行动载荷作用下的连续梁的横向振动问题

本文在考虑行动载荷质量、惯性力及阻尼影响的情况下,研究了机车通过连续梁时横向振动问题的整个过程,并得出了在任意行动载荷PF(t)作用下的连续梁的动力方程的一般解.我们具体计算了单个行动载荷为P_i+Q_isin(a_it+ε_i)时的情形并建立了行动载荷作用下的连续梁横向振动问题的动力理论.最后,做为例子,我们求解了两跨梁的横向振动问题,跨中点的挠度如图2和图3所示.     

一类一阶中立型方程解的渐近性与振动性

讨论具有连续分布滞量的一阶中立型微分方程 ,(1)给出了非振动解当t→∞时收敛于零的充分条件和方程(1)所有解振动的判据。     

某些一阶非齐次中立型微分差分方程的振动性

该文讨论了 d/dt[x(t) cx(t-τ)] P(t)x(t-σ) f(t)=0,t≥t_0一阶非齐次中立型微分差分方程的振动性.得到了一些方程振动的充分条件,推广了某些齐次方程的振动结果.     

上覆单相弹性层的饱和地基上刚性基础竖向振动的轴对称混合边值问题

运用作者提出的饱和土弹性波动方程,从理论上研究了上覆单相弹性土层的饱和地基上刚性基础的竖向振动轴对称问题,即采用Hankel积分变换技术并按混合边值条件建立了部分饱和地基上刚性基础竖向振动的对偶积分方程,并将其蜕化为完全饱和地基的情形;该对偶积分方程可化为易于数值计算的第二类Fredholm积分方程。文末的算例给出了地基表面动力柔度系数C_v随无量纲频率a₀的变化曲线。     

相依样本的经验过程振动模的收敛性

文中研究了两类重要相依样本(即φ-混合和α-混合样本)的经验过程振动模强一致收敛速度,证明了该速度与独立样本下的经验过程振动模的最优收敛速度相同.利用这些结果建立了密度函数核估计和直方图核估计的强相合性,并证明了这些强相合收敛速度达到最好速度O(n~(-1/3) log~(1/3)n)以及建立分位估计Bahadur类型的表示定理.     

一类二阶广义Emden-Fowler型微分方程的振动性

研究了具非线性中立项的一类二阶广义Emden-Fowler型泛函微分方程的振动性,考虑方程是非正则的情形(即∫_(t_0)~(+∞)a~(-1/β)(t)dt+∞的情形),利用广义黎卡提变换技术及不等式技巧,获得了方程振动的几个新型的判别准则.     

函数的振动熵

本文定义了振动函数与函数的振动熵。对函数的振动性质进行了初步的讨论。振动熵是对函数振动程度的度量(振动愈剧烈振动熵的值愈大)。导数是振动熵的特例。     

剪切变形对直线型正交异性层合圆板大幅度受迫振动的影响*

本文研究了计及横向剪切变形的直线型正交异性层合圆板在简谐载荷q₀cosωt作用下的非线性受迫振动问题.采用伽辽金方法得到强振频率与振幅关系的解析解.最后,分析了横向剪切对板振动的影响,并给出了板的非线性自由振动的非线性周期对线性周期的比值.     

含扩散项的多时滞Nicholson苍蝇模型的振动性

研究了含扩散项的多时滞Nicholson苍蝇模型在Neumann边值条件下的振动性，通过对多元函数解曲线或曲面的结构的分析和构造上下解，得到了含扩散项的多时滞Nicholson苍蝇模型在Neumann边值条件下振动的充分条件：当e^δτi-aN^＊ Piτi（aiN^＊-1）〉1/e，i=1，2，…，n时，方程的所有正解N（t，x）都关于正平衡点N^＊振动。     

自反矩阵与反自反矩阵的广义逆特征值问题

1引言在振动设计中,往往需要修改一个系统的数学模型的物理参数,这在数学上可以归结为矩阵的逆特征值问题或广义逆特征值问题（见[1]）.例如,下面给出振动系统中刚度矩阵与质量矩阵的校正问题.设ω₁,ω₂,…,ω_m（m≤n）是m个自然频率,φ₁,φ₂,…,φ_m是相应的振型,令Ω²=diag（ω₁²,ω₂²,…,ω_m²）,φ=（φ₁,φ₂,…,φ_m）.设K为待校正的刚度矩阵,M为待校正的质量矩阵,它们满足下列条件（1.1）特征方程Kφ=MφΩ²,     

Spatially homogeneous relaxation of CO molecules with resonant <Emphasis Type="Italic">VE</Emphasis> transitions

In this paper, we study vibrational relaxation of CO molecules with excited electronic states. We consider three electronic terms and account for VV exchanges of vibrational energy within each electronic term, VT transitions of vibrational energy into a translational one, and VE exchange of vibrational energy between electronic terms. The initial vibrational state of the gas is strongly nonequilibrium. The effect of VE exchange on the vibrational relaxation of CO molecules is estimated for different kinds of initial vibrational distributions, in particular, the Treanor and Gordiets ones generalized for gases with electronically excited states. The set of equations of state-to-state vibrational kinetics, together with the gas dynamic equations, is solved numerically in the zero-order approximation of the Chapman–Enskog method for the case of spatially homogeneous relaxation. The following results are obtained: neglecting VE exchanges leads to an incorrect assessment of the number density for each electronic level; however, the error is small for the ground electronic state. It is shown that VE exchanges qualitatively affect the time dependence of the vibrational temperature.     

Static and vibrational creep of a fabric-reinforced plastic in shear in the plane of the reinforcement

The results of a comparative experimental investigation of the short-term static and vibrational creep of a fabric-reinforced plastic in shear in the plane of the reinforcement are presented. The experimental procedure is described in detail. It is shown that on the investigated ranges of temperature, stress, and amplitude-frequency parameters the effect of an additional vibrational load on the creep process is unimportant.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 605–610, July–August, 1971.     

Vibrational excitation differential cross sections of low-energy electron scattering from N2 molecule

The vibrational excitation differential cross sections (DCS) of low-energy electron-N₂ scattering are studied using vibrational close-coupling (VCC) scattering method and quantum scattering potentials which include static, exchange, and polarization contributions based onab initio calculations. By including the contributions of 11 partial waves (up tol = 21), 15 vibrational states, and 16 molecular symmetries (up to ∧ = 7), the converged vibrational excitation (0→2, 0→3, 0→4) DCSs, the scattering resonance, and the vibrational multi-peak structure agree well with experimental results. Project supported by the National Natural Science Foundation of China (Grant No. 19674038) and the Science Foundation of Chinese Education Ministry.     

Algebras of Cauchy continuous maps

A condition of vibrational stabilizability for a class of linear partial differential equations is given. An example of vibrational stabilization in a nonlinear situation (Benard instability) is described.     

Recurrence plot analysis of nonlinear vibrational dynamics in H3 molecule

An ab initio classical trajectories obtained from the simulation of vibrational mode dynamics of H₃⁺ molecule were analyzed by Fourier transform and recurrence plot analysis. As has been found, at a particular value of energy supplied to vibrational modes (slightly above the zero point energy) the character of vibrational motion changes from regular to chaotic.     

Features of the construction of correction functions in the analysis of the free vibrations of mechanical systems by Bubnov''s method

Free vibrations of mechanical systems are investigated by Bubnov's method, using coordinate functions that do not satisfy all the boundary conditions of the problem. To eliminate discrepancies in the boundary conditions, correction functions are introduced, orthogonal to all coordinate functions involved in the analysis of the natural vibrations of mechanical systems. This method of constructing correction functions reveals the existence of differences between nearly equal numbers in the frequency equation and in the expressions for the vibrational modes. Moreover, for a given number N of coordinate functions, the method guarantees increased precision in computing all the natural frequencies of the mechanical system up to and including the (N + 1)th partial frequency as the number of terms of the power series in the frequency parameter representing the correction functions is increased. In the limit, as the number of terms of the power series tends to infinity, one is assured of obtaining exact values of the frequencies and vibrational modes in the indicated frequency range.     

The vibrational and electronic spectra of 5-methyl pyrimidine and 4-methyl pyrimidine

The infrared and Raman spectra of 5-methyl pyrimidine and the infrared spectrum of 4-methyl pyrimidine have been examined and vibrational assignments are given for the ground electronic states. The ultra-violet absorption spectra of these molecules corresponding to π* ←n electronic excitation have been studied and vibrational assignments are given for most of the observed bands.     

Vibrational creep of polymeric materials

An experimental study of the effect of vibration on the creep process has been carried out in the case of the rigid porous polyurethane PPU-3, as a function of the magnitude of the vibrational loading and the level of basic static stresses. It has been shown that with increase in the velocity amplitude of the dynamic stresses, the creep process is accelerated, without being accompanied thereupon by vibrational heating of the material. The possibility has been established of approximating vibrational creep curves by the integral equation of Volterra, using a discrete series of relaxation times transformed by the vibro-time analogy method.For Communication No. 3, see [1].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 223–232, March–April, 1970.     

Investigation of the dynamic characteristics of composites

The dynamic characteristics E and G and the damping capacity δ* of polymeric resins and composites based on glass, carbon, and boron fibers have been investigated. It is shown that the mechanical losses are correlated with the modulus of elasticity and the shear modulus of the resin and composites with different types of reinforcement. The vibrational strength of various structural materials is estimated.     

Effect of Holes on the Eigenmodes of Reinforced Shells of Rotation

The vibrational eigenmodes of reinforced shells of rotation with holes are examined. A solution is constructed on the basis of the linear theory of thin elastic shells using the Ritz method. Results are presented from numerical studies of the effect of holes and reinforcements on the eigenmodes and forms of the vibrations. The results are compared with experimental data.