振动轮式微机械陀螺动力学方程、振动模态及其灵敏度分析

介绍了一种新的振动轮式微机机械陀螺仪的结构及工作原理,详细推导了该陀螺的动力学方程,分析了其运动规律,并建立了该陀螺的三维有限元模型,给出了前其四阶模态振型,对灵敏度进行了分析模拟。     

碳纳米管应变传感器的性能分析：实验偏振模式的影响机制

碳纳米管作为一种拉曼力学传感介质具有优异的力学性质及共振、偏振拉曼特性。将碳纳米管散布在基体材料中,即可实现局部应力/应变的测量。受到光学衍射极限的限制,常规的远场拉曼光谱得到的是一定区域内众多碳管的平均散射信息。本文综合考虑了采样点内各方向碳管的影响,并对碳管散射的共振状态、碳管的分布状态、拉曼系统的偏振构型及偏振方向等实验因素对碳纳米管应变传感器性能的影响进行了深入分析,采用分峰和重构的方法定量地给出了不同实验模式下采样点内的拉曼信息组成以及各种实验模式的测量精度。分析和对比表明,采用双偏振构型且偏振方向沿荷载施加方向时的测量精度最高,即最优的实验模式。     

Nonlinear Response of Cylindrical Shells to Random Excitation

An analytical study of nonlinear flexural vibrations of cylindrical shells to random excitation is presented. Donnell's thin-shell theory is used to develop the governing equations of motion. Thermal effects for a uniform temperature rise through the shell thickness are included in the formulation. A Monte Carlo simulation technique of stationary random processes, multi-mode Galerkin-like approach and numerical integration procedures are used to develop nonlinear response solutions of simply-supported cylindrical shells. Numerical results include time domain response histories, root-mean-square values and histograms of probability density. Comparison of Monte Carlo results is made to those obtained by statistical linearization and the Fokker–Planck equation.     

迟滞系统受随机激励的响应计算

首先为随机激励设计了具有较高精度的滤波器，把迟滞系统受有色噪声激励的随机振动问题转化为由迟滞系统与滤波器组成的扩阶系统受白噪声激励的随机振动问题，然后详细论述了等效线性化法对此问题的具体求解，着重推导了高斯随机变量联合矩的递推关系和李亚普诺夫方程解法的实现，最后根据数字模拟结果分析了等效线性化法的精度和误差来源，给出了迟滞减振系统参数设计的有关建议。     

The Influence of Periodic Excitation on a Turbulent Separation Bubble

Turbulent separation limits the performance in many engineering applications, for example creating pressure losses in diffuser like flows or stall on aircraft wings. In the present study the turbulent boundary layer flow over a flat plate separating due to an adverse pressure gradient is studied as a model problem and the effect of periodic excitation in both time and space is investigated through direct numerical simulations. Linear stability analysis is used to analyse the sensitivity of the flow with respect to time-periodic excitations. The dependence on position, amplitude and frequency of the forcing is investigated. For a certain frequency range at sufficiently high amplitudes, it is possible to eliminate the separated region. Furthermore, three-dimensional effects are studied by applying a steady spanwise forcing as well as a both time-dependent and spanwise varying forcing. A forcing varying in spanwise direction is shown to be the most effective in eliminating the separated region, whereas two-dimensional time-periodic excitation was not as efficient as it was expected.     

薄型超声电机与定子振动模态的激发

论述了薄型超声电机的工作机理。分析了电机压电片的布置与激励信号的关系，探讨了定子弯曲模态的激发问题。设计并制作了一种新的薄型超声电机。电机转子安装在圆环定子内，能够显著减小电机厚度，电机定子采用双压电片结构，可以避免激发出定子的非轴称模态。完成了电机运转实验，电机运转平稳。     

Response Statistics of Three-Degree-of-Freedom Nonlinear System to Narrow-Band Random Excitation

The principal resonance of a 3-DOF nonlinear system to narrow-band random external excitations is investigated. The method of multiple scales is used to derive the equations for modulation of amplitude and phase. The behavior, stability and bifurcation of steady-state responses are studied by means of qualitative analysis. The effects of damping, detuning, and excitation intensity on responses are analyzed. The theoretical analyses are verified by numerical results. Both theoretical analyses and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle. Under some conditions, co-existence of two kinds of stable steady-state solutions, saturation and jump phenomena may occur. The stationary probability density function of responses for the co-existence case is obtained approximately.     

谐和与随机噪声联合作用下非线性系统的响应

研究了Duffing振子在谐和与随噪声联合激励下的响应和稳应性问题。用谐波平均法分析了系统在确定性谐和激励和随机激励联合作用下的响应,用随机平均法讨论了随机扰动项对系统晌应的影响。在一定条件下,系统具有两个均方响应值和跳跃现象。数值模拟表明本文提出的方法是有效的。     

辛体系下曲线形水中悬浮隧道对波浪激励的动力响应研究

在哈密顿体系下建立曲线形水中悬浮隧道的运动方程,即哈密顿正则方程.用哈密顿混合能变分原理处理曲线形水中悬浮隧道的两端边界条件以及径向布设的张力腿弹性支承,建立满足边界条件的线性方程组,采用分离变量法和本征向量展开法求解哈密顿正则方程.为曲线形水中悬浮隧道的动力响应分析提供一类方法.最后结合案例,运用辛方法分析波浪作用下曲线形水中悬浮隧道的弯矩和扭矩,结果表明,可以忽略扭矩对弯矩的影响.     

随机剪切柱在地震激励下的演变随机响应

随机剪切柱是指固连于地面的剪切柱的某些物理参数是随机变量 ,该模型在Niigata地震激励下的响应属于演变随机响应。本文将新近发展起来的演变随机响应问题的统一解法 ,推广到用于求解随机结构振动响应问题。首先用这一方法求出每个样本结构的随机响应 ,然后用MonteCarlo法来进一步求随机结构的集合随机响应特性。这样 ,与单纯用Monte Carlo法进行数字模拟相比 ,可使计算工作量大为减少。本文用随机剪切柱的演变随机响应问题加以说明     

窄带随机噪声激励下多自由度非线性系统的响应

在随机振动的研究中，研究较多的是系统在宽带噪声作用下的响应问题，对于非线性系统特别是多自由度非线性系统在窄带随机噪声作用下的响应问题则研究较少。本文研究了三自由度非线性系统在窄带随机噪声激励下的主共振响应和稳定性问题。用多尺度法分离了系统的快变项，给出了系统响应的振幅和相位角满足的方程。用摄动法讨论了系统随机项对系统响应的影响。当随机扰动较小时，在一定的参数范围内，对应于不同的初值，系统具有两个均方响应值，随机饱和现象也存在。当随机扰动增大时，系统可从一个大的响应突跳为一个小的响应，或从一个小的响应突跳为一个大的响应，即存在随机跳跃现象。数值模拟表明本文提出的方法是有效的。     

单自由度系统的爆炸地震演变响应

提出了一个单自由度结构系统爆炸地震随机地面振动演变响应的理论分析方法。根据爆炸地震效应的特点 ,建立了一个地面运动激励模型 ,并以TNT炸药爆炸实验测试结果为实例 ,讨论了模型中相关基本参数的确定方法及其结果。在给定结构固有频率和阻尼系数条件下 ,得到了单自由度系统的爆炸地震位移响应功率演变谱和均方根位移理论解。与在一个混凝土基座上的测试结果进行对比表明 ,得到的理论均方根位移具有较好的预测精度。     

Stochastic Dynamic Response of Multiply Supported Tuned Subsystems to Nonstationary Seismic Excitation

ABSTRACT

Stochastic dynamic response of multiple degree of freedom (MDOF) subsystems that are attached at multiple points to an MDOF supporting structure that is subjected to seismic excitation is obtained by using a modal time domain random vibration approach. An earthquake is modeled as a nonstationary, nonwhite, vector random process that has a realistic spectral shape and finite ground displacement, velocity, and acceleration. Analyses of secondary systems are decoupled from the primary system without loss of accuracy when the cascading assumption is appropriate. This makes the design process of subsystems convenient and efficient. When tuning occurs, cascading assumptions are no longer appropriate. Previously obtained results for the modal properties of combined systems in terms of modal properties of the primary system and subsystems are then utilized. Results account for tuning spatial coupling in terms of stiffness and inertia. Exact analytical expressions are obtained for the elements of the state transition matrix and the evolutionary covariance matrix of various responses. The solution is exact, within the limitations of modal analysis, since all the cross terms between modal coordinates are considered. Finally the capabilities of this approach are illustrated through analysis of an example.     

激励脉冲信号对基于周向导波的圆环损伤检测的影响

针对含有径向裂纹的圆环,本文主要研究了不同激励脉冲信号对基于周向导波的圆环损伤检测结果的影响.对具有径向裂纹以及没有裂纹的圆环,分别用不同宽度的脉冲信号激励,然后用ABAQUS程序数值计算其应变信号.由Gabor连续小波转换(CWT)处理上述应变信号以确定径向裂纹的位置.结果显示,脉冲宽度对确定裂纹位置的精确性有很大影响.根据圆环的群速弥散曲线,讨论了圆环上裂纹的确定方法.最后,为验证检测圆环损伤所选择脉冲宽度的合理性,进行了两次实验.两次实验提供了相同的结论.     

Gauss白噪声外激下Rayleigh振子的平稳响应与首次穿越

研究了Rayleigh振子在Gauss白噪声外激下的平稳响应和首次穿越。首先利用随机平均法给出了系统随机平均It^o微分方程,对平均方程的稳态概率密度做了数值分析;然后建立了条件可靠性函数的后向Kolmogorov方程及首次穿越时间条件矩的Pontragin方程;最后对三组不同的参数值分析了首次穿越的概率统计特性。     

Influence of Horizontal Excitations on Dynamic Stability of a Slender Beam Under Vertical Excitation

Experimental studies have been conducted to clarify the influence of horizontal harmonic excitations on the dynamic stability of a slender cantilever beam under vertical harmonic excitation. Three kinds of aluminum test beams with rectangular cross section have been used. The test beam being clamped at one end and free at the other end, was vertically stood, and was harmonically excited to both vertical and horizontal directions simultaneously. The direction of the horizontal excitation was taken parallel to one of the beam side faces, i.e. two directions were considered as X and Y directions which have the largest and smallest flexural rigidity, respectively. By varying the horizontal excitation amplitude, keeping the amplitude of excitation in the vertical direction, the influence of the horizontal excitation has been investigated on the principal instability regions in which unstable vibration of the fundamental vibration mode occurs. The excitation frequency in the vertical excitation was taken around twice the fundamental natural frequency 2f _{Y 1} in smallest rigidity direction, while that in the horizontal direction was taken around both the fundamental natural frequency f _{Y 1} and twice of it 2f _{Y 1}. Obtained experimental results present useful fundamental data for aseismatic design of structures under earthquake containing both vertical and horizontal excitation components.     

Periodic Response and Chaos in Nonlinear Systems with Parametric Excitation and Time Delay

In this paper, the periodic motions of a nonlinear system with quadratic,cubic, and parametrically excited stiffness terms and with time-delayterms are obtained by the incremental harmonic balance (IHB) method. Theelements of the Jacobian matrix and residue vector arising in the IHBformulation are derived in closed form. A mechanism model representingthe one-mode oscillation of beams and plates is considered as anexample. A path-following algorithm with an arc-length parametriccontinuation procedure is used to obtain the response diagrams. Thesystem also exhibits chaotic motion through a cascade of period-doublingbifurcations, which is characterized by phase planes, Poincaré sectionsand Lyapunov exponents. The interpolated cell mapping (ICM) procedure isused to obtain the initial condition map corresponding to multiplesteady-state solutions.     

The Response of an Oscillator Moving along a Parabola to an External Excitation

The behavior of a mass point moving along a parabola under theeffect of an external periodic excitation in resonance with the naturalfrequency of the oscillator is studied. The asymptotic perturbationmethod based on temporal rescaling and balancing of the harmonic termswith a simple iteration is used in order to determine the nonlinearmodulation equations for the amplitude and the phase of the oscillation.External force-response curves are shown and moreover jump phenomena arealso observed. In certain cases a second low frequency appears inaddition to the forcing frequency and then stable two-periodquasi-periodic motions are present with amplitudes depending on theinitial conditions. The value of the low frequency depends on theamplitude of the external excitation. A higher order perturbationanalysis is developed and the validity of the method is highlighted bycomparing the leading order and the higher order approximate analyticsolutions to numerical results.     

Subharmonic Response of a Quasi-Isochronous Vibroimpact System to a Randomly Disordered Periodic Excitation

A quasi-isochronous vibroimpact system is considered, i.e. a linear system with a rigid one-sided barrier, which is slightly offset from the system's static equilibrium position. The system is excited by a sinusoidal force with disorder, or random phase modulation. The mean excitation frequency corresponds to a simple or subharmonic resonance, i.e. the value of its ratio to the natural frequency of the system without a barrier is close to some even integer. Influence of white-noise fluctuations of the instantaneous excitation frequency around its mean on the response is studied in this paper. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, or velocity jumps, thereby permitting the application of asymptotic averaging over the period for slowly varying inphase and quadrature responses. The averaged stochastic equations are solved exactly by the method of moments for the mean square response amplitude for the case of zero offset. A perturbation-based moment closure scheme is proposed for the case of nonzero offset and small random variations of amplitude. Therefore, the analytical results may be expected to be adequate for small values of excitation/system bandwidth ratio or for small intensities of the excitation frequency variations. However, at very large values of the parameter the results are approaching those predicted by a stochastic averaging method. Moreover, Monte-Carlo simulation has shown the moment closure results to be sufficiently accurate in general for any arbitrary bandwidth ratio. The basic conclusion, both of analytical and numerical simulation studies, is a sort of smearing of the amplitude frequency response curves owing to disorder, or random phase modulation: peak amplitudes may be strongly reduced, whereas somewhat increased response may be expected at large detunings, where response amplitudes to perfectly periodic excitation are relatively small.     

基于实测频响函数的子结构模态综合

本文以梁型结构串联布局为应用背景,研究了导纳综合法的试验模态分析.探讨了界面自由度的选取、刚体模态的处理、预测阻尼比的可能性以及影响预测精度的因素.物理梁试验结果表明,导纳综合法能精确地预测组装结构的频响函数和所需的模态参数.