Influence of a rigid skeleton pore structure on wave propagation in a fluid-filling porous medium

This work concerns an analysis of the influence of a rigid skeleton pore structure on wave propagation in a fluid-filling porous medium. The analysis is based on the continuum theory of a deformable porous medium in which the pore structure is described by two macroparameters. Considerations comprise two questions: the influence of the pore structure on wave-propagation velocity analysed for the quasilinear case and the role of structure in the reflection-refraction wave phenomenon in fluid at the contact surface of two porous media. It has been shown that the pore structure reduces the velocity of wave and together with the angle of incidence it defines the reflection-refraction wave phenomenon.     

Nonlinear low-velocity impact on damped and matrix-cracked hybrid laminated beams containing carbon nanotube reinforced composite layers

This paper investigates the low-velocity impact response of a shear deformable laminated beam which contains both carbon nanotube reinforced composite (CNTRC) layers and carbon fiber reinforced composite (CFRC) layers. The effect of matrix cracks is considered, and a refined self-consistent model is selected to describe the degraded stiffness caused by the damage. The beam including damping effects rests on a two-parameter elastic foundation in thermal environments. Based on a higher-order shear deformation theory and von Kármán nonlinear strain–displacement relationships, the motion equations of the beam and impactor are established and solved by means of a two-step perturbation approach. The material properties of both CFRC layers and CNTRC layers are assumed to be temperature-dependent. To assess engineering application of this hybrid structure, two conditions for outer CNTRC layers and outer CFRC layers are compared. Besides, the effects of the crack density, volume fraction of carbon nanotube, temperature variation, the foundation stiffness and damping on the nonlinear low-velocity impact behavior of hybrid laminated beams are also discussed in detail.

     

The influence of variable stiffness of teeth on dynamic loads in single-gear transmission

Summary In this paper, the influence of the variable stiffness of mating gear teeth on dynamic loads occurring between teeth in a single-gear transmission is investigated using a discrete-continuous model consisting of two torsionally deformable ponderable shafts and four rigid bodies. The stiffness is described by a harmonic function of time. Considerations by means of the wave method enable to determine dynamic loads in steady as well as in transient states. Numerical calculations are concentrated on the determination of the amplitudes of dynamic loads on gear teeth with respect to revolution per minute. Received 4 March 1997; accepted for publication 12 September 1997     

LOW-FREQUENCY RESPONSES OF NONLINEARLY MOORED VESSELS IN RANDOM WAVES: COUPLED SURGE,PITCH AND HEAVE MOTIONS

The responses of a multi-degree-of-freedom model of a moored vessel are analysed, accounting for the hydroelastic interaction between the nonlinear wave hydrodynamics and the nonlinear mooring stiffness. A two-scale perturbation method developed by Sarkar & Eatock Taylor to determine low-frequency hydrodynamic forces on a single-degree-of-freedom model of a nonlinearly moored vessel has been extended to analyse the nonlinear multi-degree-of-freedom dynamics of the system. Surge, heave and pitch motions are considered. The perturbation equations of successive orders are derived. To illustrate the approach, semi-analytical expressions for the higher-order hydrodynamic force components have been obtained for a truncated circular cylinder in finite water depth. In addition to conventional quadratic force transfer functions, a new type of higher-order force transfer function is introduced. This is used to characterize the hydrodynamic forces on the vessel which arise due to nonlinearity of the mooring stiffness. These are a type of radiation force, generated by the nonlinear interaction of the fluid–structure coupled system. Based on a Volterra series model, the power spectral densities of the new higher-order forces are then derived for the case of Gaussian random seas. It is shown that the additional response arising due to nonlinear dynamics of the mooring system can significantly contribute to low-frequency drift forces and responses of the vessel. Unlike conventional non-Gaussian second-order forces which are quadratic transformations of a Gaussian random process, the new higher-order forces arising due to the nonlinear mooring stiffness are polynomials of a Gaussian random process (up to fourth order for a Duffing oscillator model). This may significantly influence the extreme responses.     

Recursive geometric integrators for wave propagation in a functionally graded multilayered elastic medium

The differential equations governing transfer and stiffness matrices and acoustic impedance for a functionally graded generally anisotropic magneto-electro-elastic medium have been obtained. It is shown that the transfer matrix satisfies a linear 1st order matrix differential equation, while the stiffness matrix satisfies a nonlinear Riccati equation. For a thin nonhomogeneous layer, approximate solutions with different levels of accuracy have been formulated in the form of a transfer matrix using a geometrical integration in the form of a Magnus expansion. This integration method preserves qualitative features of the exact solution of the differential equation, in particular energy conservation. The wave propagation solution for a thick layer or a multilayered structure of inhomogeneous layers is obtained recursively from the thin layer solutions. Since the transfer matrix solution becomes computationally unstable with increase of frequency or layer thickness, we reformulate the solution in the form of a stable stiffness-matrix solution which is obtained from the relation of the stiffness matrices to the transfer matrices. Using an efficient recursive algorithm, the stiffness matrices of the thin nonhomogeneous layer are combined to obtain the total stiffness matrix for an arbitrary functionally graded multilayered system. It is shown that the round-off error for the stiffness-matrix recursive algorithm is higher than that for the transfer matrices. To optimize the recursive procedure, a computationally stable hybrid method is proposed which first starts the recursive computation with the transfer matrices and then, as the thickness increases, transits to the stiffness matrix recursive algorithm. Numerical results show this solution to be stable and efficient. As an application example, we calculate the surface wave velocity dispersion for a functionally graded coating on a semispace.     

双介质耦合刚性基弹性层平面应变型导波模式及界面散射能量分配

过渡段动力稳定性问题已成为制约400 km/h及以上高铁路基设计的关键难题,亟需从波动和能量的角度探究由基础非均匀引发的线路系统动力响应放大机理.文章将轨下基础简化为上表面自由、底端固定的刚性基弹性层,将高铁过渡段车致弹性波传播问题提炼为非均匀介质刚性基弹性层中波的散射问题,建立双介质耦合刚性基弹性层平面应变模型,优化该类波导结构频散方程在复平面求根方法,并结合岩土类介质特征展开刚性基弹性层频散分析,以明确其多模式导波特性及散射能量分配,最后,围绕弹性层厚度、刚度比等影响因素开展对比分析.结果表明:刚性基弹性层各模式导波均具有截止频率,弹性层厚度越小,杨氏模量越大,各阶导波模式的截止频率越高;入射波在双介质刚性基弹性层发生散射后,透射场基阶模式导波会占据主体能量,随着高阶导波模式被逐一激发,反射场及透射场高阶模式能量占比会在全频率范围呈现“此消彼长”状态;交换两侧弹性层材料,改变弹性层厚度及两弹性层刚度比不会显著改变能量分布规律,但总体来看,能量更易集中在较软侧弹性层中,各模式导波在激发初始频段会更为活跃,可分配到更多能量.     

Low-Frequency Deceleration of A Filtration Wave in Layered-Inhomogeneous Permeable Formations

Analytical frequency dependences of the absorption coefficient, wavenumber, and phase velocity were constructed for filtration-wave fields in a highly permeable interlayer bounded from above and from below by layers having high permeability in the vertical direction. It is shown that as the frequency decreases, the phase velocity of the wave decreases to values below this velocity in the porous medium and low-frequency deceleration occurs.     

A fluid–structure interaction solver for the study on a passively deformed fish fin with non-uniformly distributed stiffness

Research on fish locomotion has made extensive progress towards a better understanding of how fish control their flexible body and fin for propulsion and maneuvering. Although the biologically flexible fish fins are believed to be one of the most important features to achieve optimal swimming performance, due to the limitations of the existing numerical modeling tool, studies on a deformable fin with a non-uniformly distributed stiffness are rare. In this work, we present a fully coupled fluid–structure interaction solver which can cope with the dynamic interplay between flexible aquatic animal and the ambient medium. In this tool, the fluid is resolved by solving Navier–Stokes equations based on the finite volume method with a multi-block grid system. The solid dynamics is solved by a nonlinear finite element method. A sophisticated improved IQN-ILS coupling algorithm is employed to stabilize solution and accelerate convergence. To demonstrate the capability of the developed Fluid–Structure-Interaction solver, we investigated the effect of five different stiffness distributions on the propulsive performance of a caudal peduncle-fin model. It is shown that with a non-uniformly distributed stiffness along the surface of the caudal fin, we are able to replicate similar real fish fin deformation. Consistent with the experimental observations, our numerical results also indicate that the fin with a cupping stiffness profile generates the largest thrust and efficiency whereas a heterocercal flexible fin yields the least propulsion performance but has the best maneuverability.     

Plastic size effect analysis of lamellar composites using a discrete dislocation plasticity approach

Plastic size effect analysis of lamellar composites consisting of elastic and elastic-plastic layers is performed using a discrete dislocation plasticity approach, which is based on applying periodic homogenization to the superposition method for discrete dislocation plasticity. In this approach, the decomposition of displacements into macro and perturbed components circumvents the calculation of superposing displacement fields induced by dislocations in an infinitely homogeneous medium, resulting in two periodic boundary value problems specialized for the analysis of representative volume elements. The present approach is verified by analyzing a model lamellar composite that includes edge dislocations fixed at interfaces. The plastic size effects due to dislocation pile-ups at interfaces are also analyzed. The analysis shows that, strain hardening in elastic-plastic layers arises depending on two factors, namely the thickness and stiffness of elastic layers; and the gap between slip planes in adjacent elastic-plastic layers. In the case where the thickness of elastic layers is several dozen nm, strain hardening in elastic-plastic layers is restrained as the gap of the slip planes decreases. This particular effect is attributed to the long range stress due to pile-ups in adjacent elastic-plastic layers.     

Analysis of the Propagation of Sound Waves in Partially Saturated Soils by Means of a Macroscopic Linear Poroelastic Model

In this paper, the propagation of sound waves in partially saturated soils is investigated. A macroscopic linear model that is based on the two-component model of Biot and on the Simple Mixture Model by Wilmanski is used. For the construction of the model by a micro-macro transition, see Albers, Géotechnique, 2007. We investigate a porous medium consisting of a deformable skeleton and two compressible, chemically non-reacting, pore fluids (liquid and gas). The wave analysis of the poroelastic model reveals the number of acoustic waves and the dependence of velocities and attenuations of these waves on the initial saturation and frequency. There appear four body waves: three longitudinal waves, P1, P2, P3, and one shear wave, S. The P2-wave shows a similar feature as in air–water mixtures: from the theory of suspensions, it is well known that the existence of air bubbles in water reveals a minimum in the sonic velocity. This is also the case for the P2 -speed in the unsaturated porous medium. The P1-velocity increases very abruptly for a certain degree of saturation. This provides the hope for the development of a nondestructive testing method.     

刚性元方法和块状岩体稳定性分析

本文提出的刚性元方法是一种数值分析方法,它将变形体离散为一些刚性块体(剐性元)和块体之间的可变形薄层(节理元)的组合体,在各种载荷条件下求出块体的运动以及薄层的变形和应力分布。本文联合岩石系统的失稳准则来使用刚性元方法,成功地研究了块状岩体的稳定性问题。计算实例表明,本文提出的方法可以正确地反映块状岩体的失稳机制,是一种合理和可行的岩体稳定性分析手段。     

Second-harmonic generation in an infinite layered structure with nonlinear spring-type interfaces

The second-harmonic generation characteristics in the elastic wave propagation across an infinite layered structure consisting of identical linear elastic layers and nonlinear spring-type interlayer interfaces are analyzed theoretically. The interlayer interfaces are assumed to have identical linear interfacial stiffness but can have different quadratic nonlinearity parameters. Using a perturbation approach and the transfer-matrix method, an explicit analytical expression is derived for the second-harmonic amplitude when the layered structure is impinged by a monochromatic fundamental wave. The analysis shows that the second-harmonic generation behavior depends significantly on the fundamental frequency reflecting the band structure of the layered structure. Two special cases are discussed in order to demonstrate such dependence, i.e., the second-harmonic generation by a single nonlinear interface as well as by multiple consecutive nonlinear interfaces. In particular, when the second-harmonic generation occurs at multiple consecutive nonlinear interfaces, the cumulative growth of the second-harmonic amplitude with distance is only expected in certain frequency ranges where the fundamental as well as the double frequencies belong to the pass bands of the layered structure. Furthermore, a remarkable increase of the second-harmonic amplitude is found near the terminating edge of pass bands. Approximate expressions for the low-frequency range are also obtained, which show the cumulative growth of the second-harmonic amplitude with quadratic frequency dependence.     

Cascaded quasi-zero stiffness nonlinear low-frequency vibration isolator inspired by human spine

Human motion induced vibration has very low frequency, ranging from 2 Hz to 5 Hz. Traditional vibration isolators are not effective in low-frequency regions due to the trade-off between the low natural frequency and the high load capacity. In this paper, inspired by the human spine, we propose a novel bionic human spine inspired quasi-zero stiffness (QZS) vibration isolator which consists of a cascaded multi-stage negative stiffness structure. The force and stiffness characteristics are investigated first, the dynamic model is established by Newton’s second law, and the isolation performance is analyzed by the harmonic balance method (HBM). Numerical results show that the bionic isolator can obtain better low-frequency isolation performance by increasing the number of negative structure stages, and reducing the damping values and external force values can obtain better low-frequency isolation performance. In comparison with the linear structure and existing traditional QZS isolator, the bionic spine isolator has better vibration isolation performance in low-frequency regions. It paves the way for the design of bionic ultra-low-frequency isolators and shows potential in many engineering applications.

     

Interaction of an elastic wave with a plate

Within the framework of the dynamic theory of elasticity a numerical solution is set up for an axisymmetric problem which arises in connection with the problem of measuring stresses on the boundary between a solid medium and a rigid wall. In the cylindrical r, z coordinates the medium fills the cylinder z > 0, r < R, the case R being possible when the medium occupies the half-space z > 0. The elastic medium borders on a rigid wall which in the plane z = 0 has a deformable part in the form of a circular elastic plate clamped along the edges. A plane longitudinal wave in the form of a semiinfinite step falls from infinity. The interaction of this wave with the plate is investigated, with the main attention given to the study of the effect of the problem parameters on the deflection of the plate subjected to the wave.Deceased.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 74–85, March–April, 1972.Concluding, the author thanks the participants of the Seminar on Dynamics of Solids, at the Institute of Problems of Mechanics, for the discussion of the paper.     

MSC折纸结构设计及其双稳态解析与实验

折纸是一门古老艺术,其本质是将平面材料沿着事先设计好的折痕进行折叠,进而形成一个复杂的三维结构．柔性折纸结构是实现三维结构轻量化的重要途径．因此,解析折纸结构几何特性和力学性质十分必要．本文以MSC(Magic Spiral Cube)为研究对象,通过实际折痕和虚拟折痕的方法,建立了该结构的几何模型,确定了实现完全展开和完全折叠对刚性面和可变形面的设计条件,在虚拟折痕上引入了扭转刚度,证明了该扭转刚度与柔性面变形的等效性,从而得到了MSC 折纸结构的弹性势能,得到了使结构变形的力与位移本构．通过力学特性分析,发现了MSC折纸结构具有双稳态特性,这种特性是由面内变形诱发的,与虚拟折痕刚度与弹性折痕刚度的比值有直接的关系．最后,我们对MSC折纸结构进行设计和制备,通过实验,验证了理论 模型的准确性．本文的研究结果不仅进一步加深了我们对于MSC折纸结构力学特性的认识,同时也为其工程应用提供理论基础．     

冲击波测试系统低频特性与补偿方法研究

为提高冲击波超压峰值的测量精度，多数学者把重点集中在系统高频特性研究上，以拓宽带宽的方式提高峰值测试的准确性。冲击波另外两个主要参数正压作用时间、比冲量却和测试系统的低频特性息息相关。针对实爆中出现的不同传感器正压作用时间差异较大的问题，对冲击波信号进行了边际谱分析，获得了信号的低频特性。建立了一阶参数模型来表征低频特性，通过激波管试验数据获取了7种系统的低频模型参数。采用零极点配置法设计了低频补偿模型。结果表明:冲击波测试系统低频特性严重影响冲击波信号正压作用时间测试准确性，基于低频特性补偿的数据处理方法可以有效的提高冲击波信号正压作用时间、比冲量地测试精度。     

爆炸波作用下地下防护结构与围岩的非线性动力相互作用分析

针对实际地下工程中普遍存在的材料非线性以及半无限介质域的处理问题,给出了基于时间有关基本解的时域边界元法与非线性动力有限元法的耦合方法,应用该耦合方法计算了一马蹄形截面地下防护结构与围岩受爆炸冲击波作用下非线性相互作用的时间历程,并与线弹性情况进行了比较分析。结果表明:本文的方法具有较高精度,真实地再现了波在弹性层中传播以及反射的全过程。     

An Asymptotic Model of Seismic Reflection from a Permeable Layer

Analysis of compression wave propagation in a poroelastic medium predicts a peak of reflection from a high-permeability layer in the low-frequency end of the spectrum. An explicit formula expresses the resonant frequency through the elastic moduli of the solid skeleton, the permeability of the reservoir rock, the fluid viscosity and compressibility, and the reservoir thickness. This result is obtained through a low-frequency asymptotic analysis of Biot’s model of poroelasticity. A review of the derivation of the main equations from the Hooke’s law, momentum and mass balance equations, and Darcy’s law suggests an alternative new physical interpretation of some coefficients of the classical poroelasticity. The velocity of wave propagation, the attenuation factor, and the wave number are expressed in the form of power series with respect to a small dimensionless parameter. The absolute value of this parameter is equal to the product of the kinematic reservoir fluid mobility and the wave frequency. Retaining only the leading terms of the series leads to explicit and relatively simple expressions for the reflection and transmission coefficients for a planar wave crossing an interface between two permeable media, as well as wave reflection from a thin highly permeable layer (a lens). Practical applications of the obtained asymptotic formulae are seismic modeling, inversion, and attribute analysis.