边界阻尼力对复合材料层合板主参激共振的影响

结合经典层合板理论与von Kármán理论并利用Galerkin截断,获得受面内激励具边界阻尼力的四边铰支正交对称铺设矩形层合薄板的动力学控制方程。基于多尺度法,形成了确定性激励下系统主参激共振的近似解析形式,结果表明:系统平凡响应不稳定区间带宽只与线性阻尼及激励幅值有关,而边界阻尼力的大幅增加可有效减小主参激共振时非平凡响应的幅值及共振频率范围。随后,将确定性激励扩展为窄带随机激励,结合所得Foker-Planck-Kolmogorov方程并采用有限差分法,数值分析了系统稳态响应在平凡与非平凡解支间的随机跳跃现象,结果表明:微小的边界阻尼力增量,将导致系统的稳态响应从非平凡解支跳向平凡解支。     

桩基非线性轴向受迫振动稳态幅频响应分析

用多时间尺度法得到了一端固定、另一端自由的桩基非线性轴向受迫振动系统主共振时的稳态幅频响应曲线。研究表明:桩基非线性轴向受迫振动的幅频响应曲线不仅与派生线性振动系统的固有频率、土刚度和阻尼系数有关,而且也与振幅、相位和非线性特征量有关。幅频响应曲线中会出现一种典型的振幅跳跃的非线性现象,当激励频率接近线性系统固有频率时,系统产生共振从而响应幅值增大,而且同一激励频率可能会对应于振幅的多个不同值,运动状态具有不稳定性。随着非线性系数的增大,响应曲线峰值侧向弯曲;粘性阻尼会抑制响应振幅的增大;激励振幅增大会导致响应振幅增大。     

有界窄带激励柴油机轴系扭振系统主参数共振

研究柴油机轴系扭振强非线性系统在有界窄带激励下的主参数共振响应和稳定性问题。应用改进多尺度法得到在有界窄带随机激励下柴油机轴系扭振系统的幅频响应方程,导出系统的Ito随机微分方程。通过矩法得到系统随机均方响应的近似表达式,分析各个参数对柴油机轴系扭振系统主参数共振均方值的影响。结果表明,主参数共振稳态解稳定的充分必要条件与系统二阶矩稳定的充分必要条件是一样的;随着阻尼值的增大,系统主参数共振振幅的均方值减小;随着曲轴扭转刚度的减小,系统主参数共振的均方响应曲线的斜率增大;随着随机扰动强度的增大,系统时间响应曲线和相图变化微小。     

窄带随机激励带集中质量梁的主参激共振

以受窄带随机激励带集中质量柔性梁为研究对象,采用多尺度法导出系统单模态主参激共振调谐方程组,结合FPK方程分析了力-幅特性下联合概率密度随激励幅值所出现的随机跳跃现象,结果显示:在三值响应范围内存在一外扇形峰及一内火山口峰,随着激励幅值减小,外扇形峰减弱而内火山口峰增强,表明响应逐渐从非平凡稳态响应向平凡稳态响应跳跃。     

非线性阻尼非线性刚度隔振系统参数识别

针对同时含有非线性刚度、非线性阻尼的振动系统,提出了两类参数识别方法。第一类方法是基于非线性振动系统中的振幅跳跃现象,通过跳跃点的测量得出振幅跳跃点的激励频率和幅值,用谐波平衡法识别出非线性振动系统的非线性刚度、非线性阻尼参数。第二类方法是涉及时域响应,通过希尔伯特变换获得非线性系统自由振动的响应幅值和相角,结合双非线性振动系统在瞬态激励下的解析解,获得系统的非线性刚度和阻尼。以非线性刚度非线性阻尼隔振系统为例,通过数值模拟对给出的两类参数识别方法加以验证,并对结果进行较比,识别参数相吻合。可以为实验条件下,含非线性刚度、非线性阻尼隔振系统的参数识别提供理论指导。     

窄带随机噪声作用下强非线性系统的响应

研究了Van der Pol-Duffing振子在窄带随机噪声激励下的响应问题。用参数变换法使方程出现小参数，用多尺度法分离了系统的快变项，讨论了系统的阻尼项，非线性项和随机项等参数对系统的影响，理论分析表明，当随机激励强度或带宽增大时系统的响应可从一个极限环变为一扩散的极限环，在一定的条件下系统可有两个稳定的稳态解。数值模拟表明本文提出的方法是有效的。     

简谐与随机噪声联合激励下Van der Pol-Duffing系统的响应

研究了Van der Pol—Duffing振子在简谐与随机噪声联合激励下的响应问题。用参数变换法使方程出现小参数，用多尺度法分离系统的快变项，讨论系统的阻尼项、非线性项和随机项等参数对系统响应的影响。理论分析和数值模拟表明，当随机激励强度增大时，系统的响应可从一个极限环变为一个扩散的极限环；在一定的条件下，系统可有两个稳定的稳态解及随机跳跃现象。数值模拟表明本文提出的方法是有效的。     

有界窄带激励下的电磁开关系统主共振分析

以电磁开关系统为研究对象,研究电路与磁路耦合系统在有界窄带激励下的强非线性振动问题。建立电磁开关强非线性系统在有界窄带激励下的随机微分方程。应用改进的多尺度法得到系统的幅频响应方程,对窄带激励下系统主共振的稳定性进行计算,并分析系统各参数对系统主共振均方值的影响。结果表明,增大阻尼系数可以减小系统主共振的均方值;增大激励电压可以增大系统主共振的均方值;增大电阻可以减小系统主共振的均方值;增大随机扰动强度,极限环变化不大。     

窄带随机噪声参激作用下强非线性系统的响应

将改进的L-P(ModifiedLindstedt-Poincare)方法和随机多尺度法结合起来,研究了窄带随机噪声参激作用下强非线性VanderPol-Duffing系统的响应、稳定性和分叉问题。文中首先由改进的L-P方法引入变换参数,然后用多尺度法分离了系统的快变量,求出了最大Lyapunov指数的解析表达式,得到了系统几乎必然稳定的充分必要条件,讨论了系统的参数对稳定性的影响,分析了系统在1/2亚谐共振区的性态。理论分析与数值计算表明:在一定条件下系统将发生随机跳跃,且随着随机激励带宽的增大,扩散的极限环的宽度将逐渐增大。数值模拟结果表明:MLP方法结合随机多尺度法研究强非线性随机系统的响应、稳定性和分叉问题是有效的。     

含分数阶导数项的随机Duffing振子的稳态响应分析

本文对一个含有分数阶导数项阻尼的、Gaussian白噪声激励下的Duffing振子进行了稳态响应分析。首先,基于能量平衡理论,运用等效线性化方法,计算等效系统的线性阻尼及自然频率,建立统计意义下的等效线性化系统。然后,利用平均法建立随机Ito方程,得到随机响应的Markovian近似;给出描述振子振幅概率密度函数演化的Fokker-Planck方程,并得到它的稳态解。进一步,对于含有响应振幅的等效线性系统,借助由Laplace变换得到的转换函数,得到原系统的条件功率谱密度,结合振幅的稳态概率密度作为权重函数,给出原系统功率谱密度的估计,以及响应的统计量的估计。数值模拟的结果说明所提出的功率谱密度的近似解析表达式是可靠的,它甚至适用于Duffing振子具有强非线性回复力的情形,因为它可以较好的表现出功率谱密度共振频谱加宽及多峰现象的出现。     

Calculation of a transient in a two-pole network with a thermistor

An analytical expression is derived which describes the variation of the thermistor temperature during a relay-effect transient process following an instantaneous change in the supply voltage in an R — R_T two-pole network.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 3, pp. 465–472, March, 1980.     

Interaction between a liquid and a cylindrical body touching a wall

An exact solution is obtained for the problem of interaction between the ideal liquid homogeneously moving at infinity and streamlining a round cylinder touching a solid wall.     

Stress analysis of a strip with a step and a crack

Stress analysis for a strip of which widths are different at the right and left handsides is carried out for before and after occurrence of a crack at a corner of a step. The strip is analyzed as a thin plate bending problem subject to transverse bending and torsion, and as a plane eleastic problem subject to bending in the plane and uniaxial tension. The rational mapping function of a sum of fractional expressions and complex variable method are used. Stress distribution and stress intensity factors are obtained.     

Imaging a point to a line with a single spherical mirror

Methods for imaging a single point source to a line image are discussed, and a design study of single spherical mirror systems that form aberration-free line images is presented. An expression forthe ray density along the line image is derived for such systems in the cases of (i) uniform beam profiles and (ii) Gaussian beam profiles. The resulting ray density profiles are illustrated for single spherical mirror systems over a wide range of design parameters.     

Influence lines for bending under a ring load of a free shell,a shell embedded in a soft medium and a shell containing a soft core

Summary Theoretical expressions for stresses and displacements have been derived for bending under a ring load of a free shell, a shell embedded in a soft medium, and a shell containing a soft core. Numerical work has been done for typical cases with anElliot 803 Digital Computer and influence lines are drawn therefrom.

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Einflußlinien für die Biegung einer freien Schale, einer Schale in einer weichen Bettung und einer Schale mit weichem Kern

Zusammenfassung Für die Biegung einer freien Schale, einer weich gebetteten Schale und einer Schale mit weichem Kern unter einer Ringlast werden Ausdrücke für die Spannungen und Verschiebungen hergeleitet. Die Ergebnisse wurden für einige typische Fälle mit einem DigitalrechnerElliot 803 numerisch ausgewertet. Die sich ergebenden Einflußlinien wurden graphisch dargestellt.

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Nomenclature A (),B () Functions of - a, t Mean radius and thickness of the shell - E _S , _S Young's modulus andPoisson's ratio of the shell - G _c , _c Shear modulus andPoisson's ratio of the casting or core - I ₀ (r),I ₁ (r) ModifiedBessel functions of the first kind and order zero and one respectively - K ₀ (r),K ₁ (r) ModifiedBessel functions of the second kind and order zero and one respectively - p Ring load, lb/in - U, W Displacement components in the casing or core in thez andr direction - u, w Displacement components of a middle surface point in the shell - _r , _rz Radial and shearing stress components - Independent variable of infinite integrals - k [3(1–S ²)a ²/t ²]^1/4 With 13 Figures     

Linear heat transfer in a flow around a cylinder or a sphere

It is shown that the relation between the Nusselt and Reynolds numbers determined by the Reynolds analogy is linear with self-similarity of the hydrodynamic resistance coefficient.Special Design and Technology Office Element, Odessa, Ukraine. translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, May–June, pp. 395–396, 1995.     

Interaction between a cylindrical shell in a fluid and a pulsating bubble

The dynamic behavior of a cylindrical fluid-immersed shell in a pressure wave initiated by a pulsating vapor-gas bubble that develops as a result of the action of laser radiation on the absorbing medium (metal) is examined experimentally and theoretically. The results of the experiments suggest that the amplitude of the shock wave that develops as a result of complete or partial vaporization of the absorbing medium is appreciably smaller than the amplitude of the waves due to pulsations of the bubble that is formed. Experimental data on the pattern of structural deformation are confirmed by calculations. The effect of load simulation on the behavior of the shell is established according to computational data.Translated from Problemy Prochnosti, No. 6, pp. 116–120, June, 1990.     

Resistance of a sphere in a slow flow of a viscoelastic fluid

The authors have obtained an approximate solution of the problem of the resistance of a rigid sphere in a slow flow of a Maxwell viscoelastic fluid that is in good agreement with experimental data [1] for Weissenberg numbers We ≤ 0.7. It is shown that the effect of a decrease in the coefficient of resistance of a sphere in the interval 0.1 ≤ We ≤ 0.7 established experimentally is determined in full measure by the linear viscoelastic properties of the Maxwell fluid. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 6, pp. 1138–1140, November–December, 1998.