圆柱壳在水下爆炸载荷下的流-固耦合响应分析

研究了无限域流场中两端简支圆柱壳受球形炸药爆炸冲击载荷作用的响应特性。运用Hamilton变分原理,推导出了考虑流固耦合作用圆柱壳受水下爆炸冲击载荷作用的运动方程,并分别展开成Fourier级数的形式,最后在时域上差分离散,用Galerkin方法求解,得到了在水下爆炸冲击载荷下圆柱壳的响应分析。文章着重就圆柱壳在迎爆面和背爆面的不同位置的变形位移和变形速度进行了对比分析,同时还比较了流体动压力对结构响应的影响。并将分析结果与有限元计算软件MSC.DYTRAN计算结果比较,验证了算法的可靠性。     

Nonlinear vibrations of laminated circular cylindrical shells: Comparison of different shell theories

The geometrically nonlinear forced vibrations of laminated circular cylindrical shells are studied by using the Amabili–Reddy higher-order shear deformation theory. An energy approach based on Lagrange equations, retaining modal damping, is used in order to obtain the equations of motion. An harmonic point excitation is applied in radial direction and simply supported boundary conditions are assumed. The equations of motion are studied by using the pseudo-arclength continuation method and bifurcation analysis. A one-to-one internal resonance is always present for a complete circular cylindrical shell, giving rise to pitchfork bifurcations of the nonlinear response with appearance of a second branch with travelling wave response and quasi-periodic vibrations. The numerical results obtained by using the Amabili–Reddy shell theory are compared to those obtained by using an higher-order shear deformation theory retaining only nonlinear term of von Kármán type and the Novozhilov classical shell theory.     

摆线钢球行星传动系统参数振动特性研究

摆线钢球行星传动系统为多自由度的参数振动系统,其时变啮合刚度激励会对系统的动态特性产生较大影响。该文首先综合考虑时变啮合刚度及轴承支承刚度等影响因素,建立了摆线钢球行星传动系统的平移-扭转耦合动力学模型,并推导出系统的动力学方程。然后将动力学方程转换为正则模态方程,并利用多尺度法对系统进行动力稳定性分析,推导出系统的组合共振频率及稳定性条件。最后利用摄动法计算出系统的稳态响应。研究结果表明:当偏心轴的输入转速接近和型组合共振频率时,系统将发生参数共振;当偏心轴的输入转速接近差型组合共振频率时,系统总是稳定的;系统的稳态响应中包含多种组合频率成分,并表现出多频响应叠加的特性。     

转子系统不平衡响应的灵敏度和估算方法

本文采用有限元法首次推导出系统的稳态不平衡响应关于各类参数的灵敏度公式,提出了用灵敏度公式估算不平衡响应的近似方法。在转子模型算例中,用所推公式研究了系统参数对不平衡响应的影响,并对不平衡响应进行了估算,将其与重新计算值相比较。当参数变化40%时,不平衡响应的估算误差低于3%,且估算与重算的机时比约为1∶5。     

Predicted axial temperature gradient in a viscoplastic uniaxial bar due to thermomechanical coupling

The thermomechanical response of a uniaxial bar with thermoviscoplastic constitution is predicted herein using the finite element method. After a brief review of the governing field equations, variational principles are constructed for the one-dimensional conservation of momentum and energy equations. These equations are coupled in that the temperature field affects the displacements and vice versa. Due to the differing physical nature of the temperature and displacements, first-order and second-order elements are utilized for these variables, respectively. The resulting semi-discretized equations are then discretized in time using finite differencing. This is accomplished by Euler's method, which is utilized due to the stiff nature of the constitutive equations. The model is utilized in conjunction with stress-strain relations developed by Bodner and Partom to predict the axial temperature field in a bar subjected to cyclic mechanical end displacements and temperature boundary conditions. It is found that spacial and time variation of the temperature field is significantly affected by the boundary conditions. The nomenclature used is given in an Appendix.     

Vibrations of inhomogeneous anisotropic viscoelastic bodies described with fractional derivative models

The dynamic response of plane inhomogeneous anisotropic bodies made of linear viscoelastic materials is investigated. The mechanical behavior of the viscoelastic material is described by differential constitutive equations with fractional order derivatives. The governing equations, which are derived by considering the dynamic equilibrium of the plane body element, are two coupled linear fractional evolution partial differential equations in terms of the displacements, whose order is in general greater than two with respect to time derivatives. A method is presented to establish the additional required initial conditions beside the described initial displacements and velocities. Using the Analog Equation Method (AEM) in conjunction with the Domain Boundary Element Method (D/BEM) the governing equations are transformed into a system of multi-term ordinary fractional differential equations (FDEs), which are solved using the numerical method for multi-term FDEs developed recently by Katsikadelis. Numerical examples are presented, which not only demonstrate the efficiency of the solution procedure and validate its accuracy, but also permit a better understanding of the dynamic response of plane bodies described by different viscoelastic models.     

多自由度一般积分型粘弹性阻尼减震结构的 随机响应与等效阻尼

该文对任意多自由度带支撑一般积分型粘滞和粘弹性阻尼器减震结构的随机响应与等效阻尼比的解析分析法进行了系统研究。首先建立了结构一般运动方程;然后将运动方程化为振型广义坐标的微分和积分混合地震响应方程组;继而基于多自由度随机平均法理论,获得了结构随机平均Itô方程组的解析式,推导出耗能结构各振型振子的振幅与相位瞬态联合概率密度函数、位移与速度瞬态联合概率密度函数、位移与速度瞬态响应方差的一般解析解;最后,基于与多自由度随机平均法分析完全相同的等效准则,建立了耗能结构各振型等效阻尼比的一般解析式,并根据CQC和SRSS组合方法,建立了耗能结构随机地震响应方差的解析式,给出了带支撑广义Maxwell阻尼器和广义微分模型阻尼器减震结构随机响应和各振型等效阻尼比的一般解析式,通过与一些典型问题的模态应变能法的计算精度对比分析,表明了所提方法的有效性,使耗能结构可直接应用反应谱法进行设计,从而建立了带支撑任意线性粘滞和粘弹性阻尼器一般耗能结构随机响应与特性等效阻尼分析的完备解析解法。     

Nonlinear vibrations of laminated circular cylindrical shells: Comparison of different shell theories

The geometrically nonlinear forced vibrations of laminated circular cylindrical shells are studied by using the Amabili–Reddy higher-order shear deformation theory. An energy approach based on Lagrange equations, retaining modal damping, is used in order to obtain the equations of motion. An harmonic point excitation is applied in radial direction and simply supported boundary conditions are assumed. The equations of motion are studied by using the pseudo-arclength continuation method and bifurcation analysis. A one-to-one internal resonance is always present for a complete circular cylindrical shell, giving rise to pitchfork bifurcations of the nonlinear response with appearance of a second branch with travelling wave response and quasi-periodic vibrations. The numerical results obtained by using the Amabili–Reddy shell theory are compared to those obtained by using an higher-order shear deformation theory retaining only nonlinear term of von Kármán type and the Novozhilov classical shell theory.     

功能梯度矩形板的强非线性共振分析

针对陶瓷-金属功能梯度矩形板,在给出非均匀材料应力-应变关系及非线性几何方程的基础上,应用虚功原理导出了横向简谐激励力作用下功能梯度板的非线性振动偏微分方程。对于四边简支约束功能梯度矩形板,通过位移函数的设定,利用伽辽金积分法推得了关于时间自变量的达芬型强非线性振动方程。针对强非线性系统的主共振问题,应用改进的多尺度法进行解析求解,得到了稳态运动下的幅频响应方程。通过数值算例,给出了功能梯度矩形板共振下的幅频曲线图和相图,讨论了激励幅值及频率等参数对系统非线性振动特性的影响,并对改进多尺度法和经典多尺度法的结果进行了比较。     

Coupled size-dependent behavior of shear deformable microplates

The aim of the present study is to investigate the nonlinear motion characteristics of a shear deformable microplate based on the modified couple stress theory. The microplate is modeled via the third-order shear deformation theory retaining in-plane displacements and inertia. Using the Lagrange equations together with an assumed-mode method, five sets of second-order nonlinear ordinary differential equations of motion with coupled terms are obtained. These five sets of equations (two for the in-plane motions, one for the out-of-plane motion, and two for rotations) are transformed into ten sets of first-order nonlinear ordinary differential equations. These resultant equations are then solved by means of a direct time integration technique and the pseudo-arclength continuation method in order to analyze the nonlinear response of the system. Apart from the nonlinear analysis, the linear natural frequencies of the system are obtained using an eigenvalue analysis. Results are shown through frequency–response and force–response curves. Points of interest in the parameter space in the form of time histories, phase-plane portraits, and fast Fourier transforms are also highlighted. Moreover, a comparison is made between the motion characteristics of the system based on the modified couple stress and classical continuum theories.     

隔震结构非线性随机地震响应分析的复模态法

本对多自由度双线性滞变隔震结构在过滤白噪声地震激励下的随机响应问题进行了系统研究。首先建立了结构非线性运动方程；然后根据非线性随机振动理论对运动方程进行等效线性化；最后用复模态法获得了等效线性方程的解析解，将复杂的非线性随机响应问题简化为求解一元非线性代数方程问题，并给出了算例。从而建立了多自由度隔震结构非线性随机响应复模态分析的一整套计算方法。     

基于主元-双谱支持向量机的旋转机械故障诊断方法

提出一种基于主元-双谱支持向量机的旋转机械故障诊断方法，该方法具有对故障在线监测分类和故障分类能力强的优点，能有效地从汽轮机故障的非平稳、非高斯时变信号中提取状态特征。首先研究了直接法、间接法及ARMA模型法的双谱估计特征，然后利用双谱分析主元数字特征提取技术提取这些特征，最后利用支持向量机对汽轮机小样本故障进行分类，较好地解决了故障样本不足的实际问题。诊断结果表明与常用的BP神经网络相比可以获得较高的诊断精度。     

Finite element analysis of transient free convection flow over vertical plate

A finite element method is used to study the heat-transfer response of an incompressible, laminar, transient free convection flow over a semi-infinite vertical plate. The non-dimensional governing equations are solved by the finite element method (FEM). The resulting non-linear integral equations are linearized and solved using the Newton–Raphson iteration. The resulting first-order ordinary differential equations with respect to time are solved using the implicit Euler scheme. Numerical results for the details of the velocity and temperature contours and profiles as well as heat transfer rate in terms of Nusselt number which are shown on graphs have been presented.     

基础隔震结构基于新抗震规范地震动随机模型的地震作用取值

对多自由度基础隔震结构的地震作用取值问题进行了系统研究。首先建立了结构运动方程，接着用实模态对上部结构进行解耦，针对所得运动方程为非对称质量与非经典阻尼矩阵的情况，再用复模态法解耦，最后采用基于新抗震规范的地震动随机模型，运用复模态时域法获得了体系的相对位移，由此便可以得到结构的地震作用取值。最后，通过一个例子来说明多层基础隔震结构的地震作用计算方法，同时给出了由规范的振型分解反应谱法得到的基础固定结构的地震作用取值。     

色噪声与确定性谐波联合激励下Bouc-Wen动力系统响应的统计线性化方法

提出了一种用于求解色噪声和确定性谐波联合作用下单自由度Bouc?Wen系统响应的统计线性化方法.基于系统响应可分解为确定性谐波和零均值随机分量之和的假定,将原滞回运动方程等效地化为两组耦合的且分别以确定性和随机动力响应为未知量的非线性微分方程.利用谐波平衡法求解确定性运动方程,利用统计线性化方法求解色噪声激励下的随机运...     

Post-buckling analysis of viscoelastic plates with fractional derivative models

The post-buckling response of thin plates made of linear viscoelastic materials is investigated. The employed viscoelastic material is described with fractional order time derivatives. The governing equations, which are derived by considering the equilibrium of the plate element, are three coupled nonlinear fractional partial evolution type differential equations in terms of three displacements. The nonlinearity is due to nonlinear kinematic relations based on the von Kármán assumption. The solution is achieved using the analog equation method (AEM), which transforms the original equations into three uncoupled linear equations, namely a linear plate (biharmonic) equation for the transverse deflection and two linear membrane (Poisson’s) equations for the inplane deformation under fictitious loads. The resulting initial value problem for the fictitious sources is a system of nonlinear fractional ordinary differential equations, which is solved using the numerical method developed recently by Katsikadelis for multi-term nonlinear fractional differential equations. The numerical examples not only demonstrate the efficiency and validate the accuracy of the solution procedure, but also give a better insight into this complicated but very interesting engineering plate problem     

Non-Gaussian stochastic response of nonlinear compliant platforms

A moment function method is presented to estimate the stochastic response of compliant offshore platforms with nonlinearity in stiffness based on non-Gaussian closure. For guyed towers with clump weight, the nonlinearity in stiffness is of the softening type. The random wave loading is expressed in terms of a rational spectrum, making the system Markovian. Using Ito's rule for stochastic differentiation, differential equations for moments up to the fourth order are developed. The system of equations is closed by considering the fifth and sixth cumulants to be zero. For stationary response, differential equations become algebraic equations. The moments are obtained by solving the system of nonlinear algebraic equations. It is observed that the Gaussian closure method is inadequate for defining the complete probabilistic characteristics of the response.     

具有不确定参数车轨耦合系统 随机振动灵敏度分析

对于轨道不平顺作用下具有不确定结构参数的车轨耦合系统随机振动灵敏度问题进行了研究。车辆采用多刚体动力学模型,弹性轨道采用无穷周期子结构进行模拟。在哈密顿对偶体系下建立了车轨耦合系统混合物理坐标及辛对偶坐标的动力学方程,应用解析手段推导出其相对系统不确定参数的灵敏度控制方程。进一步,基于虚拟激励法和辛方法建立了车轨耦合系统随机振动响应灵敏度分析方法。数值算例结果表明：所提出的灵敏度分析方法具有较高的计算精度,并保留了虚拟激励法高效的特性。该文所开展的工作对于车辆系统动力学参数设计与优化具有很好的参考价值。     

Non-linear active control of FG beams in thermal environments subjected to blast loads with integrated FGP sensor/actuator layers

Non-linear active control of dynamic response of functionally graded (FG) beams with rectangular cross-section in thermal environments exposed to blast loadings is presented. Two FG piezoelectric layers are bonded to the beam surfaces to act as sensor and actuator. Non-linear equations of motion of the smart beam are derived based on the first-order shear deformation theory and the von Karman geometrical non-linearity. Constant velocity feedback algorithm is used to control the dynamic response of the FG beam actively through closed loop control. The generalized differential quadrature method together with the Newmark-beta scheme is utilized to solve the non-linear partial differential equations in spatial and time domains. The resulted non-linear algebraic equations are then solved using the modified Newton–Raphson method. A detailed analysis of the influence of the geometric non-linearity, material parameters and temperature field on the active vibration control of FG beams subjected to various impulsive loads is carried out.     

浸没的圆柱壳在冲击波作用下动响应的Galerkin解法

研究了无粘、无旋和不可压缩流体中两端简支圆柱壳在给定冲击波作用下的动响应。圆柱壳的运动方程中考虑了流体动压力和冲击波压力的共同作用，通过将冲击波压力分布函数表示为Ｆｏｕｒｉｅｒ级数有限项形式，并利用Ｇａｌｅｒｋｉｎ方法对耦合方程进行数值求解，得到了圆柱壳在冲击波作用下的位移响应特性