梁波传播的固有特性

以分布参数的理论为基础，分析了梁波传播的一些固有特性，说明了它们与周期性结构的关系，讨论了支持条件对波传播特性的影响，指出了如果把近似方法应用于波传播分析中，可能引起的一些问题．本文的结果可直接应用于周期性结构的分析中     

板的非线性热弹耦合振动（Ⅰ）：近似解析解

本文以文[2,3,4]为基础,导出了板的热弹耦合非线性振动控制方程,在采用Galerkin法离散化以后,按各个变量性质分别用多尺度法或正则摄动法求得近似解析解。籍此可揭示系统各参数对非线性热弹耦合振动影响的机理和作出必要的近似计算,对工程实际具有较大的参考价值。     

条带式太阳帆的结构动力学分析

依靠光压推进,太阳帆被认为是最可行的星际探测航天器,太阳帆结构总体方案主要有两类:桅杆式和旋转式,其中,帆膜被分割成窄条的条带式太阳帆在桅杆式太阳帆中具有较为理想的结构效率,如何准确计算条带式太阳帆的结构动力学特性值得研究.本文对条带式太阳帆结构的振动特性和结构稳定性进行研究,将太阳帆看作是由若干个桅杆-膜带组件依次连接而成的整体结构,桅杆-膜带组件由4根桅杆段和4条薄膜条带组成,分段轴压作用下的桅杆与薄膜条带耦合振动.考虑帆面薄膜条带与支撑桅杆之间的耦合振动,采用分布传递函数法建立了的条带式太阳帆的结构动力学模型,推导了条带式太阳帆结构自由振动和失稳载荷的求解方法.研究表明:条带式太阳帆构型有利于提高太阳帆结构的整体刚度和结构稳定性,随着帆面薄膜条带数目的增加,太阳帆结构的振动频率和失稳载荷增大;随着帆面薄膜预应力的增大,太阳帆结构振动的基频减小,稳定性变差;随着支撑桅杆刚度的提高,太阳帆结构整体的振动频率和失稳载荷增大.本文建立的解析求解方法具有求解效率快和精度高的特点,为条带式太阳帆的结构设计和姿态控制提供了有力的分析工具.      

Non-Linear Self-Excited Random Vibrations and Stability of an SDOF System with Parametric Noises

Abstract. The paper presents the solution to the properties of stochastic response of a system with random parametric noises, which is prone to the loss of aerodynamical stability. The system is described by an equation of van der Pol type with the negative linear, and with the positive cubic dampings. The coefficients of the linear damping and of the stiffness include the multiplicative random perturbations, the external excitation being given as a sum of a deterministic function and of an additive perturbation. All three input random processes are supposed to be Gaussian and centered, with the non-zero mutual stochastic parameters, as it corresponds to the properties of real systems. The solution has been based on the method of stochastic linearisation and of the subsequent solution of the Fokker–Planck–Kolmogorov equation in the sense of the first and second stochastic moments for the transient and stationary states. There have been demonstrated several effects, which are typical for systems with parametric noises, differentiating them from the systems with constant coefficients. The principal attention has been devoted to the properties of the spectral density of the response, the character of which changes abruptly with the degree of non-linearity of the damping and of the level of random perturbations.Sommario. La presente memoria studia le proprietà della risposta stocastica di un sistema con eccitazione casuale parametrica, che tende alla perdita della stabilità aerodinamica. Il sistema è descritto mediante un'equazione del tipo di van der Pole con il termine lineare dello smorzamento negativo e il termine cubico positivo. Poichá l'eccitazione esterna è la somma di una funzione deterministica e di una perturbazione additiva, i coefficienti dello smorzamento lineare e della rigidezza comprendono le perturbazioni casuali moltiplicative. I tre processi stocastici di eccitazione sono assunti gaussiani e a media nulla con parametri stocastici incrociati diversi da zero, come si verifica per le proprietà dei sistemi reali. La soluzione è basata sul metodo della linearizzazione stocastica e della successiva soluzione dell'equazione di Fokker-Planck-Kolmogorov studiando i primi e i secondi momenti statistici per gli stati transitori e stazionari. Vengono mostrati diversi effetti, tipici dei sistemi con eccitazione parametrica, differenziandoli dai sistemi a coefficienti costanti. Particolare attenzione è rivolta alle proprietà della densità spettrale della risposta le cui caratteristiche cambiano bruscamente con il grado di non linearità dello smorzamento e del livello di casualità delle perturbazioni.     

螺旋细杆的均匀扭转振动

讨论螺旋细杆的特殊形式扭转振动，即均匀扭转振动．以非圆截面杆和有原始曲率的圆截面杆为研究对象．杆作均匀扭转振动时各截面有相同的扭角变化规律，且杆中心线的几何形状不受振动过程的影响．研究表明，扭振来源于杆截面的非对称性及杆的原始曲率．杆的扭振规律与单摆运动相似，其动力学方程存在精确解．圆环杆的均匀扭振为螺旋杆的倾角为零时的特例．     

具有区域极点约束的柔性梁鲁棒H∞振动主动控制

本文基于H∞控制理论研究了传感器和作动器非同位配置情况下,柔性悬臂梁的多模态振动抑制问题。采用频域辨识方法获取低阶名义模型,合理选取加性不确定权函数和性能权函数,将鲁棒H∞控制问题转化为标准H∞控制问题。为了避免H∞控制器设计过程中产生的零极点对消问题,在求解过程中引入区域极点约束。比较了鲁棒H∞控制器和不考虑高阶未建模动态的非鲁棒H∞控制器的控制效果,实验结果表明,设计的鲁棒H∞控制器能够有效抑制柔性梁的前三阶模态振动,而且不会发生溢出问题。     

复振型导数计算的移位多次模态加速法

本文研究了含粘性阻尼结构的复振型导数计算问题，将导数计算问题看成是一个简谐激振的响应计算问题，采用多次模态加速法和移位法，导出了复振型导数计算的移位多次模态加速法。该方法具有明确的数学和物理意义，可导出已有的各种计算方法。算例表明本方法计算复振型导数只需用很少几个模态即可保证精度，计算量大大减少。     

Characterization of piezo-film sensors for direct vibration and impact measurements

Piezo-film sensors were employed in determining the dynamic response of [(0 deg/90 deg)₄]_s s-glass/epoxy laminates and 2024 aluminum specimens. Simple beam- and plate-type sensor equations were derived based on classical plate theory incorporating the linear piezoelastic constitutive relationship. A series of vibration and impact tests were conducted for the determination of structural dynamic response. Piezo-film sensors, with a thickness and area of 110 μm and 1×1 cm², respectively, were connected directly to a voltage measurement device in these tests. The first three bending frequencies of the glass-fiber-reinforced plastic (GFRP) cantilever specimen were examined. Experimental results and those simulated by the MARC finite-element code were found to be in good agreement, with the difference between the two being less than five percent. At frequencies above 3 kHz, piezo-film transducers are capable of closely detecting structural dynamic response in the absence of charge amplification. At frequencies lower than approximately 3 kHz, however, the voltage measured directly from a piezo-film sensor underestimates structural response. A modified piezo-film sensor equation is thus proposed for lower frequency measurements. Effect of frequency and piezo-film's size on lower frequency attenuation is explicitly formulated based on a simple RC circuit analogy. Drop tests were also performed on clamped [(0 deg/90 deg)₄]_s GFRP laminates and aluminum targets, with nine piezo-film sensors being glued to the specimen's distal surface in order to determine the low-speed impact response. Specimen transient central deflection subjected to impact loading was identified based on test findings and the plate-type piezo-film sensor equation. The results were found to be in good agreement with the numerical solution obtained from the MARC finite-element code.     

水轮发电机转子偏心引起的非线性电磁振动

由于机械和电磁相互耦合,水轮发电机的电磁振动具有强非线性特征。根据不平衡磁拉力与转子偏心的非线性函数关系,通过简化的各向同性的单圆盘转子系统,建立了水轮发电机转子电磁振动的非线性系统。利用非线性振动理论的多尺度方法,从理论上分析了该系统强迫振动的稳态响应,进而研究了水轮发电机转子偏心引起的电磁振动。研究发现不平衡磁拉力使系统的涡动频率下降,使运动的中心发生变化;并且会引起两倍转频的振动。最后用模型转子仿真试验的结果验证了这些理论分析的结论。     

FREE VIBRATION OF ANISOTROPIC RECTANGULAR PLATES BY GENERAL ANALYTICAL METHOD

According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed.