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Analytical solutions for thermal vibration of nanobeams with elastic boundary conditions

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Acta Mechanica Solida Sinica 2017年第5期30卷 474-483页

作者： Jingnong Jiang Lifeng Wang state key laboratory of mechanics and control of mechanical structures Nanjing University of Aeronautics and Astronautics 210016 Nanjing China

A nonlocal Euler beam model with second-order gradient of stress taken into consideration is used to study the thermal vibration of nanobeams with elastic boundary. An analytical solution is proposed to investigate the free vibration of nonlocal Euler beams subjected to axial thermal stress. The effects of the nonlocal parameter, thermal stress and stiffness of boundary constraint on the vibration behaviors of nanobeams are revealed. The results show that natural frequencies including the thermal stress are lower than those without the thermal stress when temperature rises. The boundary-constrained springs have significant effects on the vibration of nanobeams. In addition, numerical simulations also indicate the importance of small-scale effect on the vibration of nanobeams.

关键词： Nonlocal Euler beamThermal stressVibrationElastic boundary conditionsNanobeam

Practical Green’s function for the thermal stress field induced by a heat source in plane thermoelasticity

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Applied Mathematics and mechanics(English Edition) 2020年第4期41卷 543-550页

作者： Jian HUA Ming DAI state key laboratory of mechanics and control of mechanical structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

The classical Green’s functions used in the literature for a heat source in a homogeneous elastic medium cannot lead to ?nite remote thermal stresses in the medium,so that they may not work well in practical thermal stress analyses. In this paper, we develop a practical Green’s function for a heat source disposed eccentrically into an elastic disk/cylinder subject to plane deformation. The edge of the disk/cylinder is assumed to be thermally permeable and traction-free. The full thermal stress ?eld induced by the heat source in the disk/cylinder is determined exactly and explicitly via the Cauchy integral techniques. In particular, a very simple formula is obtained to describe the hoop thermal stress on the edge of the disk/cylinder, which may be conveniently useful for analyzing the thermal stresses in microelectronic components.

关键词： heat source Green’s function thermal stress finite matrix

Formulization of Three-Dimensional Stress and Strain Fields at Elliptical Holes in Finite Thickness Plates

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Acta Mechanica Solida Sinica 2019年第4期32卷 393-430页

作者： Wei Guo Wcinlin Guo state key laboratory of mechanics and control of mechanical structures Nanjing University of Aeronautics and AstronauticsNanjing 210016 China

Stress raisers such as holes are inevitable in structures at which stress concentration occurs and the static as well as fatigue strength of the structures can be significantly weakened. Therefore, to accurately evaluate the stress concentration factor and stress fields at holes is of essential importance for structure design and service life prediction. Although stress and strain concentration and fields at holes in finite thickness plates strongly change with and along the thickness, manuals of stress concentration for engineering design are mainly based on twodimensional theory and no explicit formula is available even for circular holes in finite thickness plates. Here we obtain for the first time a complete set of explicit formulae for stress and strain concentration factors and the out-of-plane constraint factor at circular as well as elliptical holes in finite thickness plates by integrating comprehensive three-dimensional finite element analyses and available theoretical solutions. The three-dimensional stress distributions ahead of holes can also be predicted by the obtained formulae. With their accuracy and the corresponding applicable range being analyzed and outlined in detail, the formulae can serve as an important fundamental solution for three-dimensional engineering structure design and guideline for developing threedimensional analytical methods.

关键词： Three-dimensional stress and strain concentration Stress field Elliptical holes Finite thickness plate Explicit solution

Theoretical analysis on elastic buckling of nanobeams based on stress-driven nonlocal integral model

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Applied Mathematics and mechanics(English Edition) 2020年第2期41卷 207-232页

作者： Peng JIANG Hai QING Cunfa GAO state key laboratory of mechanics and control of mechanical structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

Several studies indicate that Eringen's nonlocal model may lead to some inconsistencies for both Euler-Bernoulli and Timoshenko beams, such as cantilever beams subjected to an end point force and fixed-fixed beams subjected a uniform distributed load. In this paper, the elastic buckling behavior of nanobeams, including both EulerBernoulli and Timoshenko beams, is investigated on the basis of a stress-driven nonlocal integral model. The constitutive equations are the Fredholm-type integral equations of the first kind, which can be transformed to the Volterra integral equations of the first kind. With the application of the Laplace transformation, the general solutions of the deflections and bending moments for the Euler-Bernoulli and Timoshenko beams as well as the rotation and shear force for the Timoshenko beams are obtained explicitly with several unknown constants. Considering the boundary conditions and extra constitutive constraints, the characteristic equations are obtained explicitly for the Euler-Bernoulli and Timoshenko beams under different boundary conditions, from which one can determine the critical buckling loads of nanobeams. The effects of the nonlocal parameters and buckling order on the buckling loads of nanobeams are studied numerically, and a consistent toughening effect is obtained.

关键词： Laplace transformation Volterra integral equation Fredholm integral equation stress-driven nonlocal integral model

On well-posedness of two-phase nonlocal integral models for higher-order refined shear deformation beams

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Applied Mathematics and mechanics(English Edition) 2021年第7期42卷 931-950页

作者： Pei ZHANG Hai QING state key laboratory of mechanics and control of mechanical structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

Due to the conflict between equilibrium and constitutive requirements,Eringen’s strain-driven nonlocal integral model is not applicable to nanostructures of engineering *** an alternative,the stress-driven model has been recently *** this paper,for higher-order shear deformation beams,the ill-posed issue(i.e.,excessive mandatory boundary conditions(BCs)cannot be met simultaneously)exists not only in strain-driven nonlocal models but also in stress-driven *** well-posedness of both the strain-and stress-driven two-phase nonlocal(TPN-Strain D and TPN-Stress D)models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded(FG)*** two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction *** using the generalized differential quadrature method(GDQM),the coupling governing equations are solved *** results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.

关键词： well-posedness strain-and stress-driven two-phase nonlocal(TPN-Strain D and TPN-Stress D)models refined shear deformation theory functionally graded(FG)curved beam generalized differential quadrature method(GDQM)

Stationary non-Gaussian random vibration control:A review

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Chinese Journal of aeronautics 2021年第1期34卷 350-363页

作者： Ronghui ZHENG Guoping CHEN Huaihai CHEN state key laboratory of mechanics and control of mechanical structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

This paper presents a review of the various methods for the stationary non-Gaussian random vibration *** vibration tests can be divided,according to the number of exciters,in single-shaker tests and multiple-shaker *** the stationary non-Gaussian random vibration test,the time and frequency domain characteristics of the responses should be controlled independently and *** and kurtosis are usually selected as the nonGaussian time control references(targets)while power spectral density is the frequency domain control procedure before it recalls the concepts of ***,the generation of a one frame stationary non-Gaussian random signal for both the single and multiple shakers are *** commonly used methods for the single non-Gaussian random signal generation in the random vibration test are memoryless nonlinear transformation,phase modification and Filtered Poisson *** the multiple-shaker case,the sequential phase modification and memoryless nonlinear transformation are used to generate one frame coupled multi-channel non-Gaussian random *** order to obtain a stationary and consecutive dynamic input,the time domain randomization procedure is introduced with high computational efficiency and its influences on the skewness and kurtosis are ***,two existing problems in the non-Gaussian random vibration control are addressed.

关键词： non-Gaussian random Kurtosis Skewness Power spectral density Vibration control

Two-phase nonlocal integral models with a bi-Helmholtz averaging kernel for nanorods

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Applied Mathematics and mechanics(English Edition) 2021年第10期42卷 1379-1396页

作者： Pei ZHANG Hai QING state key laboratory of mechanics and control of mechanical structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

In this work,the static tensile and free vibration of nanorods are studied via both the strain-driven(Strain D)and stress-driven(Stress D)two-phase nonlocal models with a bi-Helmholtz averaging *** adjusting the limits of integration,the integral constitutive equation of the Fredholm type is converted to that of the Volterra type and then solved directly via the Laplace transform *** unknown constants can be uniquely determined through the standard boundary conditions and two constrained conditions accompanying the Laplace transform *** the numerical examples,the bi-Helmholtz kernel-based Strain D(or Stress D)two-phase model shows consistently softening(or stiffening)effects on both the tension and the free vibration of nanorods with different boundary *** effects of the two nonlocal parameters of the bi-Helmholtz kernel-based two-phase nonlocal models are studied and compared with those of the Helmholtz kernel-based models.

关键词： two-phase nonlocal integral model bi-Helmholtz kernel tensile analysis free vibration exact solution Laplace transform

Flutter analysis of rotating beams with elastic restraints

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Applied Mathematics and mechanics(English Edition) 2022年第5期43卷 761-776页

作者： Lüsen WANG Zhu SU Lifeng WANG state key laboratory of mechanics and control of mechanical structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

The aeroelastic stability of rotating beams with elastic restraints is *** coupled bending-torsional Euler-Bernoulli beam and Timoshenko beam models are adopted for the structural *** Greenberg aerodynamic model is used to describe the unsteady aerodynamic *** additional centrifugal stiffness effect and elastic boundary conditions are considered in the form of potential energy.A modified Fourier series method is used to assume the displacement field function and solve the governing *** convergence and accuracy of the method are verified by comparison of numerical ***,the flutter analysis of the rotating beam structure is carried out,and the critical rotational velocity of the flutter is *** results show that the elastic boundary reduces the critical flutter velocity of the rotating beam,and the elastic range of torsional spring is larger than the elastic range of linear spring.

关键词： rotating beam modified Fourier series method elastic restraint flutter

Model predictive control of rigid spacecraft with two variable speed control moment gyroscopes

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Applied Mathematics and mechanics(English Edition) 2017年第11期38卷 1551-1564页

作者： Pengcheng WU Hao WEN Ti CHEN Dongping JIN state key laboratory of mechanics and control of mechanical structures Nanjing University of Aeronautics and Astronautics Nanjing 210016 China

In this paper, an attitude maneuver control problem is investigated for a rigid spacecraft using an array of two variable speed control moment gyroscopes （VSCMGs） with gimbal axes skewed to each other. A mathematical model is constructed by taking the spacecraft and the gyroscopes together as an integrated system, with the coupling interaction between them considered. To overcome the singular issues of the VSCMGs due to the conventional torque-based method, the first-order derivative of gimbal rates and the second-order derivative of the rotor spinning velocity, instead of the gyroscope torques, are taken as input variables. Moreover, taking external disturbances into account, a feedback control law is designed for the system based on a method of nonlinear model predictive control （NMPC）. The attitude maneuver can be realized fast and smoothly by using the proposed controller in this paper.

关键词： integrated system variable speed control moment gyroscope (VSCMG),nonlinear model predictive control (NMPC)