Spatial symmetrical vibrations and stability of circular arches with flexibly supported ends

In this work, exact formulae have been obtained for determining the lowest natural frequencies and critical loads of elastic circular arches with flexibly supported ends for symmetrical vibration in the direction perpendicular to the initial curvature of the arch. This investigation is concerned with three cases of load behaviour during the process of deformation. The values of the frequencies and critical loads are shown to be dependent on the opening angle of the arch, on the stiffness of the flexibly supported ends and on the ratio of the flexural rigidity to the torsional rigidity of the arch cross-section.     

Exact closed-form solutions for the natural frequencies and stability of elastically connected multiple beam system using Timoshenko and high-order shear deformation theory

A general procedure for the determination of the natural frequencies and buckling load for a set of beam system under compressive axial loading is investigated using Timoshenko and high-order shear deformation theory. It is assumed that the set beams of the system are simply supported and continuously joined by a Winkler elastic layer. The model of beam includes the effects of axial loading, shear deformation and rotary inertia. In the special case of identical beams, explicit expressions for the natural frequencies and the critical buckling load are determined using a trigonometric method. The influences of the compressive axial loading and the number of beams in the system on the natural frequencies and the critical buckling load are discussed. These results are of considerable practical interest and have wide application in engineering practice of frameworks.     

The effect of a surface impedance load on the behavior of quasi-Rayleigh waves near a cylindrical cavity

The effect of a surface impedance load on the properties of axisymmetric quasi-Rayleigh waves propagating along the boundaries of a cylindrical cavity is investigated. By solving the problem by means of the impedance method, a dispersion equation for these waves is obtained. It is shown that the equation can be represented as the condition that the determinant of the sum of impedance matrices of the load and the medium is zero. Analysis of this equation allows one to investigate the effect of the surface load on the behavior of quasi-Rayleigh waves and on their critical frequencies. The conditions that should be met by the impedance load for quasi-Rayleigh waves to be absent near the cavity or for one or two such waves to exist are determined. The choice of the load is specified for the propagating quasi-Rayleigh wave to possess preset dispersion properties. The conclusions drawn on the basis of this study are illustrated by several examples of load models that can be implemented in practice.     

FREE VIBRATIONS OF SELF-STRAINED ASSEMBLIES OF BEAMS

This paper examines the natural frequencies and modes of transverse vibration of two simple redundant systems comprising straight uniform Euler-Bernoulli beams in which there are internal self-balancing axial loads (e.g., loads due to non-uniform thermal strains). The simplest system consists of two parallel beams joined at their ends and the other is a 6-beam rectangular plane frame. Symmetric mode vibration normal to the plane of the frame is studied. Transcendental frequency equations are established for the different systems. Computed frequencies and modes are presented which show the effect of (1) varying the axial loads over a wide range, up to and beyond the values which cause individual members to buckle (2) pinning or fixing the beam joints (3) varying the relative flexural stiffness of the component beams. When the internal axial loads first cause any one of the component beams to buckle, the fundamental frequency of the whole system vanishes. The critical axial loads required for this are determined. A simple criterion has been identified to predict whether a small increase from zero in the axial compressive load in any one member causes the natural frequencies of the whole system to rise or fall. It is shown that this depends on the relative flexural stiffnesses and buckling loads of the different members. Computed modes of vibration show that when the axial modes reach their critical values, the buckled beam(s) distort with large amplitudes while the unbuckled beam(s) move either as rigid bodies or with bending which decays rapidly from the ends to a near-rigid-body movement over the central part of the beam. The modes of the systems with fixed joints change very little (if at all) with changing axial load, except when the load is close to the value which maximizes or minimizes the frequency. In a narrow range around this load the mode changes rapidly. The results provide an explanation for some computed results (as yet unpublished) for the flexural modes and frequencies of flat plates with non-uniform thermal stress distributions.     

Dynamic studies of railtrack sleepers in a track structure system

This paper discusses the dynamic response of a typical prestressed concrete railtrack sleeper due to wheel-track interaction dynamics, involving wheel and rail imperfections, under various parametric conditions. The interaction dynamics of the vehicle and track is first carried out in the time domain using MSC/NASTRAN. Using the resulting load time histories on an isolated sleeper, a detailed finite element model of the sleeper is used to analyze its dynamic behaviour. The dynamic amplification factors for deflection, ballast pressure and bending moments have been evaluated at the critical section (rail-seat and centre) for various exciting frequencies under different vehicle-track parametric conditions. The results provide a basis for improved and rational design of the sleeper.     

Vibration and buckling of a double-beam system under compressive axial loading

On the basis of the Bernoulli–Euler beam theory, the properties of free transverse vibration and buckling of a double-beam system under compressive axial loading are investigated in this paper. It is assumed that the two beams of the system are simply supported and continuously joined by a Winkler elastic layer. Explicit expressions are derived for the natural frequencies and the associated amplitude ratios of the two beams, and the analytical solution of the critical buckling load is obtained. The influences of the compressive axial loading on the responses of the double-beam system are discussed. It is shown that the critical buckling load of the system is related to the axial compression ratio of the two beams and the Winkler elastic layer, and the properties of free transverse vibration of the system greatly depend on the axial compressions.     

Estimation of critical and viscous frequencies for Biot theory in cancellous bone

The use of Biot theory for modelling ultrasonic wave propagation in porous media involves the definition of a "critical frequency" above which both fast and slow compressional waves will, in principle, propagate. Critical frequencies have been evaluated for healthy and osteoporotic cancellous bone filled with water or marrow, using data from the literature. The range of pore sizes in bone gives rise to a critical frequency band rather than a single critical frequency, the mean of which is lower for osteoporotic bone than normal bone. However, the critical frequency is a theoretical concept and previous researchers considered a more realistic "viscous frequency" above which both fast and slow waves may be experimentally observed. Viscous frequencies in bone are found to be several orders of magnitude greater than calculated critical frequencies. Whereas two waves may well be observed at all ultrasonic frequencies for water-filled cancellous bone at 20 degrees C, it is probable megahertz frequencies would be needed for observation of two waves in vivo.     

Postbuckling and vibration of end-supported elastica pipes conveying fluid and columns under follower loads

Fluid-conveying pipes with supported ends buckle when the fluid velocity reaches a critical value. For higher velocities, the postbuckled equilibrium shape can be directly related to that for a column under a follower end load. However, the corresponding vibration frequencies are different due to the Coriolis force associated with the fluid flow. Clamped–clamped, pinned–pinned, and clamped–pinned pipes are considered first. Axial sliding is permitted at the downstream end. The pipe is modeled as an inextensible elastica. The equilibrium shape may have large displacements, and small motions about that shape are analyzed. The behavior is conservative in the prebuckling range and nonconservative in the postbuckling range (during which the Coriolis force does work and the motions decay). Next, related columns are studied, first with a concentrated follower load at the axially sliding end, and then with a distributed follower load. In all cases, a shooting method is used to solve the nonlinear boundary-value problem for the equilibrium configuration, and to solve the linear boundary-value problem for the first four vibration frequencies. The results for the three different types of loading are compared.     

Effects on mass transfer of atomization and dispersion of liquids in the presence of ultrasound

By applying ultrasound at different frequencies and intensities through the bottom of a narrow tube containing liquids of varying physical properties, followed by critical analysis of the experimental data, a systematic study of the effect of these parameters on enhancement in rate of mass transfer has been made and a correlation has been proposed for prediction of such enhancement.     

Coupled flexural-torsional vibration of beams in the presence of static axial loads and end moments

The problem of coupled flexural-torsional vibration of a deep rectangular beam in the presence of a static axial load and an end moment is studied. Closed form analytical solutions are obtained for simply supported boundary conditions. Numerical results are obtained for the coupled frequencies and mode shapes (in terms of the location of axes of rotation of the cross-section) for different values of the load and the geometry parameters. The results show that the predominantly flexural frequencies of coupled flexural-torsional vibration can be obtained as uncoupled flexural frequencies of an equivalent beam-column by defining an effective axial load, and that by defining an equivalent moment parameter the presentation of the results for the predominantly flexural mode can be made in a form independent of the slenderness of the beam in the depth direction.     

Vibration and buckling of flat free-free plates under non-uniform in-plane thermal stresses

Detailed consideration is given to the modes and frequencies of a free rectangular Kirchoff plate subjected to in-plane stresses generated by prescribed non-uniform surface temperature distributions which are doubly symmetrical about the plate central axes. Physical understanding is sought of phenomena observed by previous investigators. Stress distributions corresponding to three different temperature distributions have first been studied and incorporated in a Rayleigh Ritz analysis to find natural frequencies and modes. All frequencies change as the temperature changes, some much more than others. All eventually vanish, one after the other, as the temperature reaches certain critical positive and negative values at which the plate goes into statically unstable buckling modes. Whether the frequencies rise or fall with rising temperature at the plate centre depends on the relative magnitudes of pairs of positive and negative critical temperatures. The modes of buckling at each pair of critical temperatures may differ greatly from one another and also from the vibration modes at zero temperature. The relationship between the square of the frequency and the temperature is then no longer approximately linear, although it is exactly so for certain simple in-plane stress distributions. Conditions have nevertheless been identified under which it is a very good approximation to the actual frequencies of the heated plate over wide temperature ranges.     

Influence of air layers and damping layers between gypsum boards on sound transmission

In this paper the influence on sound reduction index of a thin air layer between gypsum board layers of lightweight partitions has been examined. It has been shown that the air layer between gypsum boards causes a decrease in sound reduction index due to mass-air-mass resonance. When the thin air layer is filled with a damping layer, the sound reduction index is increased for frequencies around the critical frequencies. Predictions show similar effects to those measured.     

热力耦合作用下双层碳纳米管的扭转屈曲

考虑碳纳米管周边弹性介质和层间范德瓦耳斯力的作用,利用连续介质力学的壳体理论,建立了热力耦合作用下碳纳米管屈曲问题的控制方程,给出了相应的临界屈曲扭矩的解析解.数值模拟结果表明,在低温和室温环境下,碳纳米管的临界屈曲载荷随着温度变化量的增加而提高;在高温环境下,碳纳米管的临界屈曲载荷随着温度变化量的增加而降低. 关键词： 碳纳米管 屈曲 热力耦合     

An experimental-theoretical correlation study of non-linear bending and torsion deformations of a cantilever beam

An experimental study of the large deformation of a cantilevered beam under a gravity tip load has been made. The beam root is rotated so that the tip load is oriented at various angles with respect to the beam principal axes. Static twist and bending deflections of the tip and bending natural frequencies have been measured as a function of tip load magnitude and orientation. The experimental data are compared with the results of a recently developed non-linear structural theory. Agreement is reasonably good when bending deflections are small compared to the beam span, but systematic differences occur for larger deflections.     

Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory

Higher order shear deformation theory (HSDT) is reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion of the nonlocal theories are derived. The developed equations of motion have been applied to study buckling characteristics of nanoplates such as graphene sheets. Navier's approach has been used to solve the governing equations for all edges simply supported boundary conditions. Analytical solutions for critical buckling loads of the graphene sheets are presented. Nonlocal elasticity theories are employed to bring out the small scale effect on the critical buckling load of graphene sheets. Effects of (i) nonlocal parameter, (ii) length, (iii) thickness of the graphene sheets and (iv) higher order shear deformation theory on the critical buckling load have been investigated. The theoretical development as well as numerical solutions presented herein should serve as reference for nonlocal theories as applied to the stability analysis of nanoplates and nanoshells.     

ITER过渡馈线直线段管的优化设计与屈曲分析

根据强度原则,用有限元静力分析方法优化了馈线系统直线段管中的圆管和波纹管相关结构的设计参数;根据能量准则,通过特征值屈曲分析和非线性屈曲分析方法,用有限元法稳定性的判据计算出长跨度的薄壳直线段管发生失稳时的临界载荷为1.21MPa,验证了该结构在正常工况(安全系数为12.1)和故障状态工况(安全系数为6.05)下不会发生失稳现象,为ITER馈线系统的下一步研制提供了基础。     

An experimental test of the critical behaviour of fracture precursors

The statistical properties and the localization of fracture precursors on heteregeneous materials is studied by recording their acoustic emission as a function of the applied load. It's found that the microcrack cluster together as the load increases and the instantaneous acoustic energy has an invariant power law distribution. The integrated acoustic energy presents a critical divergency close to the failure load for the sample. These result support the idea that fracture can be viewed as a critical phenomenon. Finally a measure of the concentration of microcraks, which allows us to predict the failure load, is introduced. These properties are studied also when a periodic load is applied to the sample. It's found that the Kaiser effect is not strictly satisfied in heteregeneous materials. Received: 23 January 1998 / Revised: 20 April 1998 / Accepted: 17 June 1998     

Strange attractor for the renormalization flow for invariant tori of hamiltonian systems with two generic frequencies

We analyze the stability of invariant tori for Hamiltonian systems with two degrees of freedom by constructing a transformation that combines Kolmogorov-Arnold-Moser theory and renormalization-group techniques. This transformation is based on the continued fraction expansion of the frequency of the torus. We apply this transformation numerically for arbitrary frequencies that contain bounded entries in the continued fraction expansion. We give a global picture of renormalization flow for the stability of invariant tori, and we show that the properties of critical (and near critical) tori can be obtained by analyzing renormalization dynamics around a single hyperbolic strange attractor. We compute the fractal diagram, i.e., the critical coupling as a function of the frequencies, associated with a given one-parameter family.     

The effect of critically moving loads on the vibrations of soft soils and isolated railway tracks

The dynamic response of the railway track is strongly influenced by the underlying soil. For a soft soil and very high train speeds or for a very soft soil and regular train speeds, the train speed can be close to the speed of elastic waves in the soil. This paper presents a detailed study of the so-called “moving-load effect”, i.e. an amplification of the dynamic response due to the load movement, for the tracks on soft soil. The analysis is carried out by evaluating the related integrals in the wavenumber domain. The influence of the load speed is quantified for a large set of parameters, showing that the effect on the soil vibration is reduced with increase of the frequency, track width and inverse wave velocity. Therefore, the moving-load effect associated with vibratory train loads is negligible whereas the amplification associated with the moving dead weight of the train can be significant. The strong moving-load effect on a perfectly homogeneous soil, however, can be strongly diminished by a layered or randomly varying soil situation. This theoretical result is affirmed by measurements at a test site in Germany where the trains run on a very soft soil at a near-critical speed. The results for soft soils are compared with experimental and theoretical results for a stiff soil. It is found that the influence of the stiffness of the soil is much stronger than the moving-load effect. This holds for the soil vibration as well as for the track vibration which both show a minor dependence on the load speed but a considerable dependence on the soil stiffness in theory and experiment.Railway tracks can include soft isolation elements such as rail pads, sleeper shoes and ballast mats. For these types of isolation elements and normal soil conditions, the influence of the load speed is usually negligible. There is only one isolation measure for which the moving load may be effective: a track which is constructed as a heavy mass-spring system. The resonance of this track system is shifted to lower frequencies and amplitudes for increasing train speed. A critical train speed can be reached if the mass-spring system has a marginal bending stiffness along the track.     

Atomistic finite element model for axial buckling and vibration analysis of single-layered graphene sheets

In this article, an atomistic model is developed to study the buckling and vibration characteristics of single-layered graphene sheets (SLGSs). By treating SLGSs as space-frame structures, in which the discrete nature of graphene sheets is preserved, they are modeled using three-dimensional elastic beam elements for the bonds. The elastic moduli of the beam elements are determined via a linkage between molecular mechanics and structural mechanics. Based on this model, the critical compressive forces and fundamental natural frequencies of single-layered graphene sheets with different boundary conditions and geometries are obtained and then compared. It is indicated that the compressive buckling force decreases when the graphene sheet aspect ratio increases. At low aspect ratios, the increase of aspect ratios will result in a significant decrease in the critical buckling load. It is also indicated that increasing aspect ratio at a given side length results in the convergence of buckling envelops associated with armchair and zigzag graphene sheets. The influence of boundary conditions will be studied for different geometries. It will be shown that the influence of boundary conditions is not significant for sufficiently large SLGSs.