Propagation of Harmonic Waves in a Cylindrical Shell (Timoshenko Model)

Equations for studying the axisymmetric deformation of a cylindrical shell are derived on the basis of Timoshenko shell theory. A dispersion equation is set up to study natural harmonic waves in a cylindrical isotropic shell. A numerical approach to plotting dispersion diagrams is proposed. The wave velocities obtained coincide with analytical solutions     

The propagation of elastic stress waves in a conical shell under axial impulsive loading

The propagation of elastic stress waves in a conical shell subjected to axial impulsive loading is studied in this paper by means of the finite element calculation and model experiments. It is shown that there are two axisymmetrical elastic stress waves propagating with different velocities, i.e., the longitudinal wave and the bending wave. The attenuation of these waves while propagating along the shell surface is discussed. It is found in experiments that the bending wave is also generated when a longitudinal wave reflects from the fixed end of the shell, and both reflected waves will separate during the propagation due to their different velocities. Southwest Institute of Structural Mechanics     

轴向冲击载荷作用下锥壳中弹性应力波传播的计算和实验研究

本文利用有限元分析和模型实验研究了在轴向冲击载荷作用下,锥壳中弹性应力波的传播、计算和实验结果表明,结构中存在着弹性纵波和弹性弯曲波的传播,它们传播的速度各不相同,使壳面承受不同的应力状态;讨论了纵波和弯曲波随壳面的衰减;实验指出,由于边界的影响,即使纵波的反射也会产生新的反射弯曲波沿锥面传播。     

Mathematical model of spiral waves propagating in the aorta

The spiral waves in the viscous incompressible fluid flow within an arterial vessel modeled by a thin elastic isotropic shell are studied. Asymptotic expansions are constructed for two types of spiral waves. The first type is spiral long wall waves generated (owing to the viscous fluid no-slip at the inner shell wall) by the longitudinal and twist harmonic waves that propagate along the wall. For these waves the amplitude distribution over the vessel cross-section has the form of a boundary layer localized near the inner shell surface. The second is short small-amplitude waves that practically fill the entire vessel cross-section. It is shown that for the short waves the transfer mechanismis the steady-state flow, the role of the longitudinal wall waves and the elastic characteristics of the shell being in this case insignificant.     

Circumferential Traveling Waves in Filled Cylindrical Shells

Consideration is given to deformation in the form of traveling circumferential waves in circular cylindrical shells with a liquid. The effect of the liquid on the phase velocity in the carrier shell is studied depending on the waveformation parameters and initial conditions     

Periodic Modes in the Forced Nonlinear Vibrations of Filled Cylindrical Shells with an Initial Deflection

The features of the forced nonlinear vibrations of imperfect (with initial deflections) cylindrical shells fully filled with a fluid are studied. It is established that apart from the traditional single-wave deformation modes, complex modes such as traveling circumferential waves may exist in the resonance zones of shells.     

Analytical model of sound transmission through laminated composite cylindrical shells considering transverse shear deformation

Composite structures are often used in the aerospace industry due to the advantages offered by a high strength to weight ratio. Sound transmission through an infinite laminated composite cylindrical shell is studied in the context of the transmission of airborne sound into the aircraft interior. The shell is immersed in an external fluid medium and contains internal fluid. Airflow in the external fluid medium moves with a constant velocity. An exact solution is obtained by simultaneously solving the first-order shear deformation theory （FSDT） of a laminated composite shell and the acoustic wave equations. Transmission losses （TL） obtained from numerical solutions are compared with those of other authors. The effects of structural properties and flight conditions on TL are studied for a range of values, especially, the Mach number, stack sequences, and the angle of warp. Additionally, comparisons of the transmission losses are made between the classical thin shell theory （CST） and FSDT for laminated composite and isotropic cylindrical shells.     

Transient radiation by a submerged fluid-filled cylindrical shell

The radiation by a submerged fluid-filled cylindrical shell in response to a transient external pressure pulse is considered, and a semi-analytical model based on the Reissner–Mindlin shell theory is employed to simulate the interaction numerically. Two types of radiated waves that have been previously seen in experimental images for a submerged evacuated cylindrical shell are observed in both the external and internal fluids, the symmetric Lamb waves S₀ and the antisymmetric Lamb (or pseudo-Rayleigh) waves A₀. The third type of radiated waves is also observed that has not been explicitly imaged either experimentally or numerically for a submerged evacuated cylindrical shell, and it is demonstrated that these waves are the Scholte–Stoneley waves A. The effect that the complex structure of the radiated field has on the wave phenomena in the internal fluid is analyzed for shells of several different thicknesses, and the results of this analysis are summarized in the form of diagrams suitable for the use at the pre-design stage.     

有限长圆柱壳中轴对称弹性瞬态波

有限长的计及剪切变形和转动惯性的弹性圆柱壳的轴对称运动方程经过Laplace变换后转化为一组相空间中的方程。对该方程组作了一些适当的处理后,应用广义射线法,得到了相空间中位移和内力的射线法表达式。采用快速Fourier变换作Laplacl逆变换,即可得到圆柱壳受轴对称冲击载荷时的弹性瞬态波解。     

Fluid trapping by two partially shrouded rotating cylinders

In this paper we examine the prospect of using localized flow control for biomimetic fluid trapping. The problem is of interest for applications that call for guided transport of fluid volumes.The study shows that trapping can be achieved with the help of two partially shrouded rotating cylinders in a side-by-side arrangement. Secondary flows that manifest successful trapping resemble recirculation zones forming under the crests of peristaltic deformation waves, in particular with respect to their response to increasing incident flow velocity. Varying the rotation speed of the cylinders provides means to control the amount of trapped fluid.Numerical calculations to support these conclusions are presented in the paper for 0≤Re≤100 and h≈2, where Re and h are, respectively, the Reynolds number and the center-to-center distance between two cylinders divided by the cylinder diameter. Experimental validation of numerical results is performed for 0≤Re≤4.     

地震作用下水库坝体与水体相互作用数值模拟

地震作用下水库坝体受迫振动,推动坝后水体波动,造成水体动压作用于坝体,形成坝-水耦合作用,影响坝体安全.为了评估坝体振动引起的水面波动及坝体所受动水荷载作用,建立坝体动边界条件下的不可压水体运动数学模型,模拟了地震波作用下的坝后水体波动和动力荷载.结果 表明,在忽略坝体自身弹性变形的条件下,地震作用下坝体激发的水体表面...     

Propagation of Harmonic Waves in an Orthotropic Cylindrical Shell on Elastic Foundation

An equation is derived, using Timoshenko shell theory, to analyze axisymmetric strain fields in an orthotropic cylindrical shell on an elastic foundation. Also a dispersion equation is derived to study the natural harmonic waves in a shell depending on the properties of the elastic foundation. The wave velocities computed by the numerical method proposed are in agreement with the analytical solutions, which confirms the reliability of the results     

Improvement of moving particle semi‐implicit method for simulation of progressive water waves

Precise simulation of the propagation of surface water waves, especially when involving breaking wave, takes a significant place in computational fluid dynamics. Because of the strong nonlinear properties, the treatment of large surface deformation of free surface flow has always been a challenging work in the development of numerical models. In this paper, the moving particle semi‐implicit (MPS) method, an entirely Lagrangian method, is modified to simulate wave motion in a 2‐D numerical wave flume preferably. In terms of consecutive pressure distribution, a new and simple free surface detection criterion is proposed to enhance the free surface recognition in the MPS method. In addition, a revised gradient model is deduced to diminish the effect of nonuniform particle distribution and then to reduce the numerical wave attenuation occurring in the original MPS model. The applicability and stability of the improved MPS method are firstly demonstrated by the calculation of hydrostatic problem. It is revealed that these modifications are effective to suppress the pressure oscillation, weaken the local particle clustering, and boost the stability of numerical algorithm. It is then applied to investigate the propagation of progressive waves on a flat bed and the wave breaking on a mild slope. Comparisons with the analytical solutions and experimental results indicate that the improved MPS model can give better results about the profiles and heights of surface waves in contrast with the previous MPS models. Copyright © 2017 John Wiley & Sons, Ltd.     

On the interaction of water waves and seabed by the porous medium model

The interaction of water waves and seabed is studied by using Yamamoto's model, which takes into account the deformation of soil skeletal frame, compressibility of pore fluid flow as well as the Coulumb friction. When analyzing the propagation of three kinds of stress waves in seabed, a simplified dispersion relation and a specific damping formula are derived. The problem of seabed stability is further treated analytically based on the Mohr-Coulomb theory. The theory is finally applied to the coastal problems in the Lian-Yun Harbour and compared with observations and measurements in soil-wave tank with satisfactory results. The project supported by the National Science Foundation of China     

Complex surface rays associated with inhomogeneous skimming and Rayleigh waves

The Rayleigh wave, that propagates at the free surface of semi-infinite anisotropic medium, is composed of three inhomogeneous partial waves, each propagating along the surface with a different attenuation along the depth. Since this wave does not exhibit an attenuation on the surface, let us call it the homogeneous Rayleigh wave. The associated slowness corresponds to the real solution of the Rayleigh dispersion equation. Besides this classical solution, an infinite number of complex solutions of the Rayleigh dispersion equation exits. For such particular Rayleigh waves, the slowness vector, i.e. the identical component on the surface of the slowness of each partial waves, is taken to be complex. Thus, these Rayleigh waves are attenuated on the surface and as shown here, their attenuation is normal to the ray direction (or the energy velocity direction). Similarly to the infinite inhomogeneous plane waves which can be associated with complex rays, we call these waves, inhomogeneous Rayleigh waves. We use the inhomogeneous skimming waves, which are inhomogeneous plane waves, and the inhomogeneous Rayleigh waves to explain differently the usual diffraction phenomena on the free surface which cannot be explained by the real ray theory. For example, the arrival time of the wave packet observed beyond the cusp is in perfect accordance with the arrival time of some specific inhomogeneous Rayleigh waves. We show that these results are in agreement with the computation of the Green function. They apply to the theory of surface waves in linear elastodynamics with intrinsic anisotropy as well as to the theory of surface waves in linearised (incremental) elastodynamics with strain-induced anisotropy (also known as small-amplitude waves superimposed on the large static homogeneous deformation of a non-linear solid).     

Nonstationary motion of a shell on the surface of a heavy fluid

A three-dimensional nonstationary problem of vibrations of a flexible shell moving on the surface of an ideal heavy fluid. The forces due to surface tension are ignored. The problem is formulated in the space of the acceleration potential. The potential of the pulsating source is found by solving the Euler equation and the continuity equation taking into account the free-surface conditions (linear theory of small waves) and the conditions at infinity. The density distribution function of the dipole layer is determined from the boundary conditions on the surface of the shell. Formulas for determining the shape of gravity waves on the fluid surface and the natural frequencies of vibrations of the shell are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 66–75, July–August, 2009.     

Nonlinear steady states of hyperelastic membrane tubes conveying a viscous non-Newtonian fluid

We study possible steady states of an infinitely long tube made of a hyperelastic membrane and conveying either an inviscid, or a viscous fluid with power-law rheology. The tube model is geometrically and physically nonlinear; the fluid model is limited to smooth changes in the tube’s radius. For the inviscid case, we analyse the tube’s stretch and flow velocity range at which standing solitary waves of both the swelling and the necking type exist. For the viscous case, we first analyse the tube’s upstream and downstream limit states that are balanced by infinitely growing upstream (and decreasing downstream) fluid pressure and axial stress caused by fluid viscosity. Then we investigate conditions that can connect these limit states by a single solution. We show that such a solution exists only for sufficiently small flow speeds and that it has a form of a kink wave; solitary waves do not exist. For the case of a semi-infinite tube (infinite either upstream or downstream), there exist both kink and solitary wave solutions. For finite-length tubes, there exist solutions of any kind, i.e. in the form of pieces of kink waves, solitary waves, and periodic waves.     

Edge Resonance in Structurally Orthotropic Cylindrical Shells

Possibilities for edge resonances to occur in structurally orthotropic cylindrical shells through which harmonic waves propagate are studied. It is shown that such resonances may be generated by axisymmetric longitudinal flexural waves propagating in a rigidly clamped semi-infinite shell __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 93–101, July 2005.     

园柱壳中环裂纹对弹性波的散射

本文在经典弹性薄壳运动方程基础上,分析了圆柱壳中环向穿透裂纹对扭转波和膨胀波的散射,求得了反射系数及相应的动态应力强度因子。通过检查能量平衡关系验证了所用方法的正确性。     

Shear wave dispersion and attenuation in periodic systems of alternating solid and viscous fluid layers

The attenuation and dispersion of elastic waves in fluid-saturated rocks due to the viscosity of the pore fluid is investigated using an idealized exactly solvable example of a system of alternating solid and viscous fluid layers. Waves in periodic layered systems at low frequencies are studied using an asymptotic analysis of Rytov’s exact dispersion equations. Since the wavelength of shear waves in fluids (viscous skin depth) is much smaller than the wavelength of shear or compressional waves in solids, the presence of viscous fluid layers necessitates the inclusion of higher terms in the long-wavelength asymptotic expansion. This expansion allows for the derivation of explicit analytical expressions for the attenuation and dispersion of shear waves, with the directions of propagation and of particle motion being in the bedding plane. The attenuation (dispersion) is controlled by the parameter which represents the ratio of Biot’s characteristic frequency to the viscoelastic characteristic frequency. If Biot’s characteristic frequency is small compared with the viscoelastic characteristic frequency, the solution is identical to that derived from an anisotropic version of the Frenkel–Biot theory of poroelasticity. In the opposite case when Biot’s characteristic frequency is greater than the viscoelastic characteristic frequency, the attenuation/dispersion is dominated by the classical viscoelastic absorption due to the shear stiffening effect of the viscous fluid layers. The product of these two characteristic frequencies is equal to the squared resonant frequency of the layered system, times a dimensionless proportionality constant of the order 1. This explains why the visco-elastic and poroelastic mechanisms are usually treated separately in the context of macroscopic (effective medium) theories, as these theories imply that frequency is small compared to the resonant (scattering) frequency of individual pores.