单桩水平及水平-摇摆耦合振动分析

采用Novak薄层法,分析了单桩的水平及水平-摇摆耦合振动。然后,引进Novak和韩英才的边界层理论,全面分析和对比了匀质弹性、匀质粘弹性和非匀质粘弹性地基中单桩的动力阻抗,考察了各种因素对单桩动力阻抗的影响程度。在推导单桩水平动力阻抗的过程中,采用克雷洛夫函数和初参数法求解单桩的水平振动微分方程,从而能够方便地考虑桩长和桩底土对单桩动力阻抗的影响。计算表明,当桩的长径比较小时,桩底土对单桩动力阻抗有重要的影响。     

Estimate of the effect of vibrations on quartz gravity meters

Summary Relations for computing the minimum amplitudes of ground vibrations which generate oscillations of the gravity meter reading beam at the limit of the resolution of the optical system, have been derived. The minimum amplitudes in the ground displacement period range of0.1 to10 s, for the assumed values of the fundamental parameters of quartz gravity meters (i.e. the periods and damping constants of the pendulum and the mechanico-optical magnification of the pendulum deflections), range from tenths of a micrometre to units of micrometres. Larger displacement amplitudes, due to, e.g., earthquakes and traffic, disrupt gravity measurements.     

Free non-radial vibrations of the earth

Summary Earthquake shear waves with period around 12.2 min have been lately reported byM. Båth (1958), who suggests that these might be due to torsional vibrations of the whole mantle on some axis through the centre of the earth. An attempt has been made here to put forward a theory which accounts for such vibrations. The general elastokinetic equation for a heterogeneous isotropic medium is solved for a free spherical shell overlying a liquid core, and the solution is investigated for the first two modes. The frequency equation is solved for a shell and the limiting cases of a full sphere and an infinitely thin shell. Application is then made for various approximate mantle models, and periods are found which are in fair agreement with the observed. It is then shown that if the rigidity of the core is taken into consideration a closer agreement with the observed might be attained.

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Zusammenfassung Seismische Transversalwellen mit einer Periode von rund 12.2 min sind neulich vonM. Båth (1958) beobachtet worden, der vermutet, dass sie Torsionsschwingungen des ganzen Erdmantels um eine Achse durch das Erdzentrum sind. Ein Versuch wird hier gemacht eine Theorie für solche Schwingungen zu entwickeln. Die allgemeine elastokinetische Gleichung für ein heterogenes, isotropisches Medium wird für eine freie, sphärische Schale über einem flüssigen Kern gelöst, und die Lösung wird für die zwei ersten Schwingungsformen untersucht. Die Frequenzgleichung wird für eine Schale und für die Grenzfälle einer ganzen Sphäre und einer unendlich dünnen Schale gelöst. Die Lösungen werden dann auf verschiedene, approximative Mantel-Modellen angewendet, und Perioden werden gefunden, die ziemlich gute Übereinstimmung mit der beobachteten Periode zeigen. Es wird danach gezeigt, dass, falls die Righeit des Erdkerns in Betracht gezogen wird, eine noch bessere Übereinstimmung mit der beobachteten Periode erreicht wird.

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This research was supported by Eng.Herbert E. Linden of Beverly Hills, California.     

Free vibrations of simply supported nonhomogeneous isotropic rectangular plates of bilinearly varying thickness and elastically restrained edges against rotation using Rayleigh-Ritz method

This paper addresses the free transverse vibrations of thin simply supported nonhomogeneous isotropic rectangular plates of bilinearly varying thickness with elastically restrained edges against rotati...     

Torsional vibrations of elastic foundation on saturated media

A comprehensive analytical solution is developed to examine the torsional vibration of an elastic foundation on a semi-infinite saturated elastic medium for the first time. First, the governing equations of saturated media are solved by use of Hankel transform techniques. Then, based on the assumption that the contact between the foundation and the half-space is perfectly bonded, this dynamic mixed boundary-value problem can lead to dual integral equations, which are further reduced to the standard Fredholm integral equations of the second kind and solved by numerical procedures. Numerical examples are given at the end of the paper. The numerical results indicate that the response of the elastic foundation strongly depends on the material and geometrical properties of both the saturated soil-foundation system and the load acting on the foundation. In most of the cases, the dynamic behavior of an elastic foundation on saturated media significantly differs from that of a rigid plate bearing on the elastic half-space.     

Rocking vibrations of rigid disk on saturated poroelastic medium

The dynamic response of a rigid disk on a saturated poroelastic half space and subjected to harmonic rocking excitation is studied. The mixed boundary-value problem for the case of relaxed contact condition between the disk and the poroelastic half space is reduced to a Fredholm integral equation of the second kind, which is solved numerically. The dynamic compliance coefficient for the rocking vibration of a rigid disk on a poroelastic half space is presented.     

Natural vibrations of shear wall buildings on flexible supports

A shear wall building is considered as an assembly of plane and curvilinear shear walls tied together by floor slabs to act as a composite unit. Based on this conception and the continuous medium approach, the governing dynamic equations and boundary conditions are derived from energy principles, using Vlasov's theory of thin-walled beams. All primary and secondary inertia forces, as well as the influence of elastic foundation flexibility, have been taken into consideration. A numerical solution of the dynamic equations is achieved by employing the Ritz-Galerkin technique, yielding both natural frequencies and mode shapes. The technique is applicable to buildings containing coupled and non-coupled, open section shear walls oriented in plan in any arbitrary manner. The use of the method is illustrated by the example of a complex building with unsymmetric plan, and the analytical natural frequencies of two shear wall building models are compared with those obtained experimentally by other investigators.     

Horizontal vibrations of a disk on a poroelastic half-space

This paper analytically examines the horizontal vibration of a rigid disk on a saturated poroelastic half-space. The pressure-solid displacement form of the harmonic equations of motion for asymmetric dynamic problem are developed from the form of the equations originally presented by Biot. Making use of a new method the solution of the above equations is obtained. According to the mixed boundary -value conditions, the dual integral equations of the horizontal vibration of a rigid disk on a saturated poroelastic half-space are established. By appropriate transforms, it is shown that the dual integral equations can be reduced to a pair of Fredholm integral equations of the second kind, whose solutions are then computed. Numerical results for the horizontal dynamic compliance coefficient are given at the end of this paper.     

The effect of column mass on shear building vibrations

In the usual assignment of mass for shear building models, the mass of the columns is lumped with the mass of the floor at each floor level. In order to account for frequencies of modes higher than N in an N-storey building, however, additional column masses must be identified. In this note, such additional masses are located at the mid-height of each column, and the characteristics of the shapes and frequencies of the resulting higher mode set are investigated.     

In-situ experimental investigation of the influence of structure characteristics on subway-induced building vibrations

Many types of buildings have been widely constructed in the vicinity of subway lines in China. Normal life and business activities are hampered by excessive subway-induced vibrations. This study aims to determine the influence of structure characteristics on structure-borne vibrations, generally based on experimental results. Vibration measurements were performed in four typical sites in Wuxi, China, involving over-track buildings, along-track buildings, frame structure buildings and a masonry building. Special structure designs like structure transfer floor were also included. Then, the captured data was analyzed in the time domain and the frequency domain. Furthermore, the influence of building location, structure type and structure layout was investigated. Finally, vibrations were evaluated with ISO and Chinese criteria and structure optimization for vibration attenuation was proposed. It is found that over-track buildings are more severely affected than along-track buildings. Higher frequency contents(20-60 Hz) in over-track buildings and lower frequency contents(0-10 Hz) in along-track buildings should be seriously considered in vibration control. Weaker structure member joints and lower material strength would be beneficial to over-track buildings while the inverse situation would be beneficial to along-track buildings. The application of structure transfer floor-generally stiffer structure members and structure discontinuity-is also beneficial.     

Experimental analysis of track-ground vibrations on a stretch of the Portuguese railway network

This paper presents a comprehensive experimental campaign developed on a stretch of the Portuguese railway network. The experimental work includes three fundamental and complementary components: the characterization of the ground, the characterization of the track and the measurement of the vibrations generated by railway traffic. The characterization of the ground was performed using a combination of conventional and geophysical tests (cross-hole and SASW). The mechanical characterization of the track was performed through receptance tests and the rail unevenness profile was accurately measured. The vibrations due to the passage of more than 20 trains were measured. First, a selection of the results is presented and analysed in detail; later, the variability of the responses is briefly discussed. The presented data may be used by other researchers (e.g. in the validation of their prediction models), since it can be downloaded from www.fe.up.pt/~csf/DataCarregado.zip.     

Influence of instruments on the H/V spectral ratios of ambient vibrations

For an optimal analysis of the H/V curve, it appears necessary to check the instrument signal to noise ratio in the studied frequency band, to ensure that the signal from the ground noise is well above the internal noise. We assess the reliability and accuracy of various digitizers, sensors and/or digitizer-sensor couples. Although this study is of general interest for any kind of seismological study, we emphasize the influence of equipment on H/V analysis results. To display the impact of the instrumental part on the H/V behavior, some series of tests have been carried out following a step-by-step procedure: first, the digitizers have been tested in the lab (sensitivity, internal noise...), then the three components sensors, still in the lab, and finally the usual user digitizers-sensors couple in lab and outdoors. In general, the digitizer characteristics, verified during this test, correspond well to the manufacturer specifications, however, depending on the digitizer, the quality of the digitized waveform can be very good to very poor, with variation from a channel to another channel (gain, time difference etc.). It appears very clearly that digitizers need a warming up time before the recording to avoid problems in the low-frequency range. Regarding the sensors, we recommend strongly to avoid the use of “classical” accelerometers (i.e., usual force balance technology). The majority of tested seismometers (broadband and short period, even 4.5 Hz) can be used without problems from 0.4 to 25 Hz. In all cases, the instrumentation should be checked first to verify that it works well for the defined study aim, but also to define its limit of use (frequency, sensitivity...).     

Sensitivity of the Gs 12 gravity meter to vibrations

nuaa m¶rt;ua u mam unmauaumaGs 12 No. 129 a uauu ¶rt;uana amm 0.02–30. a uu a uau nam auu au u auma naamauma a mua ma u n¶rt;a mumm a ¶rt;uu ¶rt;ama ammau uu .     

On the growth of unsteady boundary layers on porous flat plates

Summary An investigation is carried out on the unsteady boundary layer induced in an incompressible, homogeneous, viscous fluid bounded by (i) an infinite horizontal porous plate aty=0, or (ii) two parallel horizontal rigid porous plates aty=0 andy=d. The unsteady motion is generated in the above fluid configurations by moving the plate(s) impulsively in its (their) own plane with a prescribed time-dependent velocity. Solutions for the unsteady velocity field are exactly solved by the Laplace transform treatment combined with the theory of residues. The structures of the associated boundary layers are determined. The effects of suction on the solutions and the boundary layers are investigated in detail, the limiting behaviour of the unsteady solution as timet is examined and Physical interpretations of the mathematical results are given. Finally, the frictional stresses on the plates are stated without detailed calculation.     

On the asymptotic amplitude of vibrating plates

Summary The asymptotic behaviour of the amplitude of a vibrating plate is investigated by treating the relevant differential equation as a second-order evolution equation in a Hilbert space.     

Free vibrations of open-section shear walls

The coupled torsional-flexural vibration of open-section shear walls, braced by connecting beams at each floor level, is analysed on the basis of Vlasov's theory of thin-walled beams. The basic dynamic equations and boundary conditions are derived from Hamilton's principle, and a numerical solution obtained by the Ritz-Galerkin method. In addition to the primary torsional and flexural inertias, secondary effects due to rotatory and warping inertia forces have also been taken into account. The method is suitable for both rigid and flexible base conditions. A series of numerical examples is presented in which analytical results are compared with available experimental data, and the effects of secondary inertia forces, base flexibility and connecting beams upon the vibration characteristics of such shear walls are examined for two different structural forms.     

Free vibrations of coupled shear walls

The continuous connection method of analysis is extended to deal with the free vibrations of a coupled shear wall structure. The natural modes and frequencies are determined from the Galerkin technique, and the dynamic response following an imposed lateral displacement is evaluated. A comparison is made between theoretical predictions of natural frequencies and the results from tests on model structures.     

Minimizing structural vibrations with absorbers

In a companion paper¹ the authors show that the parameters of an absorber which will minimize the resonant response of a simple elastic body can be determined from known results by treating the body as an equivalent single degree-of-freedom system. In this paper cylindrical shells are considered as examples of dynamically complex structures, for which the ratio of the natural frequencies of adjacent modes tends towards unity. It is shown that as dynamic complexity increases optimum absorber parameters for the reduction of resonant response deviate increasingly from those for an equivalent single degree-of-freedom system. Absorbers can be used also to reduce the random response of structures. Simple expressions for optimum parameters are given for an undamped main system, which has one degree of freedom and is subjected to white noise excitation. Optimum absorber parameters for beams, plates and cylindrical shells show similar qualitative behaviour for random and harmonic response with the concept of an equivalent single degree-of-freedom system being applicable only for the simpler structures.