Dimensionless wave numbers evolution of a three spans simply supported beam when the intermediate supports are moving along the whole beam

Continuous beams simply supported with several intermediate supports are very common in engineering achievements everywhere. The paper shows the evolution of the dimensionless wave number in 3D format, respectively of the eigenfrequencies for a continuous beam with three openings when the intermediate supports take any position inside the beam. The frequency equation for calculating the dimensionless wave number is presented and the modal function is given with an example for the case where the eigenfrequency has the maximum value at fist vibration mode.

SH-wave velocity in a fiber-reinforced anisotropic layer overlying a gravitational heterogeneous half-space

Purpose – The purpose of this paper is to investigate the existence of SH-waves in fiber-reinforced layer placed over a heterogeneous elastic half-space. Design/methodology/approach – The heterogeneity of the elastic half-space is caused by the exponential variations of density and rigidity. As a special case when both the layers are homogeneous, the derived equation is in agreement with the general equation of Love wave. Findings – Numerically, it is observed that the velocity of SH-waves decreases with the increase of heterogeneity and reinforced parameters. The dimensionless phase velocity of SH-waves increases with the decreases of dimensionless wave number and shown through figures. Originality/value – In this work, SH-wave in a fiber-reinforced anisotropic medium overlying a heterogeneous gravitational half-space has been investigated analytically and numerically. The dispersion equation for the propagation of SH-waves has been observed in terms of Whittaker function and its derivative of second degree order. It has been observed that on the removal of heterogeneity of half-space, and reinforced parameters of the layer, the derived dispersion equation reduces to Love wave dispersion equation thereby validates the solution of the problem. The equation of propagation of Love wave in fiber-reinforced medium over a heterogeneous half-space given by relevant authors is also reduced from the obtained dispersion relation under the considered geometry.

Shear Wave Propagation in Multilayered Medium including an Irregular Fluid Saturated Porous Stratum with Rigid Boundary

The present investigation is concerned with the study of propagation of shear waves in an anisotropic fluid saturated porous layer over a semi-infinite homogeneous elastic half-space lying under an elastic homogeneous layer with irregularity present at the interface with rigid boundary. The rectangular irregularity has been taken in the half-space. The dispersion equation for shear waves is derived by using the perturbation technique followed by Fourier transformation. Numerically, the effect of irregularity present is analysed. It is seen that the phase velocity is significantly influenced by the wave number and the depth of the irregularity. The variations of dimensionless phase velocity against dimensionless wave number are shown graphically for the different size of rectangular irregularities with the help of MATLAB.

FE Analysis of Stress Concentrations in Composite Plates with Multiple Holes for Zigzag Multi-Fastened Joints

Most fatigue failures in aeronautical structures occur at fastened joints due to stress concentration (SC). Since more and more advanced composites are applied in aircrafts instead of conventional alloys, SC in CFRP composite plates with zigzag-arranged multiple holes has been investigated by finite element method in this paper. It is found that the static SC factor (SCF) of CFRP plates varies with the dimensionless bore and zigzag angle by a greater change than isotropic plates, and that the dynamic response amplitude and frequency of the SCF depend on the dimensionless bore and the dimensionless wave number related with material properties and the exciting frequency.

THE EFFECT OF TIDE LEVEL ON THE TSUNAMI RESPONSE OF COASTAL HARBORS

The tsunamis generated by the February 27, 2010 Chilean earthquake and the great Japan Tohoku earthquake on March 11, 2011 arrived at several Pacific Coast harbors when the tide levels were at low tides and persisted for several tidal cycles. Despite the significant difference in the recorded wave amplitude observed at Crescent City harbor between these two events, the energy spectrum as a function of frequency has been found to contain several spikes corresponding to the frequency range of 3×〖10〗^(-4)~10×〖10〗^(-4) Hz. This pattern in spectral density is different from several prior tsunamis observed and analyzed for Crescent City Harbor as presented by Lee, Xing and Magoon (2008). In the present study we present the reasons behind the differences in the response behavior associated with these two events. We prove that they are due to the effect of tide levels. We also show that in order to correctly decipher the resonant response characteristics to incident wave the response curves should be expressed as a function of the dimensionless wave number. The tsunami waves recorded at tide gauge station in San Diego Harbor (Southern California) are also analyzed and discussed.

Analytical Localization Lengths in an One-Dimensional Disordered Electron System

Analytical approximations of the Lyapunov exponent are derived for a random displacement model with equal potential barriers and random positions of the scatterers. Two asymptotic regions are considered corresponding to high and low reflectivity of the single scattering potential. The analytical results are in terms of a distribution function W for certain phases of the transfer matrices. A functional equation for W is derived and numerically solved. This serves to validate the analytical asymptotic formulas which turn out to be accurate in the high and low reflectivity regions with dimensionless wave number K < 2 and K > 6, respectively. The high wave number asymptotics allows for an analytical examination of the sufficient conditions for Anderson localization

A Dynamical Model for Studying the Stability of Thermo-Solutal Convection Under the Effect of Vertical Vibration

This paper concerns the thermal stability analysis of porous layer saturated by a binary fluid under the influence of mechanical vibration. The linear stability analysis of this thermal system leads us to study the following damped coupled Mathieu equations: BH¨+B(π2+k2)+1H˙+(π2+k2)−k2k2+π2RaT(1+Rsinω*t*)H=k2k2+π2(NRaT)(1+Rsinω*t*)Fε*BF¨+Bπ2+k2Le+ε*F˙+π2+k2Le−k2k2+π2NRaT(1+Rsinω*t*)F=k2k2+π2RaT(1+Rsinω*t*)H where RaT is thermal Rayleigh number, R is acceleration ratio (bω2/g), Le is the Lewis number, k is the dimensionless wave-number, ε* is normalized porosity and N is the buoyancy ratio (H and F are perturbations of temperature and concentration fields). In the follow up, the non-linear behavior of the problem is studied via a generalization of the Lorenz model (five coupled non-linear differential equations with periodic coefficients). In the presence or absence of gravity, the stability limit for the onset of stationary as well as Hopf bifurcations is determined.

Peristaltic transport of an Oldroyd-B fluid in a planar channel

The effects of an Oldroyd-B fluid on the peristaltic mechanism are examined under the long wavelength assumption. Analytical expressions for the stream function, the axial velocity, and the pressure rise per wavelength are obtained up to the second order in the dimensionless wave number. The effects of the various parameters of interest on the flow are shown and discussed.

Approximation zones of the Saint-Venant equations f flood routing with overbank flow

The classification of river waves as gravity, diffusion or kinematic waves, corresponds to different forms of the momentum equation in the Saint-Venant system. This paper aims to define approximation zones of the Saint-Venant equations for flood routing in natural channels with overbank flow in the flooded area. Using linear perturbation theory, the different terms in the Saint-equations were analysed as a function of the balance between friction and inertia. Then, using non-dimensionalised variables, flood waves were expressed as a function of three parameters: the Froude number of the steady uniform flow, a dimensionless wave, number of the unsteady component of the motion and the ratio between the flooded area zone width and the main channel width. Finally, different theoretical cases, corresponding to different flooded area zone widths were analysed and compared. Results show that, when the width of the flooded area increases, the domain of application of the diffusive wave and the inematic wave models is restricted. Keywords: Saint-Venant equations; river waves; overbank flow

WAVE INTERACTION WITH MOORED SLOPING BREAKWATER

Interaction of periodic waves with a moored inclined floating breakwater has been studied theoretically and numerically. The floating breakwater is inclined at a well defined angle with the sea bottom; its seaward end in protruding above the water surface. In static equilibrium, without incoming waves, the body weight, the buoyance force, and the restoring forces from the mooring lines which are modeled using linear springs keep the breakwater at a fixed angle. The theoretical formulation is based on a suitable variational principle. For the numerical solution a combination of finite element approximation as well as eigen function expansion technique is used. The result is obtained in terms of wave transmission and reflection coefficient as well as the sway, heave and roll motion of the breakwater. The sensitivity of the solution on the parameters such as the bottom gap size, angle of inclination, and the mooring line stiffness are investigated over a range of incident wave transmission coefficient for dimensionless wave number hk > 0.60 ( k is wave number, h is the water depth). The results suggest that a certain degree of sheltering effect can be realized by employing this type of sloping breakwater.