一类中立型差分方程的频率振动性

利用数列的频率测度的概念及其性质,讨论了一类中立型差分方程的解的频率振动性,得到了解的正振动与负振动的振动准则.在此基础上,指出了文献[3]中的引理5与定理3的错误,并且给出了对应的正确结论及严格证明.

多时滞差分方程的频率振动性(英文)

讨论了多时滞差分方程的频率振动性，获得的振动判定准则。

一类差分方程的频率振动解

本文讨论了一类差分方程的解的频率振动性,建立了新的频率振动性定理,给出了如下中立型差分方程的解的频率振动的充分条件,从而简化和改进了文献[3]中的相应条件与结论:△(xn+cnxn-k)=f(n,xn-1),n=0,1,2,…其中k≥1与l≥1均为正整数,1Cn∩∞n=0是一实数列,f是定义在Z×R上的函数。

Experimental Studies on High-Frequency Performance of the Inverse Control Magneto-Rheological Damper

Severe vibration of underground structures may be induced under blast loads. According to the characteristics of the explosion-induced ground shock wave, a new-type damper, inverse control magneto-rheological（MR） damper was designed to control the vibration, The high-frequency performance test of the MR damper was carried out on the small shaking table. It is shown that the performance can be modeled by use of the modified Bouc-Wen model, and the Parameters of the model keep stable in the range of 15--50 Hz.

Effects of Bearing Type on Seismic Response of Small Base Isolation System Using Friction Bearings

In this study, dynamic characteristics of the small base isolation system using new friction bearings are investigated by excitation experiment, and compared to other one using previous bearings. Peak amplitude of the acceleration response waves on the small base isolation system is decreased to about 10%-25% compared to the input waves. Also root mean square amplitude is decreased to about 10%-40%. In case of the ball embedded a cylindrical sponge, the new bearing, the damping ratio increases with increasing width of the cylindrical sponge. The natural frequency does not change. On the other hand, in case of the marble plate that is previous bearing, the damping ratio increases with increasing curvature radius of the marble plate, the natural frequency also increases. Therefore, the small base isolation system using new friction bearing provides better performance. The responses of the base isolation system indicate nonlinier effects by friction force.

Vibration transmissibility characteristics of smart spring vibration isolation system

The objective of this work was to study the vibration transmissibility characteristics of the undamped and damped smart spring systems. The frequency response characteristics of them were analyzed by using the equivalent linearization technique, and the possible types of the system motion were distinguished by using the starting and ending frequencies. The influences of system parameters on the vibration transmissibility characteristics were discussed. The following conclusions may be drawn from the analysis results. The undamped smart spring system may simultaneously have one starting frequency and one ending frequency or only have one starting frequency, and the damped system may simultaneously have two starting frequencies and one ending frequency. There is an optimal control parameter to make the peak value of the vibration transmissibility curve of the system be minimum. When the mass ratio is far away from the stiffness ratio, the vibration transmissibility is small. The effect of the damping ratio on the system vibration transmissibility is significant while the control parameter is less than its optimal value. But the influence of the relative damping ratio on the vibration transmissibility is small.

Quantum Chemical Calculations and Experimental Studies on 2,3-Diphenyl-tetrazole-5-thione

Diphenyl-tetrazole-5-thione has been synthesized and characterized by X-ray diffraction analysis and FTIR spectra. The extended MO calculations by using density functional theory (DFT) and self-consistent field molecular orbital Hartree-Fock theory with 6-31gG* basis set were carried out. The optimized structure and atomic charge distributions have been investi- gated, showing the exocyclic sulfur atom has the biggest negative charge value and this site is the most likely site of protonation and methylation as well as the potential coordination site with metallic ions. The predicted harmonic vibration frequencies are compared to the experimental values. On the basis of vibrational analyses, the thermodynamic properties of this compound at different temperature have been calculated, revealing the correlations between C0p, m, S0m, H0m and temperature.

Natural frequency of tapered high pier considering pile-soil interaction

In seismic design of tapered high pier, the analysis of natural vibration frequency is of great importance. According to the engineering features of tapered high pier in mountainous area, a vibration calculation model was set up considering the tapered pier characteristics and pile-soil interaction. Based on Southwell frequency composition theory, it consists of elastic deformation of bridge pier and the rigid deformation of group piles, which are respectively solved by the finite-element method and energy method, and then the natural frequency is derived. The comparison between the measured and calculated results shows that the calculation errors with and without considering pile-soil interaction are 4.9% and 14.7%, respectively. Additionally, the main parameters (pier height, section variation coefficient and lateral foundation horizontal proportional coefficient) affecting natural frequency were investigated. The result shows that natural frequency ascends with the increase of the lateral foundation horizontal proportional coefficient; and it is quite necessary to consider the pile-soil interaction in natural frequency calculation of tapered high pier.

Dynamic Properties of Long Large Cross-section Underground Structures in Dynamic Seismic Analysis

Seismic safety of underground structures is one of the main concerns in underground space exploitation. As the first step for dynamic seismic response analysis, the free vibration of long large cross-section underground structures is studied in the present paper. The general free transverse vibration motion equation of long large cross-section underground structure is derived with the comprehensive consideration of internal and external damping, effects of shear, cross-sectional rotational inertia and axial force, and a twoparameter soil model. In this way, Timoshenko＇s beam theory is extended. Two limit cases of free transverse vibration of underground structures are discussed. Parameter study shows that in general wave propagation velocities in structures increase with soil elastic parameters. However the influence of Winkler＇s parameter k is significant while the effect of the second soil elastic parameter gp is insignificant. The free vibration frequency of underground structures increases with relative wave number and soil elastic parameters. Unlike the influence of soil elastic parameters on wave propagation velocities, the influence of soil elastic parameters k and gp on the vibration frequency of underground structures have the same order; therefore the influence of the second soil parameter gp on the free vibration of underground structures should not be neglected in dynamic seismic analysis of underground structures

Development of an Accurate Numerical Methodology for Predicting the First Three Modes of Vibration of an Electric Motor Fixed on a Rigid Base

This paper proposes a numerical methodology for the prediction of the first three modes of vibration of an electric motor fixed on a rigid base. A deep literature review supported the production of four ad hoc prototypes that aided the development of the proposed approach. Tests carried out with the prototypes led to the procurement of the modal parameters be used to calibrate the numerical models, as well as the FRF （frequency response function） curves be used to validate the numerical solution. The validated model allowed structural changes to be then promoted on the prototypes, in order to make them more robust to variations in manufacturing and assembling processes. The mentioned adjustments and structural changes were accomplished by means of a process of structural optimization using Genetic Algorithm. The solution was developed based on the commercial finite element code ANSYS. The practical results obtained in this study show that a numerical model for modal analysis of an electric motor fixed on a rigid base with errors less than 3% for the first three modes of vibration can be achieved, allowing positive structural changes to be performed in the machine design that result in the minimization of manufacturing reworks associated with the dynamic behavior of the studied motor.

Transverse vibration of pre-tensioned nonlocal nanobeams with precise internal axial loads

This paper investigates the transverse vibration of a simply supported nanobeam with an initial axial tension based on the nonlocal stress field theory with a nonlocal size parameter. Considering an axial elongation due to transverse vibration, the internal axial tension is not precisely equal to the external initial tension. A sixth-order nonlinear partial differential equation that governs the transverse vibration for such nonlocal nanobeam is derived. Using a perturbation method, the relation between natural frequency and nonlocal nanoscale parameter is derived and the transverse vibration mode is solved. The external axial tension and nonlocal nanoscale parameter are proven to play significant roles in the nonlinear vibration behavior of nonlocal nanobeams. Such effects enhance the natural frequency and stiffness as compared to the predictions of the classical continuum mechanics models. Additionally, the frequency is higher if the precise internal axial load is considered with respect to that when only the approximate internal axial tension is assumed.