage nondestructively from the ultrasonic measure data is proposed. The numerical simulation is performed for the Sic-Al composites. The effective velocity is computed to show the influences of interface damage. By using the genetic algorithm,the interfacial damage is evaluated from the synthetic experimental data with various levels of error. The numerical results show the feasibility of the method proposed to approximately evaluate the interfacial damage in a composite material with reinforced particles based on ultrasonic data.

关键词： scattering effective waves spring model interfacial damage genetic algorithm

Propagation of elastic wave in nanoporous material with distributed cylindrical nanoholes

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Science China(Physics,Mechanics & Astronomy) 2013年第8期56卷 1542-1550页

作者： QIANG Fangwei wei peijun LIU XiQiang Department of Applied Mechanics University of Science and Technology Beijin Department of Mathematics & Physics PLA University of Science and Technology

The effective propagation constants of plane longitudinal and shear waves in nanoporous material with random distributed parallel cylindrical nanoholes are studied. The surface elastic theory is used to consider the surface stress effects and to derive the nontraditional boundary condition on the surface of nanoholes. The plane wave expansion method is used to obtain the scattering waves from the single nanohole. The multiple scattering effects are taken into consideration by summing the scat- tered waves from all scatterers and performing the configuration averaging of random distributed scatterers. The effective propagation constants of coherent waves along with the associated dynamic effective elastic modulus are numerically evaluat- ed. The influences of surface stress are discussed based on the numerical results.

关键词： multiple scattering nanohole coherent wave effective velocity effective modulus