考虑压电材料非线性特性时旋转式超声电机定子的主共振响应

考虑压电材料非线性本构关系，建立了旋转式超声电机定子的非线性动力学模型，利用解析与数值方法研究超声电机定子的主共振响应，以揭示压电材料非线性本构关系对定子振动特性的影响，为深入研究旋转行波超声电机的动力学机理奠定基础．     

亚音速气流中复合材料悬臂板的非线性振动响应研究

随着材料科学的发展,越来越多的新型材料应用到了工程实践中.在气流激励的作用下,对于以航空航天工程为背景、采用复合材料的板壳结构的非线性动力学问题仍是动力学领域的研究热点.本文研究了复合材料悬臂板在亚音速气流条件下的非线性振动和响应.根据理想不可压缩流体的流动条件和Kutta–Joukowski升力定理,基于升力面理论,利用涡格法计算了三维有限长平板机翼上的亚音速气动升力.将亚音速气动力施加到复合材料悬臂板上,利用Hamilton原理,考虑Reddy三阶剪切变形理论并引入冯·卡门非线性应变位移关系,建立了有限长平板的非线性动力学微分方程.利用有限元方法考察了不同几何参数下层合板悬臂板的固有特性,通过比较不同材料和几何参数的线性系统的固有频率,得到不同比例的内共振关系.利用Galerkin方法将偏微分方程截断为两自由度非线性常微分方程,在这里考虑了1:2的内部共振关系并利用多尺度法进行了摄动分析.对应多个选取参数,得到了频率响应曲线.结果展示了硬化弹簧型行为和跳跃现象.     

亚音速气流中复合材料悬臂板的非线性振动响应研究

随着材料科学的发展,越来越多的新型材料应用到了工程实践中.在气流激励的作用下,对于以航空航天工程为背景、采用复合材料的板壳结构的非线性动力学问题仍是动力学领域的研究热点.本文研究了复合材料悬臂板在亚音速气流条件下的非线性振动和响应.根据理想不可压缩流体的流动条件和 Kutta--Joukowski升力定理,基于升力面理论,利用涡格法计算了三维有限长平板机翼上的亚音速气动升力.将亚音速气动力施加到复合材料悬臂板上,利用Hamilton原理,考虑Reddy三阶剪切变形理论并引入冯$\cdot$卡门非线性应变位移关系,建立了有限长平板的非线性动力学微分方程.利用有限元方法考察了不同几何参数下层合板悬臂板的固有特性,通过比较不同材料和几何参数的线性系统的固有频率,得到不同比例的内共振关系.利用Galerkin方法将偏微分方程截断为两自由度非线性常微分方程,在这里考虑了1:2的内部共振关系并利用多尺度法进行了摄动分析.对应多个选取参数,得到了频率响应曲线.结果展示了硬化弹簧型行为和跳跃现象.      

复合材料水翼水动力与结构强度特性数值研究

针对复合材料水翼存在的流固耦合求解问题,结合其自身特有属性,对复合材料水翼结构变形特性进行了数值仿真计算研究.研究建立了复合材料水翼流固耦合数值计算模型,并将数值计算结果与Zarruk等的实验结果进行对比,验证模型的正确性,得出复合材料水翼尖端扭转角随雷诺数的增加而增加的研究结论.基于数值计算模型,系统地研究了不同铺层角对复合材料水翼水动力特性及强度特性的影响,结果表明:不同铺层角复合材料水翼的尖端扭转角,随铺层角的增大而减小,而其尖端位移量随铺层角的增大先减小后增大.为了削弱工程常数的影响对复合材料水翼变形的影响,研究提出了无量纲扭转角和无量纲位移量,进一步探究复合材料水翼结构的弯扭耦合作用对其变形特性的影响.最后利用蔡-吴失效准则进行复合材料水翼强度特性的判断和分析,结果表明:不同铺层角复合材料水翼的蔡-吴系数,随铺层角的增大呈现先减小后增大的趋势,其中0°铺层时的复合材料水翼蔡-吴系数最小,50°铺层时的复合材料水翼的蔡-吴系数最大.     

温度场中非线性弹性地基上矩形薄板的主共振-主参数共振

为了研究温度场中非线性地基上矩形薄板受简谐激励的主共振-主参数共振问题,应用弹性力学理论建立其动力学方程,应用Galerkin方法将其转化为非线性振动方程.利用非线性振动的多尺度分析方法求得系统主共振-主参数共振的近似解,并进行数值计算.分析温度、地基系数、阻尼、几何参数、激励等对系统主共振-主参数共振的影响.得到了随参数变化响应曲线的变化规律.     

复合材料水翼水动力与结构强度特性数值研究

针对复合材料水翼存在的流固耦合求解问题,结合其自身特有属性,对复合材料水翼结构变形特性进行了数值仿真计算研究.研究建立了复合材料水翼流固耦合数值计算模型,并将数值计算结果与Zarruk等的实验结果进行对比,验证模型的正确性,得出复合材料水翼尖端扭转角随雷诺数的增加而增加的研究结论.基于数值计算模型,系统地研究了不同铺层角对复合材料水翼水动力特性及强度特性的影响,结果表明:不同铺层角复合材料水翼的尖端扭转角,随铺层角的增大而减小,而其尖端位移量随铺层角的增大先减小后增大.为了削弱工程常数的影响对复合材料水翼变形的影响,研究提出了无量纲扭转角和无量纲位移量,进一步探究复合材料水翼结构的弯扭耦合作用对其变形特性的影响.最后利用蔡$\!$-$\!$-$\!$吴失效准则进行复合材料水翼强度特性的判断和分析,结果表明:不同铺层角复合材料水翼的蔡$\!$-$\!$-$\!$吴系数,随铺层角的增大呈现先减小后增大的趋势,其中0$^\circ$铺层时的复合材料水翼蔡$\!$-$\!$-$\!$吴系数最小,50$^\circ$铺层时的复合材料水翼的蔡$\!$-$\!$-$\!$吴系数最大.      

温度变化对不同边界梁非线性振动及特性影响

温度变化有可能导致工程结构产生温度应力,引起结构振动特性发生改变.因此针对工程中常见的受轴力作用梁,基于Hamilton变分原理,在梁的应力-应变关系中引入温度变化,推导其非线性运动微分方程.针对三类边界条件(铰支-铰支、铰支-固支和固支-固支),开展特征值分析及模态离散.利用摄动法求解系统非线性自由振动和主共振响应的近似解,并得到其幅频响应方程.通过算例研究温度变化对梁非线性振动特性影响.研究结果表明:梁固有频率和温度变化呈现出反比例关系;温度变化与梁非线性振动时硬弹簧特性的程度呈正比例关系;温度变化对小幅和大幅振动时的响应幅值影响恰恰相反;相同温度变化条件对不同边界梁的振动特性影响有定量差异;温度变化会导致梁的位移场曲线发生定量改变.总之梁结构的线性和非线性振动特性受温度响明显,且需特别关注其边界条件.     

考虑损伤效应的悬索非线性共振响应分析

悬索在其施工、运营和维护阶段会不可避免地遭受损伤,导致振动特性发生改变。本文基于哈密顿变分原理,引入与损伤程度、范围和位置相关的三个无量纲参数,建立损伤效应影响下悬索面内动力学模型,并推导其无穷维的非线性动力学微分方程。利用高阶多尺度法得到系统发生主共振响应时的幅频响应方程及稳态解。数值算例表明,悬索线性和非线性共振响应特性与损伤效应密切相关。悬索一旦发生损伤,其张力减小,垂跨比增加,将形成新的静力构形。受损悬索的固有频率将下降,且随着损伤程度增加而进一步减小。损伤会导致悬索正/反对称模态频率的交点发生偏移,影响系统内共振响应特性;损伤会引发系统振动特性发生明显定量和定性改变,但是垂跨比不同,其共振响应特性受损伤影响会有明显区别;损伤甚至会直接改变系统稳态响应幅值以及稳定解的数量,导致系统产生明显大幅振动,影响结构安全。     

具有复合正交异性铺层和偏心加筋的圆柱壳体的屈曲问题

本文导出了具有正交异性复合铺层和偏心加筋的圆柱壳体在轴压、横向压力或它们的任意组合作用下的屈曲问题的近似解,文中提出的方法使壳中不同铺层及偏心加筋引起的弯曲与拉伸间的耦合研究成为可能。以前的研究方法表明由于忽略了弯一拉耦合效应,所予测的屈曲结果是不完全正确的。     

船用复合材料螺旋桨研究进展

复合材料具有比强度高,阻尼性能好及可调整纤维铺层以控制结构变形等优点.复合材料应用于螺旋桨将改善螺旋桨的推进性能和振动特性.通过对国内外复合材料螺旋桨研究成果的回顾、总结和归纳,得出了传统的算法已不满足复合材料螺旋桨的设计和预报要求,复合材料螺旋桨的设计和预报算法需考虑桨叶变形引起的空间流场变化的结论.分析了可借助纤维增强材料所具有的弯扭耦合特性,调整桨叶纤维材料铺层和桨叶结构形式来提高螺旋桨推进效率的规律性.总结了复合材料螺旋桨研究中的关键技术和复合材料螺旋桨设计流程,并指出了复合材料螺旋桨未来研究的趋势.      

Stability analysis of a nonlinear rotating asymmetrical shaft near the resonances

An asymmetrical rotating shaft with unequal mass moments of inertia and flexural rigidities in the direction of principal axes is considered. In this system, there are two excitation sources, including a harmonic excitation due to the dynamic imbalances and a parametric excitation due to shaft asymmetry. Nonlinearities are due to the in-extensionality of the shaft and large amplitude. In this study, harmonic and parametric resonances due to the mentioned effects are considered. The influences of inequality of mass moments of inertia and flexural rigidities in the direction of principal axes, inequality between two eccentricities corresponding to the principal axes and external damping on the stability and bifurcation of steady state response of the rotating asymmetrical shaft are investigated. In addition, the characteristic of stable stationary points and loci of bifurcation points as function of damping coefficient are determined. In order to analyze the resonances of the system the multiple scales method is applied to the complex form of partial differential equations of motion. The achieved results show a good agreement with those of numerical computation.     

Dynamic stability and bifurcation of a nonlinear in-extensional rotating shaft with internal damping

In this paper, stability and bifurcations in a simply supported rotating shaft are studied. The shaft is modeled as an in-extensional spinning beam with large amplitude, which includes the effects of nonlinear curvature and inertia. To include the internal damping, it is assumed that the shaft is made of a viscoelastic material. In addition, the torsional stiffness and external damping of the shaft are considered. To find the boundaries of stability, the linearized shaft model is used. The bifurcations considered here are Hopf and double zero eigenvalues. Using center manifold theory and the method of normal form, analytical expressions are obtained, which describe the behavior of the rotating shaft in the neighborhood of the bifurcations.     

Two-mode combination resonances of an in-extensional rotating shaft with large amplitude

In this paper, two-mode combination resonances of a simply supported rotating shaft are investigated. The shaft is modeled as an in-extensional spinning beam with large amplitude. Rotary inertia and gyroscopic effects are included, but shear deformation is neglected. The equations of motion are derived with the aid of the Hamilton principle and then transformed to the complex form. The method of harmonic balance is applied to obtain analytical solutions. Frequency-response curves are plotted for the combination resonances of the first and the second modes. The effects of eccentricity and external damping are investigated on the steady state response of the rotating shaft. The loci of saddle node bifurcation points are plotted as functions of external damping and eccentricity. The results are validated with numerical simulations.     

Nonlinear vibrations of blade with varying rotating speed

This paper investigates the nonlinear dynamic responses of the rotating blade with varying rotating speed under high-temperature supersonic gas flow. The varying rotating speed and centrifugal force are considered during the establishment of the analytical model of the rotating blade. The aerodynamic load is determined using first-order piston theory. The rotating blade is treated as a pretwist, presetting, thin-walled rotating cantilever beam. Using the isotropic constitutive law and Hamilton??s principle, the nonlinear partial differential governing equation of motion is derived for the pretwist, presetting, thin-walled rotating beam. Based on the obtained governing equation of motion, Galerkin??s approach is applied to obtain a two-degree-of-freedom nonlinear system. From the resulting ordinary equation, the method of multiple scales is exploited to derive the four-dimensional averaged equation for the case of 1:1 internal resonance and primary resonance. Numerical simulations are performed to study the nonlinear dynamic response of the rotating blade. In summary, numerical studies suggest that periodic motions and chaotic motions exist in the nonlinear vibrations of the rotating blade with varying speed.     

Resonant dynamics in a rotordynamic system with nonlinear inertial coupling and shaft anisotropy

The response of a nonlinear, damped Jeffcott rotor with anisotropic stiffness is considered in the presence of an imbalance. For sufficiently small external torque or large imbalance, resonance capture or rotordynamic stall can occur, whereby the rotational velocity of the shaft is unable to increase beyond the fundamental resonance between the rotational and translational motion. This phenomena provides a mechanism for energy transfer from the rotational to the translational mode. Using the method of averaging a reduced-order model is developed, valid near the resonance, that describes this resonant behavior. The equilibrium points of these averaged equations, which correspond to stationary solutions of the original equations and rotordynamic stall, are described as the applied torque, damping, and anisotropy vary. As the anisotropy increases, assumed to arise from increasing shaft cracks, the torque required to eliminate the possibility of stall increases. However, when the system is started with zero initial conditions, the minimum torque required to pass through the resonance is approximately constant as the anisotropy increases. The predictions from the reduced-order model are verified against numerical simulations of the original equations of motion.     

Resonances of an in-extensional asymmetrical spinning shaft with speed fluctuations

In this study, main and parametric resonances of an asymmetrical spinning shaft with in-extensional nonlinearity and large amplitude are simultaneously investigated. The main resonance is due to inhomogeneous part of the equations of motion, which is due to dynamic imbalances of shaft whereas the parametric resonances are due to parametric excitations due to speed fluctuations and a shaft asymmetry. The shaft is simply supported with unequal mass moments of inertia and flexural rigidities in the direction of principal axes. The equations of motion are derived by the extended Hamilton principle. The stability and bifurcations are obtained by multiple scales method, which is applied to both partial and ordinary differential equations of motion. The influences of asymmetry of shaft, speed fluctuations, inequality between two eccentricities corresponding to the principal axes and external damping on the stability and bifurcation are studied. To investigate the effect of speed fluctuations on the bifurcations and stability the loci of bifurcation points are plotted as function of damping coefficient. The numerical solutions are used to verify the results of multiple scales method. The results of multiple scales method show a good agreement with those of numerical solutions.     

Nonlinear harmonic response characteristics and experimental investigation of cantilever hard-coating plate

The nonlinear harmonic response of a cantilever hard-coating plate which is made of a layer of anisotropic hard-coating material and isotropic metal substrate is investigated based on the theory of high-order shear deformation of plate. Firstly, based on the theories of von Karman and Reddy’s three-order shear deformation, the nonlinear dynamic equations of hard-coating plate are built by Hamilton variation principle. Secondly, to obtain nonlinear governing equation of hard-coating plate under transverse load, these equations are discretized in Galerkin method. The system averaged equations with 1:3 internal resonances are obtained by the method of multiple scales, and the multi-periodic responses behavior of cantilever hard-coating plate under transverse loading could be presented. Finally, the vibration response experiment of hard-coating plate is conducted, and the multi-periodic responses are also present for the hard-coating plate with three-to-one internal resonance. Besides, through the vibration response experiment of uncoated titanium alloy plate, the damping characteristic of hard coating is further analyzed.     

Forced vibration analysis of the milling process with structural nonlinearity,internal resonance,tool wear and process damping effects

In this paper, forced vibration analysis of an extended dynamic model of the milling process is investigated, in the presence of internal resonance. Regenerative chatter, structural nonlinearity, tool wear and process damping effects are included in the proposed model. Taking into account the average and first order expansion of Fourier series for cutting force components; their closed form expressions are derived. Moreover, in the presence of large vibration amplitudes, the loss of contact effect is included in this model. Analytical approximate response of the nonlinear system is constructed through the multiple-scales approach. Dynamics of the system is studied for two cases of primary and super-harmonic resonance, associated with the internal resonance. Under steady state motion, the effects of structural nonlinearity, cutting force coefficients, tool wear length and process damping are investigated on the frequency response functions of the system. In addition, existence of multiple solutions, jump phenomenon and energy transfer between vibration modes are presented and compared for tow cases of primary and super-harmonic resonances.     

Nonlinear vibration of a rotating laminated composite circular cylindrical shell: traveling wave vibration

In this paper, the large-amplitude (geometrically nonlinear) vibrations of rotating, laminated composite circular cylindrical shells subjected to radial harmonic excitation in the neighborhood of the lowest resonances are investigated. Nonlinearities due to large-amplitude shell motion are considered using the Donnell’s nonlinear shallow-shell theory, with account taken of the effect of viscous structure damping. The dynamic Young’s modulus which varies with vibrational frequency of the laminated composite shell is considered. An improved nonlinear model, which needs not to introduce the Airy stress function, is employed to study the nonlinear forced vibrations of the present shells. The system is discretized by Galerkin’s method while a model involving two degrees of freedom, allowing for the traveling wave response of the shell, is adopted. The method of harmonic balance is applied to study the forced vibration responses of the two-degrees-of-freedom system. The stability of analytical steady-state solutions is analyzed. Results obtained with analytical method are compared with numerical simulation. The agreement between them bespeaks the validity of the method developed in this paper. The effects of rotating speed and some other parameters on the nonlinear dynamic response of the system are also investigated.     

A simple spinning laminated composite shaft model

A simple spinning composite shaft model is presented in this paper. The composite shaft contains discrete isotropic rigid disks and is supported by bearings that are modeled as springs and viscous dampers. Based on a first-order shear deformable beam theory, the strain energy of the shaft are found by adopting the three-dimensional constitutive relations of material with the help of the coordinates transformation, while the kinetic energy of the shaft system is obtained via utilizing the moving rotating coordinate systems adhered to the cross-sections of shaft. The extended Hamilton’s principle is employed to derive the governing equations. In the model the transverse shear deformation, rotary inertia and gyroscopic effects, as well as the coupling effect due to the lamination of composite layers have been incorporated. To verify the present model, the critical speeds of composite shaft systems are compared with those available in the literature. A numerical example is also given to illustrate the frequencies, mode shapes, and transient response of a particular composite shaft system.