In-plane free vibration analysis of cable-arch structure

Cable-stayed arch bridge is a new type of composite bridge, which utilizes the mechanical characters of cable and arch. Based on the supporting members of cable-stayed arch bridge and of erection of arch bridge using of the cantilever construction method with tiebacks, we propose a novel mechanical model of cable-arch structure. In this model, the equations governing vibrations of the cable-arch are derived according to Hamilton's principle for dynamic problems in elastic body under equilibrium state. Then, the program of solving the dynamic governing equations is ultimately established by the transfer matrix method for free vibration of uniform and variable cross-section, and the internal characteristics of the cable-arch are investigated. After analyzing step by step, the research results approve that the program is accurate; meanwhile, the mechanical model and method are both valuable and significant not only in theoretical research and calculation but also in design of engineering.     

Free vibration analysis of planar curved beams by wave propagation

In this paper, a systematic approach for the free vibration analysis of a planar circular curved beam system is presented. The system considered includes multiple point discontinuities such as elastic supports, attached masses, and curvature changes. Neglecting transverse shear and rotary inertia, harmonic wave solutions are found for both extensional and inextensional curved beam models. Dispersion equations are obtained and cut-off frequencies are determined. Wave reflection and transmission matrices are formulated, accounting for general support conditions. These matrices are combined, with the aid of field transfer matrices, to provide a concise and efficient method for the free vibration problem of multi-span planar circular curved beams with general boundary conditions and supports. The solutions are exact since the effects of attenuating wave components are included in the formulation. Several examples are presented and compared with other methods.     

Modal analysis by free vibration response only for discrete and continuous systems

This work aims to develop the algorithm for modal analysis by free vibration response only (MAFVRO), in particular for the general or non-proportional viscous damping system model. If the structural displacement or acceleration response due to free vibration can be measured, the system response matrices, including the displacement, velocity and acceleration, can be obtained through numerical differential or integration methods. These response matrices can then be applied to the developed MAFVRO method to determine the structural modal parameters. The numerical differential and integration methods are introduced and adopted to establish the modal parameter prediction program for the non-proportional damping model of MAFVRO. This work also shows the applications of MAFVRO to the multiple degree-of-freedom (mdof) systems and the cantilever beam, respectively. Both the discrete and continuous systems are demonstrated for the feasibility of the MAFVRO algorithm. The developed method uses the free vibration output response only and can obtain the structural modal parameters successfully.     

多级阻振质量阻隔振动波的传递特性研究

利用波动理论的分析、处理方法,分析了多级平行阻振质量阻隔振动波传递的特性,给出了多级阻振质量对平面弯曲波传递的阻抑公式,讨论了平面弯曲波传递时形成的穿透频段和堵塞频段,并进行了相应的算例分析,采用有限元法对多级阻振质量的隔振性能进行了数值计算,结果表明:阻振质量对偏离法向角的弯曲波分量的阻抑较强,传递能量的损失较大;多级阻振质量能够较好地阻抑结构声的传递,且阻抑效果随着阻振级数的增加而增大;在有几个阻振质量的情况下,通过改变它们的平行性,可以提高其隔振效果;且如果将不同质量、不同横截面形状的阻振质量前后交错配置,同样可以使总的隔振效果提高,这对于多级阻振质量在船体结构减振降噪中的应用具有重要的参考意义。     

Asymmetric wave propagation in nonlinear systems

A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As a reference system, we consider a layered nonlinear, nonmirror-symmetric model described by the one-dimensional discrete nonlinear Schr?dinger equation with spatially varying coefficients embedded in an otherwise linear lattice. We construct a class of exact extended solutions such that waves with the same frequency and incident amplitude impinging from left and right directions have very different transmission coefficients. This effect arises already for the simplest case of two nonlinear layers and is associated with the shift of nonlinear resonances. Increasing the number of layers considerably increases the complexity of the family of solutions. Finally, numerical simulations of asymmetric wave packet transmission are presented which beautifully display the rectifying effect.     

In-plane vibration characterization of microelectromechanical systems using acousto-optic modulated partially incoherent stroboscopic imaging

A technique using acousto-optic modulated partially incoherent stroboscopic imaging for measurement of in-plane motion of microelectromechanical systems (MEMS) is presented. Vibration measurement is allowed by using flashes of the partially incoherent light source to freeze the positions of the microstructure at 12 equally spaced phases of the vibration period. The first-order diffracted beam taken out by an acousto-optic modulator (AOM) from the light beam of a laser is made partially incoherent by a rotating diffuser and then serves as the stroboscopic light source. Both the MEMS excitation signal and the flash control signal are provided by a dual-channel function generator. The main advantage of this measurement method is the absence of a stroboscopic generator and a high speed digital camera. Microscale prototypes are fabricated and tested. Quantitative estimates of the harmonic responses of the prototypes are obtained from the recorded images. The results agree with those obtained with a commercial MEMS motion analyzer^TM with relative errors less than 2%.     

In-plane vibration of a thick circular ring

Dynamic stiffness matrices are derived for the in-plane vibration of thick circular rings where the effects of transverse shear and rotatory inertia cannot be neglected. The accuracy of the expressions is demonstrated by comparison of calculated and experimental frequencies for very thick rings of circular and rectangular cross-section.     

Nonlinear wave propagation in discrete and continuous systems

In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.     

In-plane vibration analysis of curved carbon nanotubes conveying fluid embedded in viscoelastic medium

The effect of the induced vibrations in the carbon nanotubes (CNTs) arising from the internal fluid flow is a critical issue in the design of CNT-based fluidic devices. In this study, in-plane vibration analysis of curved CNTs conveying fluid embedded in viscoelastic medium is investigated. The CNT is modeled as a linear elastic cylindrical tube where the internal moving fluid is characterized by steady flow velocity and mass density of fluid. A modified-inextensible theory is used in formulation and the steady-state initial forces due to the centrifugal and pressure forces of the internal fluid are also taken into account. The finite element method is used to discretize the equation of motion and the frequencies are obtained by solving a quadratic eigenvalue problem. The effects of CNT opening angle, the elastic modulus and the damping factor of the viscoelastic surrounded medium and fluid velocity on the resonance frequencies are elucidated. It is shown that curved CNTs are unconditionally stable even for a system with sufficiently high flow velocity. The most results presented in this investigation have been absent from the literature for fluid-induced vibration of curved CNTs embedded in viscoelastic foundations.     

Measuring high-frequency wave propagation in railroad tracks by joint time-frequency analysis

The behavior of high-frequency elastic waves propagating in railroad tracks is relevant to the field of rail noise generation and long-range rail inspection. While a large amount of theoretical and numerical work exists to predict transient vibrations propagating in rails, obtaining experimental data has been particularly challenging due to the multimode and dispersive behavior of the waves.In this work a joint time-frequency analysis based on the Gabor wavelet transform is employed for characterizing longitudinal, lateral and vertical vibrational modes propagating in rails in the 1000- range. The Gabor transform optimizes the time-frequency resolution of the measurements and theoretically requires a single excitation point and a single measurement point. These features make the analysis well-suited for the study of wave propagation in rails.The theory of the wavelet transform is reviewed in the context of dispersive measurements. Accelerometer data were taken from a section of rail subject to impulse dynamic testing in the laboratory. The group (energy) velocity dispersion curves and the frequency-dependent attenuation of the waves were successfully extracted from the wavelet scalograms of the accelerometer signals.     

Quantum theory of wave propagation and linear amplification in free electron lasers

A quantum field theory of free electron lasers is formulated and evaluated for the case of linear propagation and amplification of thermal noise and radiation emitted spontaneously and from shot noise.     

Random vibration analysis of stochastic time-varying systems

The analysis of the free and forced vibration of a randomly time-varying system is the subject matter of this paper. This is a complicated problem which has received relatively little discussion in the literature. Herein two methods are presented, apart from the digital simulation technique, of finding the response moments. The first one is a series technique which can be considered as a generalization of the well known Galerkin method. The second method belongs to the class of closure techniques. Upon presuming some of the joint distributions to be Gaussian, equations are derived for the first two response moments. It is shown further that the non-Gaussian output density can be approximately predicted by a simple transformation. Detailed numerical results are obtained and compared with computer simulated response statistics. It is demonstrated that the methods developed here are highly efficient. In particular it is found that the Gaussian closure approximation has a wide range of application.     

三层流体系统非线性界面内波传播理论的研究

基于波陡很小的假设, 利用摄动法, 讨论了任意深度的二维不可压缩、无黏性、无旋的三层流体系统. 在刚性上边界、平底不可渗透条件下, 给出了界面内波传播的统一理论以及描述其波剖面的近似非线性演化方程(NEEs). 最后讨论了几种特殊情形下的近似NEEs.结果表明文献导出的理论结果为本文的特殊情形.     

The decoupling of damped linear systems in free or forced vibration

The purpose of this paper is to extend classical modal analysis to decouple any viscously damped linear system in non-oscillatory free vibration or in forced vibration. Based upon an exposition of how exponential decay in a system can be regarded as imaginary oscillations, the concept of damped modes of imaginary vibration is introduced. By phase synchronization of these real and physically excitable modes, a time-varying transformation is constructed to decouple non-oscillatory free vibration. When time drifts caused by viscous damping and by external excitation are both accounted for, a time-varying decoupling transformation for forced vibration is derived. The decoupling procedure devised herein reduces to classical modal analysis for systems that are undamped or classically damped. This paper constitutes the second and final part of a solution to the “classical decoupling problem.” Together with an earlier paper, a general methodology that requires only the solution of a quadratic eigenvalue problem is developed to decouple any damped linear system.     

Wave mode diffusion and propagation in structural wave guide under Varying Temperature

A numerical approach is presented to study the guided wave propagation through periodic specimen with thermal dependence of material properties. There is a great interest in extending the skills of the wave finite element (WFE) method to figure out the variations in the wave propagation properties due to temperature fluctuations. Thermal effects on the dispersion curves thereby on group velocity are discussed. Comparisons between numerical results and analytical developments for various temperatures are given to prove the effectiveness of the proposed approach to predict the sensitivity of guided wave propagation characteristics in presence of temperature variations.     

In-plane propagation of millimeter waves in periodic magnetoactive semiconductor structures

Non-transmission bands of electromagnetic waves propagating along the layers in periodic structures are studied in the steady magnetic field perpendicular both to the uniaxis and the direction of propagation. The band control range (36÷75 GHz) inn-InSb/Al₂O₃ structures with the carrier densities 4 10¹³ ≤n ≤ 8 10¹⁴ cm⁻³ in magnetic fieldsB _o ≤ 2 T at temperatures 77 ≤T ≤ 200 K is found to agree with the calculated in the effective medium approximation. Attenuation down to −50 dB within the band is observed. The band lineshape is found to indicate additional effects related to the finite layer thickness and periodicity termination predicted by a more rigorous theory of dispersion.