Second-order wave interaction with a vertical plate

The second-order interaction of monochromatic water waves with a rigid vertical plate is investigated numerically and experimentally. The plate has a finite width and is projected from one of the side-walls of a wave-tank. This geometry reduces the wave cases to normal incidence but permits a semi-analytical resolution based on eigenfunction expansions. Obtained numerical results are shown to be insensitive to the width of the tank beyond some value, and to converge quickly with the truncation orders of the expansions, in spite of the second-order potential having a logarithmic singularity at the plate edge. Second-order free-surface elevations are compared with values derived from experimental measurements at the BGO-First offshore wave-tank. Good agreement is reported. It is with much pleasure and admiration for his achievements that we dedicate this work to Nick Newman.     

Hydroelastic wave diffraction by a vertical cylinder

A linear three-dimensional problem of hydroelastic wave diffraction by a bottom-mounted circular cylinder is analysed. The fluid is of finite depth and is covered by an ice sheet, which is clamped to the cylinder surface. The ice stretches from the cylinder to infinity in all lateral directions. The hydroelastic behaviour of the ice sheet is described by linear elastic plate theory, and the fluid flow by a potential flow model. The two-dimensional incident wave is regular and has small amplitude. An analytical solution of the coupled problem of hydroelasticity is found by using a Weber transform. We determine the ice deflection and the vertical and horizontal forces acting on the cylinder and analyse the strain in the ice sheet caused by the incident wave.     

Second-order Wagner theory of wave impact

The paper deals with the two-dimensional unsteady problem of the impact of a liquid parabola onto a rigid flat plate at a constant velocity. The liquid is assumed ideal and incompressible and its flow potential. The initial stage of the impact is the main concern in this study. The non-dimensional half-width of the contact region between the impacting liquid and the plate plays the role of a small parameter in this problem. The flow region is subdivided into four parts: (i) the main flow region, the dimension of which is of the order of the contact-region width, (ii) the jet-root region, where the curvature of the free surface is very high and the flow is strongly nonlinear, (iii) the jet region, where the flow is approximately one-dimensional, (iv) the far-field region, where the flow is approximately uniform at the initial stage of impact. A second-order solution in the main flow region has been derived and matched to the first-order inner solution in the jet-root region. The matching conditions provide an estimate of the dimension of the contact region for small time. Pressure distributions in both the main flow region and the inner region are derived. The accuracy of the obtained asymptotic formulae is estimated. The second-order hydrodynamic force acting on the plate is obtained and compared with available experimental data. A fairly good agreement is reported.     

On wave propagation in a micropolar elastic cylinder

An asymptotic analysis of the free vibrations of a micropolar elastic cylinder is earned out postulating the displacements, the micro-rotations and the frequency as power series in the nondimensional $\text{? = 2π}\text{radius/(wave length)}$.     

Diffraction of a plane wave by a two-layer dielectric cylinder

We have investigated the characteristic features of diffraction of a plane wave by extended two-layer dielectric cylinders with complex indices of refraction. Translated from Izmeritel'naya Tekhnika, No. 4, pp. 30–31, April, 1996.     

Thermoelastic wave characteristics in a hollow cylinder using the modified wave finite element method

This paper represents a modified formulation of the wave finite element (WFE) method for propagating analysis of thermoelastic waves in a hollow cylinder without energy dissipation. The 2D-high-order spectral element with the Gauss–Legendre–Lobatto integration is applied into the WFE method, which produces the diagonal mass matrix. Based on the assumption of harmonic displacement fields by Fourier series expansion, the general discretization wave equation is simplified from the 3D problem to 2D. Dispersion properties of elastic wave propagation in the hollow cylinder are computed considering the choice of the spectral element orders, and the results indicate the high efficiency and high accuracy of the modified formulation compared with that of the software Disperse. Then, using the modified formulation, the thermoelastic dynamic equation of the cylinder is derived from the generalized thermoelasticity theory. The propagation of the thermoelasticwave (including two kinds of wave modes) in the cylinder without energy dissipation is discussed in differentcases. Finally, wave structures along the radial direction of thermoelastic wave modes are shown at thenondimensional frequency 1.25, which can be used for the recognition of different modes.     

Thermomechanical correction to the drag force on a sphere and a cylinder moving in HeII

The drag force on a sphere and a cylinder moving in HeII is considered on the basis of the full system of the two-fluid dissipative hydro-dynamical equations. It is shown, that due to the thermomechanical effect in superfluid there exists a specific correction to the drag force on a body. The value of this thermomechanical correction F has the order of the ratio1 _T/R or1 _T ² /R² (R is the size of the body, and1 _T is the length of the formation of the convective heat flow). The value of F grows at low temperatures, where1 _T is proportional to the characteristic time of the phonon-roton scattering process, and in the region near the -point, where1 _T has the same temperature dependence as the order parameter correlation length 1_T (T–T)^–2/3. The effects under discussion can be investigated experimentally by measurements of the mobility of small objects. A comparison is given with the data of the mobility of positive and negative ions in HeII near the -point.     

新型大扫描范围原子力显微镜的研究

研制了一种大扫描范围原子力显微镜(AFM)。设计了新的扫描驱动电路,使单幅图像的扫描范围大幅度提高;用步进电机和扫描器配合扫描,得到序列图像,序列图像拼接后获得大范围样品图像。实验结果表明,采用这一方法,在±150V 的电压驱动下,AFM 的扫描范围可增大到10 ìm?1 mm 的量级,同时保持 1 nm 量级的测试分辨力。     

Natural convection from a vertical cylinder at very large Prandtl numbers

Summary The natural convection from a vertical cylinder, is determined in the limiting case of very large Prandtl number, the Grashof number remaining finite.     

On spherical X-ray wave focusing upon backscattering from a parabolic cylinder crystal

The focusing of a spherical X-ray wave upon the Bragg backscattering from a crystal uniaxially bent to form a parabolic cylinder is theoretically studied. Based on geometrical optics, an analytical formula for the size of the crystal surface area involved in the diffraction reflection in the backscattering mode is derived. The analytical expression for the wave intensity distribution at the focus is analyzed and compared to that obtained previously.     

波浪锥型圆柱流固耦合振动机理研究EI北大核心CSCD

为增强及控制无叶片风力俘能结构能量采集效率,该研究将表面结构斜率参数引入波浪型圆柱,发展了一种新型波浪锥型圆柱,试验研究在雷诺数Re=3900下不同波长比、波幅比、斜率参数的波浪锥型圆柱涡激振动响应特性。研究发现:在不同折合流速下,斜率k=0.05的锥型圆柱和波长比λ/D _(m)=1.75、波幅比α/D _(m)=0.10、斜率k=0.05的波浪锥型圆柱最大振幅较直圆柱分别增长26.4%和12.6%,且锁频区间得以拓展;当折合流速在锁频区间内时,在波浪锥型圆柱绕流尾流中观察到了“2S”、“2P”漩涡脱落模式,并且“2P”漩涡脱落模式在往下游发展的过程中有转变为“2C”模式的趋势。该研究可为无叶片风力俘能结构涡致振动的增大和发电效率的提升提供理论支持。     

Guided wave propagation in an elastic hollow cylinder coated with a viscoelastic material

The propagation of ultrasonic guided waves in an elastic hollow cylinder with a viscoelastic coating is studied. The principle motivation is to provide tools for performing a guided wave, nondestructive inspection of piping and tubing with viscoelastic coatings. The theoretical boundary value problem is solved that describes the guided wave propagation in these structures for the purpose of finding the guided wave modes that propagate with little or no attenuation. The model uses the global matrix technique to generate the dispersion equation for the longitudinal modes of a system of an arbitrary number of perfectly bonded hollow cylinders with traction-free outer surfaces. A numerical solution of the dispersion equation produces the phase velocity and attenuation dispersion curves that describe the nature of the guided wave propagation. The attenuation dispersion curves show some guided wave modes that propagate with little or no attenuation in the coated structures of interest. The wave structure is examined for two of the modes to verify that the boundary conditions are satisfied and to explain their attenuation behavior. Experimental results are produced using an array of transducers positioned circumferentially around the pipe to evaluate the accuracy of the numerical solution.     

High-frequency diffraction of a electromagnetic plane wave by an imperfectly conducting rectangular cylinder

We shall consider the problem of determining the scattered far-wave field produced when a plane E-polarized wave is incident on an imperfectly conducting rectangular cylinder. On the basis of the uniform asymptotic solution for the problem of the diffraction of a plane wave by a right-angled impedance wedge, in conjunction with Keller’s method and multiple diffraction, a high-frequency far-field solution to the problem is given for two edge diffractions.     

Subharmonic resonance of a trapped wave near a vertical cylinder by narrow-banded random incident waves

It is well-known that near an infinite linear array of periodically spaced cylinders trapped waves of certain eigenfrequencies can exist. If there are only a finite number of cylinders in an infinite sea, trapping is imperfect. Simple harmonic incident waves can excite a nearly trapped wave at one of the eigen frequencies through a linear mechanism. However, the maximum amplification ratio increases monotonically with the number of the cylinders; hence the solution is singular in the limit of infinitely many cylinders. Recently, a nonlinear theory of subharmonic resonance of perfectly trapped waves has been completed. In this article the theory is further extended to random incident waves with a narrow spectrum centered near twice the natural frequency of the trapped wave. The effects of detuning and bandwidth of the spectrum are examined. Dedicated to Professor J. N. Newman on his 70th birthday. We wish to express our profound admiration for Professor Newman’s scientific contributions and leadership in the ship-hydrodynamics discipline. The relation between this article and an early work of his reflects in part his impact on us.     

Solution for wave propagation through a circular cylinder mounted on different topography ripple-bed profile shoals using DRBEM

In this paper, the dual reciprocity boundary element method wave model that is governed by a modified mild-slope equation is developed. Instead of addressing the infinite boundary condition, the model automatically satisfies the Sommerfeld radiation condition. This work examines the effects of both the bottom curvature and the slope-squared terms. The conducted numerical experiments have a topography that is composed of a cylinder mounted on two kinds of basic shoal: types 1 and 2 cubic. In addition, numerical experiments that combine two cubic type islands with ripple-beds are performed.The results show that the curvature term dominates the calculation of the sinusoidal-varying topography; even a disturbance in the topography is insignificant. In contrast to smooth topographies, the bottom curvature and the slope-squared terms are not dominant. Thus, the extended terms can be neglected if the seabed is smooth and gentle. When the topographies are combined with ripple-beds, the difference in the dimensionless wave amplitudes along the sidewall of the types 1 and 2 cubic islands is found to be 2.9 and 3.02, respectively. According to our study of cubic islands that are combined with ripple-beds, we can conclude with certainty that even though the variation of the seabed is very slight, the curvature and the slope-squared terms cannot be neglected for an uneven bottom.     

Scattering of antiplane shear wave by a piezoelectric circular cylinder with an imperfect interface

Summary We present analytical solutions for the scattering of an antiplane shear wave by a piezoelectric circular cylinder with an imperfect interface. We first consider the simple case in which the imperfection is homogeneous along the interface. Two typical imperfect interfaces are addressed: 1) mechanically compliant and dielectrically weakly conducting interface, and 2) mechanically compliant and dielectrically highly conducting interface. The expressions for the directivity pattern and scattering cross-section of the scattered shear waves are derived. We then investigate the more difficult problem in which the imperfection is circumferentially inhomogeneous along the interface. A concise expression for an inhomogeneously compliant and weakly conducting interface is derived by means of matrix notation. Numerical examples are presented to demonstrate the effect of the imperfection and the circumferential inhomogeneity of the interface on the directivity patterns and scattering cross-sections of the scattered shear wave. The circumferentially inhomogeneous interface is also utilized to model the interface where an arbitrary number of cracks exist. Results show that when every part of the interface is rather compliant, large low-frequency peaks of the scattered cross-sections, which correspond to the resonance scattering, can be observed no matter if the interface is homogeneous or inhomogeneous. The appearance of large low-frequency peaks can be well explained by estimating the natural frequency of the corresponding reduced mass-spring system where the cylinder is assumed as a rigid body. Peaks of the scattered cross-sections spanning from low frequencies to high frequencies can be observed for a cylinder with a partially debonded interface.     

Second-order effects on the wave propagation in elastic, isotropic, incompressible, and homogeneous media

In this paper we propose a perturbation method to investigate the propagation of the ordinary waves in second-order elastic, isotropic, incompressible, and homogeneous materials. This method allows us to determine the first-order terms of the speeds and the amplitudes both of the principal waves and the waves in any propagation direction, when the undisturbed region is subjected to an arbitrary isochoric deformation. Another application of this method is presented when the undisturbed region is subjected to a simple shear. Finally, some numerical results are presented in Mooney-Rivlin materials.     

Numerical solution of a problem involving the interaction of a shock wave with a cylinder in a supersonic flow

We describe a difference scheme of second-order accuracy for calculating axially symmetric flows containing shock waves, and we apply our computational results to the interaction of a shock wave with the end of a cylinder moving at supersonic speed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 6, pp. 1033–1039, December, 1971.