非线性动力系统的频率近似法

给出非线性动力系统周期振动的频率近似法，本法将描述动力系统的非线性微分方程，化为以相角为自变量，振动频率为未知函数的积分方程，将弹性恢复力表示为线性及非线性两部分，从而得到积分方程的近似解，即频率的近似表达式。     

大量程闭环MEMS加速度计非线性分析与优化法

为研究大量程翘翘板摆式闭环MEMS加速度计系统的输出非线性,分别从质量块受力不平衡所产生的平动效应以及电路零位引起质量块闭环平衡位置偏差两个主要误差源入手,建立了两种误差引起加速度计非线性的数学模型,并采用ANSYS和Simulink软件对传感器结构及系统进行了仿真验证,确定了该模型的正确性及非线性的优化方法。最后,按照以上分析进行了样机制作和离心测试。试验结果表明,通过减小翘翘板摆式结构质量块的平动效应,可将±150g量程加速度计的非线性由5.4979′10-2减小至5.320′10~(-3),在此基础上通过减小质量块闭环平衡位置偏差,可进一步将加速度计的非线性减小至2.772′10~(-3)。     

强非线性动力系统的频率增量法

提出一类强非线性动力系统的暧时频率增量法,将描述动力系统的二阶常微分方程,化为以相位为自变量、瞬廛频率为未知函数的积分方程;用谐波平衡原理,将求解瞬时频率的积分问题,归结为求解以频率增量的Fourier系数为独立变量的线性代数方程组;给出了若干例子。     

一种谐振式微加速度计表芯非线性动力学分析及实验

在研制基于静电刚度谐振式微加速度计过程中,发现增大激励电压可以提高输出信噪比,但响应的振动幅度将不稳定,同时谐振频率也将会出现漂移。针对上述问题,建立了静电驱动微机械谐振系统等效行为模型,非线性动力学理论分析结果与实验现象一致,总结出需要从加速度计结构参数优化和减小激励电压两个方面来减小频率漂移和提高分辨率。将结构优化准则应用到制造的微加速度计上,实验结果表明:在5 V敏感电压下,闭环条件下单梁加速度计灵敏度为58 Hz/g,分辨率为3.5 mg。     

计算圆板大振幅非线性振动频率的平均刚度法

本文用平均刚度法研究圆板大振幅非线性振动的频率问题，导出了相应的非线性广义特征值方程，构造了一种避免发散并能加速收敛的加权平均迭代法，计算结果与Ｋａｎｔｏｒｏｖｉｃｈ时间平均法的解十分吻合。     

非线性碟簧动力吸振器的宽带数值优化设计及其应用

提出了非线性碟簧动力吸振器的宽带数值优化设计,推广了前人在非线性动力吸振器领域的研究．首先提出了计算耦合非线性动力吸振器的主系统的稳态响应的平均法,然后采用数值优化法详细的研究了非线性动力吸振器的宽带优化设计,系统讨论了质量比、主系统阻尼比、吸振器阻尼比、系统频率比、激励频率比、位移比、吸振器刚度非线性系数和吸振器阻尼非线性系数与抑振带宽的关系;最后考虑了非线性动力吸振器的应用实例,指出非线性动力吸振器可以显著拓宽抑振频带．     

非线性粘弹性大挠度梁的动力学模型及其简化

本文建立了描述几何非线性均匀梁动力学行为的偏微分－－积分方程,梁的材料满足Ｌｅａｄｅｍａｎ非线性本构关系,对于两端简支的情形用Ｇａｌｅｒｋｉｎ方法进行了截断简化为常微分－－积分方程,然后引进附加变量的方法进一步简化为常微分方程组。     

非线性碟簧动力吸振器的宽带数值优化设计及其应用

提出了非线性碟簧动力吸振器的宽带数值优化设计，推广了前人在非线性动力吸振顺领域的研究，首先提出了计算耦合非线性动力吸振器的主系统的稳态响应的平均法，然后采用数值优化法详细的研究了非线性动力吸振器的宽带优化设计，系统讨论了质量比、主系统阴尼比、吸振器阴尼比、系统频率比、激励频率比、位移比、吸振器刚度非线性系数和吸振器阻尼非线性系数与抑带宽的关系，最后考虑了非线性动力吸振器的应用实例，指出非线性动力吸     

石英振梁加速度计谐振器的结构设计

石英谐振器的设计是实现高精度石英振梁加速度计的关键。首先对石英晶体的最优切型切角结构进行研究,确定石英晶体的最优切型切角为(xyt)5°。其次,理论分析并通过仿真验证了石英谐振器的结构参数对石英振梁加速度计标度因数的影响,并对石英谐振器的结构参数进行了优化。最后,对石英谐振器进行了模态仿真,并分析了石英谐振器的尺寸制作偏差对标度因数的影响。用有限元分析方法得到了石英谐振器的理想振型,且石英振梁加速度计的标度因数为40 Hz/g。理论及仿真结果表明该石英谐振器可应用于高标度因数石英振梁加速度计中。     

时滞非线性动力吸振器的减振机理

对一个带有时滞非线性动力吸振器的两自由度结构,采用多尺度法研究了时滞非线性动力吸振器对主系统的减振性能,得到了主系统的振幅-时滞响应曲线.研究结果表明,对时滞非线性动力吸振器,可以通过调节反馈增益系数和时滞控制主系统的振动. 研究还发现,对确定的反馈增益系数,可以存在时滞的一些调节区域,时滞非线性动力吸振器可以减小主系统的振动. 并且在时滞的这些可调区域里,存在一个``最大减振点'对应这一反馈增益系数下主系统振幅的最小值.对不同的反馈增益系数,``最大减振点'对应的主系统的振幅也不同.因此能够找到一组反馈增益系数和时滞量的最佳值,最大程度地减小主系统的振动.研究结果表明,当反馈增益系数和时滞量调到最佳值时,主系统的振动较无时滞非线性动力吸振器可以减少90{\%}左右, 数值模拟也证实了解析结果的正确性.      

提高石英音叉陀螺驱动信号稳定性的数字电路设计

石英音叉陀螺通常采用模拟解调电路,现有模拟电路驱动电路幅度稳定性不高,限制了石英音叉陀螺整机性能,可以采用数字电路提高驱动幅度稳定性。文中先讨论了驱动信号幅度影响石英音叉陀螺性能的原因;然后设计了数字电路,采用数字信号处理算法实现了数字电路闭环驱动,并对数字电路闭环驱动的自动增益控制误差进行了分析;最后,对模拟电路和数字电路的驱动幅度稳定性进行了对比测试,定温情况下,模拟电路驱动幅度稳定性的均方差为4.77×10-4V,数字电路的幅度稳定性的均方差达到8.26×10-5V,模拟电路幅度稳定性在全温范围的均方差为0.0680 V,数字电路的均方差仅为0.0006V。实验表明,数字电路的驱动信号幅度稳定性显著提高。     

石英音叉陀螺信号解调原理和角速度提取算法

介绍了石英音叉陀螺输出信号的成分,通过将其误差信号分解为一组相互正交的信号,建立了输出信号的模型.提出了一种利用基于锁相环(PLL)的正交矢量型锁定放大器解调石英音叉陀螺信号的方案,该方案利用锁相环作为锁定放大器的参考通道,它能消除驱动信号漂移的影响,并为正交矢量型锁定放大器提供一组互相正交的参考信号.正交矢量型锁定放大器提供被测信号的矢量信息,它输出的同相分量和正交分量通过旋转校正算法消除误差信号,从而提取出角速度信号.     

Parameter tuning of ADRC and its application based on CCCSA

Active disturbance rejection controller can effectively adjust uncertain factors and the disturbance of the model by compensation. However, this advantageous controller has met with a technical bottleneck in its extensive use of engineering application because of its multiplicity of the parameters and the difficulty of integrating them. This paper proposes a chaotic cloud cloning selection algorithm by referring to cloud model and immune cloning selection, generating initial population by employing chaotic initialization to improve the quality of the initial antibodies, realizing mutation with basic normal cloud generator to improve the diversity of antibodies. Then the chaotic cloning selection algorithm is applied to the optimization of parameter integration. This new algorithm is tested and verified as to its convergence speed, convergence precision, and robustness with classic function. The results of simulation experiments for a time-delay system demonstrate that the optimized control system not only possesses excellent control performance but also exhibits strong robustness and anti-interference ability.     

Plane nonaxisymmetric deformation of a viscoelastic cylinder with consideration of its physical and geometric nonlinearity

The nonaxisymmetric plane problem of the nonlinear theory of viscoelasticity is solved for a cylinder reinforced by an elastic circular shell. The cylinder has an internal cut resembling a Maltese cross in shape. The identification of the nonlinear endochronous theory of aging viscoelastic materials is conducted by a genetic algorithm method on the basis a nonmonotonic experimental stress-strain dependence. Some numerical results obtained for the stress-strain state of this cylinder under the action of internal pressure are discussed with consideration of the above physical nonlinearity and the finite logarithmic strains.     

Amplitude modulation and its relation to streamwise convection velocity

The paper is devoted to show the relation between the amplitude modulation and the convection velocity in a turbulent boundary layer. The analysis has been performed based upon velocity profiles measured with the hot-wire technique in a turbulent boundary layer with pressure gradient corresponding to turbomachinery conditions. The VITA detection method of small-scale structures was used in order to show the impact of the pressure gradient on phase averaged time-traces changes in the aspect of amplitude modulation. The physical significance of the large scales influence on the small scales, formerly known as the amplitude modulation, has been elucidated. It was demonstrated that the measure of amplitude modulation can be used as an indicator of the convection velocity of coherent structures. The convection velocity profile can be described in the inner region using the amplitude modulation term when the proper scale is applied. The convection velocity prediction in favourable and adverse pressure gradients shows that t the strongest impact of the pressure gradient occurs in the buffer layer. The stronger increase occurs in the buffer layer. It was also found that the skewness factor of phase-averaged VITA waveforms, is very similar in shape with the cross-product term of the streamwise skewness factor, which quantifies amplitude modulation. It indicates that the well-known modification of quadrant events in pressure gradient flows is a result of the amplitude modulation phenomenon.     

Acoustic nonlinearity of bubbly liquids

Sources contributing to the acoustic nonlinearity of a gas/liquid mixture are discussed and calculations of a coefficient _eff for the second-order nonlinearity of the mixture are performed based on source strength density functions for parametric acoustic arrays and on formation with source distance of the second harmonic to a monochromatic wave propagating through the mixture. Some procedures for experimental determination of _eff are suggested, and it is concluded on basis of the calculations that the dynamic bubble nonlinearity will yield the predominant contribution to the acoustic nonlinearity of the mixture, in particular at resonance.     

Degeneration character of gels under cyclic loading and its constitutive relation

An interesting degeneration behavior of gel materials under cyclic load is found in experiment. In order to explain this phenomenon, a constitutive model is proposed to simulate the microstructure of gels. Further the corresponding constitutive relation and its simplified form that contains six parameters is proposed to describe the nonlinearity and degeneration of gels under cyclic loading and unloading. The data of compression experiments for two typical gels are simulated by computer. The theoretical results are consistent with experiments very well.     

Extended irreversible thermodynamics and its relation with other continuum approaches

We present an introduction to extended irreversible thermodynamics (EIT) as applied to polymer solutions in the presence of shear flow and of diffusion flux. We discuss with special attention the definition of chemical potential in non-equilibrium situations and its use in the analysis of shear-induced phase transitions. In the second part, we compare EIT with other contemporary continuum approaches: theories with internal variables, the GENERIC approach, and the matrix model. All these theories share an emphasis on the relations between dynamics and thermodynamics at a deeper level than in the classical theory, but each of them has some peculiar advantage in the analysis of some specific aspects of physical problems.     

单层平面索网幕墙结构的几何非线性问题研究

单层平面索网支承式玻璃幕墙结构是近年来在国内外应用较为广泛的一种新型幕墙结构形式,由于单层平面索网不具有负高斯曲面形式,结构在平面外方向的刚度偏柔,表现出较明显的几何非线性特征.本文采用连续化方法建立了单层平面索网结构考虑几何非线性影响的静力平衡方程和振动方程,得到了结构刚度的解析表达式,并采用谐波平衡法求得非线性频率的简化解析表达式,以此为基础研究了单层平面索网结构的静力非线性和动力非线性问题.研究结果表明:结构的非线性和结构的初始位置密切相关;结构的非线性频率主要取决于索的初始应变、结构振动幅值与跨度的比值,几何非线性对于结构动力性能的影响要小于对结构静力性能的影响;本文得到的结构在地震荷载和平均风荷载作用下的非线性振动方程和非线性频率为结构在地震荷载和脉动风荷载作用下动力响应的求解奠定了基础.