An explicit representation of steady state response of a beam on an elastic foundation to moving harmonic line loads

A closed‐form deflection response of a beam rest is presented in this paper using the integral transform method. The theory of linear partial differential equations is used to represent the deflection of beam subjected to a moving harmonic line load in integration form. The solution is finally carried out using the inverse Fourier transform. To evaluate the integration analytically, poles of the integrand are identified with the help of algebraic equation theory. Residue theorem is then utilized to represent the integration as a contour integral in the complex plane. Closed‐form deflections and numerical results are provided for different combinations of load frequency and velocity. Copyright © 2002 John Wiley & Sons, Ltd.     

A critical state model for sands dependent on stress and density

An elastoplastic model for sands is presented in this paper, which can describe stress–strain behaviour dependent on mean effective stress level and void ratio. The main features of the proposed model are: (a) a new state parameter, which is dependent on the initial void ratio and initial mean stress, is proposed and applied to the yield function in order to predict the plastic deformation for very loose sands; and (b) another new state parameter, which is used to determine the peak strength and describe the critical state behaviour of sands during shearing, is proposed in order to predict simply negative/positive dilatancy and the hardening/softening behaviour of medium or dense sands. In addition, the proposed model can also predict the stress–strain behaviour of sands under three-dimensional stress conditions by using a transformed stress tensor instead of ordinary stress tensor. Copyright © 2004 John Wiley & Sons, Ltd.     

PROPAGATION OF 30—60 DAY LOW FREQUENCY OSCILLATIONS AND THEIR INFLUENCE UPON THE SUBTROPICAL WESTERLIES JET STREAM DURING NORTHERN HEMISPHERE WINTER

Based on daily ECMWF gridpoint data of two winters during 1981—1983 including an ENSOyear,propagation of low frequency oscillations(LFO)during Northern Hemisphere winters andtheir influences upon 30—60 day oscillations of the subtropical jet stream are studied with the sta-tistical methods as complex empirical orthogonal function(CEOF)and so on.Results show that inthe winter of a normal year(1981—1982),30—60 day oscillations in the subtropical zone aremainly in the northern and southern flanks of exit region of jet stream.In the ENSO year(1982—1983),they are mainly in the vicinity of entrance and exit regions of jet stream.Intraseasonalchanges of subtropical jet stream manifested themselves as latitudinal fluctuation or longitudinalprogression or regression of about 40 day period.There are marked differences between propagat-ing passages of low frequency modes responsible for changes of subtropical jet stream in the normalyear(1981—1982)and in the ENSO year(1982—1983).Changes of oscillation amplitude showobvious phases.In general,the one in late winter is stronger than that in early winter,strongestone occurs in February.     

A note on turbulent perturbations of salinity in a partially mixed estuary

Measurements of salinity perturbations in a partially mixed estuary have been used to evaluate the usefulness of an inductive salinometer and to determine some of the characteristics of the salinity perturbations. The salinometer performed satisfactorily under most conditions. Although internal wave like effects were present, the turbulence fluctuations were dominant. The salinity fluctuations and the turbulent fluxes $\text{sw}$ and $\text{su}$ were found to behave in a manner similar to the density fluctuations in a thermally stratified atmospheric boundary layer and a laboratory open channel flow. A quadrant analysis suggested that the contribution of each quadrant to the turbulent flux changed with Ri. The turbulence parameters ν and c_γ were found to decrease and increase respectively as Ri increases.     

Cokriging nonstationary data

Universal cokriging is used to obtain predictions when dealing with multivariate random functions. An important type of nonstationarity is defined in terms of multivariate random functions with increments which are stationary of orderk. The covariance between increments of different variables is modeled by means of the pseudo-cross-covariance function. Criteria are formulated to which the parameters of pseudo-cross-covariance functions must comply so as to ensure positive-definiteness. Cokriging equations and the induced cokriging equations are given. The study is illustrated by an example from soil science.     

The possiblity of detection of ultracool dwarfs with the UKIRT Infrared Deep Sky Survey

We present predictions for the numbers of ultracool dwarfs in the Galactic disc population that could be detected by the WFCAM/UKIDSS Large Area Survey and Ultra Deep Survey. Simulated samples of objects are created with masses and ages drawn from different mass functions and birthrates. Each object is then given absolute magnitudes in different passbands based on empirically derived bolometric correction versus effective temperature relationships (or model predictions for Y dwarfs). These are then combined with simulated space positions, velocities and photometric errors to yield observables such as apparent magnitudes and proper motions. Such observables are then passed through the survey selection mechanism to yield histograms in colour. This technique also produces predictions for the proper motion histograms for ultracool dwarfs and estimated numbers for the as yet undetected Y dwarfs. Finally, it is shown that these techniques could be used to constrain the ultra-low-mass mass function and birthrate of the Galactic disc population.     

Distribution of nonlinear wave crests

The distribution of nonlinear wave crests is examined on the basis of a theoretical probability density previously given elsewhere (J. Eng. Mech. 120 (1994) 1009). Certain errors contained in the original theoretical density are corrected, and the corresponding exceedance distribution is derived. The resulting theoretical forms of the probability density and exceedance distribution are then slightly simplified and compared with nonlinear wave data gathered under hurricane conditions. The results indicate that the proposed theoretical forms describe the observed distributions of large wave crests better than the Rayleigh law. However, the quantitative accuracy of the predictions is somewhat poor, as is typical of approximate theories based on Gram–Charlier-type expansions.     

Acoustic plane-wave scattering from a rough surface over a random fluid medium

Acoustic plane-wave scattering from a rough surface overlying a fluid half-space with a sound-speed distribution subject to a small random variation is considered. Under the assumption that the surface roughness and medium randomness are statistically independent, the scattered field may be derived by first solving for the mean field in the medium, and then incorporating with boundary-perturbation method to obtain the total mean field and the power spectral density of the scattered field. The employed algorithm is compatible to the analysis available in the existing literature so that the formulations are conveniently integrated. The results for the power spectral density have shown that the effects of medium inhomogeneities on the rough surface scattering are limited in a spectral regime where the scattered components have shallow grazing angles. The distribution of the power spectral density over the space is primarily governed by the power spectrum and correlation lengths of the rough surface.     

Fully nonlinear numerical wave tank (NWT) simulations and wave run-up prediction around 3-D structures

A finite-difference scheme and a modified marker-and-cell (MAC) algorithm have been developed to investigate the interactions of fully nonlinear waves with two- or three-dimensional structures of arbitrary shape. The Navier–Stokes (NS) and continuity equations are solved in the computational domain and the boundary values are updated at each time step by the finite-difference time-marching scheme in the framework of a rectangular coordinate system. The fully nonlinear kinematic free-surface condition is implemented by the marker-density function (MDF) technique developed for two fluid layers.To demonstrate the capability and accuracy of the present method, the numerical simulation of backstep flows with free-surface, and the numerical tests of the MDF technique with limit functions are conducted. The 3D program was then applied to nonlinear wave interactions with conical gravity platforms of circular and octagonal cross-sections. The numerical prediction of maximum wave run-up on arctic structures is compared with the prediction of the Shore Protection Manual (SPM) method and those of linear and second-order diffraction analyses based on potential theory and boundary element method (BEM). Through this comparison, the effects of non-linearity and viscosity on wave loading and run-up are discussed.