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Analytical solution and semi-analytical solution for anisotropic functionally graded beam subject to arbitrary loading

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Science china(Physics,mechanics & Astronomy) 2009年第8期52卷 1244-1256页

作者： HUANG DeJin1,2,DING HaoJiang1 & CHEN WeiQiu3 1 Key Laboratory of Soft Soils and Geoenvironmental engineering,Ministry of Education,zhejiang university,hangzhou 310027,china 2 Faculty of engineering,Ningbo university,Ningbo 315211,china 3 department of engineering mechanics,zhejiang university,hangzhou 310027,china Key Laboratory of Soft Soils and Geoenvironmental engineering Ministry of Education Zhejiang University Hangzhou China Faculty of engineering Ningbo University Ningbo China department of engineering mechanics Zhejiang University Hangzhou China

Analytical and semi-analytical solutions are presented for anisotropic functionally graded beams subject to an arbitrary load,which can be expanded in terms of sinusoidal *** plane stress problems,the stress function is assumed to consist of two parts,one being a product of a trigonometric function of the longitudinal coordinate(x) and an undetermined function of the thickness coordinate(y),and the other a linear polynomial of x with unknown coefficients depending on *** governing equations satisfied by these y-dependent functions are *** expressions for stresses,resultant forces and displacements are then deduced,with integral constants determinable from the boundary *** the analytical solution is derived for the beam with material coefficients varying exponentially or in a power law along the thickness,the semi-analytical solution is sought by making use of the sub-layer approximation for the beam with an arbitrary variation of material parameters along the *** present analysis is applicable to beams with various boundary conditions at the two *** numerical examples are presented for validation of the theory and illustration of the effects of certain parameters.

关键词： anisotropic material functionally graded arbitrary loading stress function analytical solution semi-analytical solution

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Guided wave propagation in multilayered piezoelectric structures

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Science china(Physics,mechanics & Astronomy) 2009年第7期52卷 1094-1104页

作者： GUO YongQiang1, CHEN WeiQiu2,3 & ZHANG YongLiang4 1 Key Laboratory of mechanics on Disaster and Environment in Western china, Ministry of Education, and School of Civil engineering and mechanics, Lanzhou university, Lanzhou 730000, china 2 Key Laboratory of Soft Soils and Geoenvironmental engineering, Ministry of Education, and department of Civil engineering, zhejiang university, hangzhou 310058, china 3 department of engineering mechanics, zhejiang university, hangzhou 310027, china 4 School of Civil engineering, Lanzhou Jiaotong university, Lanzhou 730070, china Key Laboratory of mechanics on Disaster and Environment in Western china Ministry of Education and School of Civil Engineering and Mechanics Lanzhou University Lanzhou China Key Laboratory of Soft Soils and Geoenvironmental engineering Ministry of Education and Department of Civil Engineering Zhejiang University Hangzhou China department of engineering mechanics Zhejiang University Hangzhou China School of Civil engineering Lanzhou Jiaotong University Lanzhou China

A general formulation of the method of the reverberation-ray matrix (MRRM) based on the state space formalism and plane wave expansion technique is presented for the analysis of guided waves in multilayered piezoelectric structures. Each layer of the structure is made of an arbitrarily anisotropic piezoelectric material. Since the state equation of each layer is derived from the three-dimensional theory of linear piezoelectricity, all wave modes are included in the formulation. Within the framework of the MRRM, the phase relation is properly established by excluding exponentially growing functions, while the scattering relation is also appropriately set up by avoiding matrix inversion operation. Consequently, the present MRRM is unconditionally numerically stable and free from computational limitations to the total number of layers, the thickness of individual layers, and the frequency range. Numerical examples are given to illustrate the good performance of the proposed formulation for the analysis of the dispersion characteristic of waves in layered piezoelectric structures.

关键词： multilayered piezoelectric structures the method of reverberation-ray matrix guided waves dispersion characteristic

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RECURSIVE FORMULATIONS FOR DYNAMIC ANALYSIS OF A SMART CRACKED BEAM BASED ON THE METHOD OF REVERBERATION-RAY MATRIX

RECURSIVE FORMULATIONS FOR DYNAMIC ANALYSIS OF A SMART CRACK...

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2010全国压电和声波理论及器件技术研讨会

作者： Wei YAN~1,Jin-biao CAI~2,Wei-qiu CHEN~3,Ji WANG~4 1 Faculty of Architectural,Civil engineering and Environment,Ningbo university, Ningbo 315211,china 2 department of Civil engineering,zhejiang university,Zijingang Campus, hangzhou 310058,china 3 department of engineering mechanics,zhejiang university,Yuquan Campus, hangzhou 310027,china 4 Faculty of Mechanical engineering and mechanics,Ningbo university,Ningbo 315211,china

An accurate electro-mechanical impedance(EMI) model for analytical crack detection of a Timoshenko beam is established based on the improved reverberation-ray matrix method via the recursive formulations. The crack is treated as a massless rotational spring.A pair of PZT patches with free ends symmetrically bonded onto the beam is assumed in a state of pure one-dimensional axial motion under an out-of-phase harmonic electric force and hence a pure bending excitation of the beam is created.A Kelvin-type viscoelastic law is introduced into the EMI model to account for the bonding effect in order to improve the signature sensitivity to *** order to develop the recursive formulations to reduce the size of the final equations in the method of reverberation-ray matrix(MRRM),new scattering relations are established by a matrix reduction ***,an analytical expression of impedance containing crack parameters as well as other physical parameters is derived for crack detection of beams.

关键词： EMI damage detection method of reverberation-ray matrix recursive formulations

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Bridging properties of the debonded interface with frictional sliding

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Progress in Natural Science:Materials International 2006年第2期16卷 153-162页

作者： LIU Pengfei, TAO Weiming, YU Xuezhong and GUO Yimu ( department of engineering mechanics, zhejiang university, hangzhou 310027, china Second Affiliated Hospital, zhejiang university, hangzhou 310009, china) department of engineering mechanics Zhejiang University Hangzhou 310027 China Second Affiliated Hospital Zhejiang University Hangzhou 310009 China

A theoretical model simulating the properties of frictional bridging is presented and relatively perfect stress solutions for the fiber and matrix are obtained. Based on the energy equilibrium in the process of interfacial debonding, an expression for the energy release rate G is derived to explore the interfacial fracture properties. By introducing an interfacial debonding criterion G≥Γi, a method for determining the critical debond length is proposed and the bridging constitutive relationship is also obtained. Numerical calculations are conducted for the fiber-reinforced composite SCS-6/Ti-6Al-4V and the results are also compared with those obtained by using other existing models.

关键词： interfacial stress transfer frictional sliding energy release rate bridging constitutive relationship fiber-reinforced composites.

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STOCHASTIC OPTIMAL CONTROL OF HYSTERETIC SYSTEMS UNDER EXTERNALLY AND PARAMETRICALLY RANDOM EXCITATIONS

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Acta Mechanica Solida Sinica 2003年第1期16卷 61-66页

作者： Ying Zuguang Zhu Weiqiu (department of mechanics,zhejiang university,hangzhou 310027,china) department of mechanics Zhejiang University Hangzhou 310027 China

A stochastic optimal control method for nonlinear hysteretic systems under externally and/or parametrically random excitations is presented and illustrated with an example of hysteretic column system. A hysteretic system subject to random excitation is first replaced by a nonlinear non-hysteretic stochastic system. An It$\hat {\rm o}$ stochastic differential equation for the total energy of the system as a one-dimensional controlled diffusion process is derived by using the stochastic averaging method of energy envelope. A dynamical programming equation is then established based on the stochastic dynamical programming principle and solved to yield the optimal control force. Finally, the responses of uncontrolled and controlled systems are evaluated to determine the control efficacy. It is shown by numerical results that the proposed stochastic optimal control method is more effective and efficient than other optimal control methods.

关键词： stochastic optimal control hysteretic systems random vibration stochastic averaging

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SOME THERMODYNAMIC PROPERTIES OF Pd-In ALLOYS

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Acta Metallurgica Sinica(English Letters) 1997年第4期10卷 311-317页

作者： YL. Chen(department of Materials Science and engineering, zhejiang university, hangzhou 310027, china) zhejiang Univ Hangzhou China

Some thermodynamic parnmeters of Pd-In alloys with 2 to 70 at. H indium have been determined in the temperuture range 800 to 1000℃ from e.m.f measurements ongalvanic cells with an onsen-cotzducting solid electrolyte. Heats of tnising calculated hem the activities are in excellent agreement with calorimetric data. The relative partial excess hee enengy of indiurn assumes unnsually larpe negative values ap to-174kJ/mol for Pd-rich alloys. Two efficts are discussed to account for the non-idealproperties: The rise Of Fermi enerpy as the valence electron8 of indium enter the 4dand 5sP bands of the alloy and the lattice distortion brought about by the differentmolar volumes of the cofnponents. The rise of the Fermi enerpy, as determlned fromthe activity data, indicates a strict adherence of the alloys to the rigid band model.

关键词： galvanic cell activity data Fermi energy,lattice distortion rigid band model

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HYDRIDING INFLUENCE OF INDIUM ON Pd-In ALLOYS

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中国有色金属学会会刊：英文版 1996年第3期6卷 63-67页

作者： Chen Yanglin(department of Materials Science and engineering, zhejiang university, hangzhou 310027) department of Materials Science and engineering Zhejiang University Hangzhou 310027 China

ＨＹＤＲＩＤＩＮＧＩＮＦＬＵＥＮＣＥＯＦＩＮＤＩＵＭＯＮＰｄ－ＩｎＡＬＬＯＹＳ￥ＣｈｅｎＹａｎｇｌｉｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｅｒｉａｌｓＳｃｉｅｎｃｅａｎｄＥｎｇｉｎｅｅｒｉｎｇ，ＺｈｅｊｉａｎｇＵｎｉｖｅ... 详细信息

ＨＹＤＲＩＤＩＮＧＩＮＦＬＵＥＮＣＥＯＦＩＮＤＩＵＭＯＮＰｄ－ＩｎＡＬＬＯＹＳ￥ＣｈｅｎＹａｎｇｌｉｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｅｒｉａｌｓＳｃｉｅｎｃｅａｎｄＥｎｇｉｎｅｅｒｉｎｇ，ＺｈｅｊｉａｎｇＵｎｉｖｅｒｓｉｔｙ，Ｈａｎｇｚｈｏｕ３１０...

关键词： hydriding valence electrons lattice dilatation Fermi energy

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FLUID FLOW IN ROTATING HELICAL SQUARE DUCTS

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Journal of Hydrodynamics 2003年第3期15卷 49-56页

作者： Chen Hua-jun, Zhang Ben-zhao, Zhang Jin-suo department of mechanics, zhejiang university, hangzhou 310027, china, Dept. of Mech. Zhejiang Univ. Hangzhou 310027 China

A numerical study is made for a fully developed laminar flow in rotatinghelical pipes. Due to the rotation, the Coriolis force can also contribute to the secondary *** interaction between rotation, torsion, and curvature complicates the flow characteristics. Theeffects of rotation and torsion on the flow transitions are studied in details. The results showthat there are obvious differences between the flow in rotating ducts and in helical ducts withoutrotation. Certain hitherto unknown flow patterns are found. The effects of rotation and torsion onthe friction factor are also examined. Present results show the characteristics of the fluid flow inrotating helical square ducts.

关键词： secondary flow rotating ducts helical ducts

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Derivation of Martin-Hou Equation of State from Hard-particle Perturbation Theory

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Chemical Research in Chinese Universities 2000年第1期16卷 49-56页

作者： ZHANG Bing-jian (department of Chemistry, zhejiang university, hangzhou 310027, P. R. china) HOU Yu-chun (department of Chemical engineering, zhejiang university, hangzhou 310027, P. R. china) 浙江大学浙江杭州 310027

In this paper, the Martin-Hou equation of state is derived by using a power series representation of radial distribution function and an analytic representation of multi-section potential based on the Barker-Henderson hard-particle perturbation theory including high-order terms. In the derivation, a theoretical form of Martin-Hou equation was obtained. It had a similar form and the same capability to predict P-V-T properties as the Martin-Hou equation and no additional data were required for evaluating the constants. The characteristic constants of the theoretical expression have certain relationships with the molecular parameters.

关键词： Perturbation theory Martin-Hou equation of state Theoretical expression P-V-T properties Molecular parameter

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Feedback minimization of first-passage failure of quasi integrable Hamiltonian systems

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Acta Mechanica Sinica 2007年第4期23卷 437-444页

作者： Maolin Deng Weiqiu Zhu department of mechanics,State Key Laboratory of Fluid Power Transmission and Control,zhejiang university,hangzhou 310027,china department of mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou China

Abstract A nonlinear stochastic optimal control strategy for minimizing the first-passage failure of quasi integrable Hamiltonian systems （multi-degree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations） is proposed. The equations of motion for a controlled quasi integrable Hamiltonian system are reduced to a set of averaged It6 stochastic differential equations by using the stochastic averaging method. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximization of reliability and mean first-passage time are formulated. The optimal control law is derived from the dynamical programming equations and the control constraints. The final dynamical programming equations for these control problems are determined and their relationships to the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the mean first-passage time are separately established. The conditional reliability function and the mean first-passage time of the controlled system are obtained by solving the final dynamical programming equations or their equivalent Kolmogorov and Pontryagin equations. An example is presented to illustrate the application and effectiveness of the proposed control strategy.

关键词： Nonlinear stochastic system First-passage time Reliability Stochastic control Dynamical programming

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