Bi-linear reduced-order models of structures with friction intermittent contacts

The dynamic analysis of structures with localized nonlinearities, such as intermittent contacts of cracked structures, is a computationally demanding task because of the large size of the models involved. Thus, high-resolution finite element models are often reduced using a variety of specialized techniques which exploit spatial coherences in the dynamics. In addition, when a steady-state forced response analysis is performed, direct time integration can be replaced with multi-harmonic balance methods. Recently, a technique based on bi-linear normal modes has been successfully applied to piecewise-linear oscillators. The key idea of that approach is to represent the spatial coherences in the system dynamics with two sets of normal modes with special boundary conditions, referred to as bi-linear modes. In this paper, the bi-linear modal representation is extended to the case of intermittent contacts with friction. Furthermore, a novel reduced order modeling method is developed for the 0th order harmonic used in multi-harmonic balance methods. The forced response of a cracked structure is used to demonstrate the proposed methods.     

A new skin friction balance and selected measurements

A new skin friction balance with moving belt has been developed for measurement of the surface shear stress component in the direction of belt motion. The device is described in this paper with typical measurement results. This instrument is symmetric in design with small moving mass and negligible internal friction. It is 3.8 cm high, 3.8 cm long and 2.1 cm wide, with the sensing surface 0.7 cm wide and 1.5 cm long, and it can be made in various sizes. The unique design of this instrument has reduced some of the errors associated with conventional floating-element balances. The instrument can use various sensing systems and the ouput signal is a linear function of the wall shear stress. Measurements show good agreement with data obtained by the floating element balances and flat plate prediction techniques. Dynamic measurements have been made in a limited range. The overall uncertainty of measurement is estimated to be ±2%.     

基于能量原理的连续体结构安定分析

基于安定分析的静力定理,建立了一种以结构吸收的塑性能为安定判断准则,应用一种特殊的加载方式求解连续体结构安定问题的数值方法.应用这种能量方法对两个经典安定分析算例进行了计算,与相关结果进行对比表明能量法的有效性和可靠性.该方法摆脱了传统分析方法中的数学规划运算,有较高的求解效率,可方便地应用于实际工程中.     

Nonlinear vibrations of structures induced by dry friction

The chattering of machine tools, the squealing noise generated by tram wheels in narrow curves and the noise of band saws are examples of physical processes in which elastic structures exhibit self-sustained stick-slip vibrations. The nonlinear contact forces are often due to dry friction. Periodic, multiperiodic, and chaotic motions can occur, depending on the parameters.Because the governing equations of motion are non-integrable, solutions can only be determined by numerical integration methods. The numerical investigations of continuous structures requires themodal approach to reduce the number of degrees of freedom.As an example, a beam system has been investigated numerically and experimentally in this paper. The nonlinear motion of a point of the continuous structure has been measured by a specially developedlaser vibrometer.The friction characteristic has been measured directly and identified from a measured time series by means of amodal state observer. The correlation dimension, which represents a lower bound of thefractal dimension, has been calculated using thecorrelation integral method from a measured time series of the beam system.     

含有滑动摩擦的两体碰撞中的动能损失

讨论的是一般运动刚体在含有滑动摩擦的情况下的两体碰撞．首先根据欧勒动力 学方程和质心运动定理导出了在碰撞的两个阶段二碰撞点沿公法线和公切线的相对速度的变 化量, 其次利用动量定理导出了系统动能的损失与二碰撞点速度的关系, 最后根据这两个结 论导出了系统动能损失的计算公式, 并给出所得结论成立的条件．     

Determination of rough-surface skin friction coefficients from wake profile measurements

A technique for determining the skin friction coefficients from wake profile measurements is described, and is applied to symmetric turbine airfoils with rough surfaces, which operate in a compressible, high-speed flow environment. The procedure involves the measurement of profiles of streamwise momentum in the wakes which form downstream of different airfoils with different levels of surface roughness. Different physical phenomena which affect such wake profiles are discussed and related to different effects, such as surface roughness, form drag, flow separation zones, and laminar-to-turbulent transition. With the same inlet experimental condition for each case, overall skin friction coefficients for the rough airfoils are determined. Resulting values increase considerably as the magnitude of equivalent sandgrain roughness size increases.List of symbols A test airfoil surface area - A _i test section inlet area - A _e test section exit area - c chord length of airfoil - C _f/2 skin friction coefficient - (C _f/2)_smooth skin friction coefficient for smooth airfoil - (C _f/2)_rough skin friction coefficient for rough airfoil - F _s force from surface shear stress - F _p force from form drag due to airfoil blockage and separated flow - F _w force imposed by the top and bottom test section walls - F _s,smooth force from surface shear stress for smooth airfoil - F _s,rough force from surface shear stress for rough airfoil - h height of test section - k roughness height - k _s equivalent sand grain roughness - L total length of airfoil surface from leading edge to trailing edge - p airfoil passage effective pitch - P _o stagnation pressure - P _oe exit local stagnation pressure - P _oe, exit freestream stagnation pressure - P _oi inlet stagnation pressure - P _s static pressure - P _se exit static pressure - s distance along airfoil surface from leading edge - u local streamwise velocity - u _i local streamwise velocity at test section inlet - u _e local streamwise velocity at test section exit - u local freestream streamwise velocity at test section exit - w width of test section - x linear distance along airfoil centerline from airfoil leading edge - y normal coordinate measured from airfoil centerline Greek symbols ratio of specific heats - _s roughness parameter - _i local static air density at test section inlet - _e local static air density at test section exit - local static air density in freestream at test section exit     

Skin friction measurements on reflective surfaces using nematic liquid crystal

 A new liquid crystal technique for full surface skin friction measurements is introduced. With the new technique, the transmission of light through nematic liquid crystal viewed in reflection provides a quantitative measurement of the skin friction. The measurement technique is discussed with the aid of a model which describes the rotation dynamics of the liquid crystal molecules. Calibration experiments performed in a laminar flow duct demonstrate that the model captures the essential physics of the new technique. The measurement of skin friction downstream of a three dimensional roughness element in an incompressible laminar boundary layer is then presented as a demonstration of the utility of the technique. Received: 5 June 1998/Accepted: 13 November 1998     

Self-excited vibration caused by dry friction between two elastic structures

Based on our previous work^[1], self-excited vibration of a multi-degree-of-freedom system caused by dry friction between two elastic structures is investigated using the Chinese cultural relic dragon washbasin as an example. Some new characteristics of the self-excited vibration in this kind of system are found. The conditions under which self-excited vibration occurs at low-order or high-order modes are discussed. Effects of changes in parameters of the system on the self-excited vibration are analyzed. The vibration mechanism of the water droplets spurting phenomenon of the Chinese cultural relic dragon washbasin is further explained. This investigation presents a new idea for modeling the self-excited vibration caused by dry friction interaction between two elastic structures. The project supported by the National Natural Science Foundation of China     

Recent advancement of flow-induced piezoelectric vibration energy harvesting techniques: principles,structures, and nonlinear designs

Energy harvesting induced from flowing fluids (e.g., air and water flows) is a well-known process, which can be regarded as a sustainable and renewable energy source. In addition to traditional high-efficiency devices (e.g., turbines and watermills), the micro-power extracting technologies based on the flow-induced vibration (FIV) effect have sparked great concerns by virtue of their prospective applications as a self-power source for the microelectronic devices in recent years. This article aims to conduct a comprehensive review for the FIV working principle and their potential applications for energy harvesting. First, various classifications of the FIV effect for energy harvesting are briefly introduced, such as vortex-induced vibration (VIV), galloping, flutter, and wake-induced vibration (WIV). Next, the development of FIV energy harvesting techniques is reviewed to discuss the research works in the past three years. The application of hybrid FIV energy harvesting techniques that can enhance the harvesting performance is also presented. Furthermore, the nonlinear designs of FIV-based energy harvesters are reported in this study, e.g., multi-stability and limit-cycle oscillation (LCO) phenomena. Moreover, advanced FIV-based energy harvesting studies for fluid engineering applications are briefly mentioned. Finally, conclusions and future outlook are summarized.

     

Stochastic response and reliability of electromagnetic energy harvester with mechanical impact and Coulomb friction

Nonlinear Dynamics - Combining the complex factors of mechanical impact, Coulomb friction, harmonic excitation, and Gaussian white noise, an electromagnetic energy harvesting system is analytically...     

地震作用下摩擦耗能减震结构优化

提出了地震作用下摩擦耗能支撑参数优化的一种新的数学模型。它的特点是在给定的几条地震波作用下,在满足框架的规范层间位移角限值要求下,框架各层安装的耗能支撑刚度之和最小,从而实现安装较少的耗能装置而能达到相同的抗震要求。本文利用遗传算法求解该优化问题,并编制了基于遗传算法的几条地震波分别作用下的摩擦耗能框架结构支撑参数弹塑性动力优化分析程序GAOFF。最后给出了一6层框架在三条地震波分别输入下的优化算例,分析结果表明本文方法是有效的。     

高效耗能摩擦阻尼钢筋混凝土框架结构减震性能分析

研究了高效耗能摩擦阻尼器的减震机理。利用力学原理,分析了地震作用下高效耗能摩擦阻尼器的摩擦阻尼力放大系数变化规律,推导了设置高效耗能摩擦阻尼器结构的等效阻尼比计算公式。在此基础上,对分别设置传统摩擦阻尼器和高效耗能摩擦阻尼器的框架结构进行了地震反应分析,结果表明,高效耗能摩擦阻尼器通过将较小的摩擦阻尼力放大可以显著降低结构地震反应,减震效果良好;利用本文给出的等效阻尼比分析得出结构顶层位移反应幅值,与阻尼等效前相应值误差不超过10%。     

A method to solve the efficiency-accuracy trade-off of multi-harmonic balance calculation of structures with friction contacts

The steady-state nonlinear forced response of systems with frictional damping can be computed in the frequency domain through the Harmonic Balance Method (HBM). A critical point is the selection of the number of harmonic terms used to represent the solution. In linear systems, this number is easily determined by the harmonic content of the forcing function (e.g. mono-harmonic). However, if nonlinearities are present, higher order harmonics may need to be included to ensure a proper representation of friction forces and displacements, with a detrimental effect on the computational time.The paper presents a novel method to solve the efficiency-accuracy trade-off of harmonic selection for nonlinear systems. This method warns the user whenever the number of retained harmonic terms is inadequate. As a result, it enables the user to run the simulation with a low number of retained harmonics, e.g. designers are typically interested in the first harmonic of the solution. The calculation is repeated with a larger harmonic support only when strictly necessary to keep the error below a user-defined threshold.The method is first compared to existing adaptive HBM techniques, highlighting its novel contributions. It is then carefully validated against high-order multi-harmonic calculations and against direct time integration. Its performance in terms of accuracy vs. computational time is highlighted. The method is then implemented in a state-of-the-art numerical tool for the design of underplatform dampers for turbine blades. Finally, its outcome is compared with experimental results.     

Flow structures,nonlinear inertial waves and energy transfer in rotating spheres

We investigate flow structures, nonlinear inertial waves and energy transfer in a rotating fluid sphere, using a Galerkin spectral method based on helical-wave decomposition (HWD). Numerical simulations of flows in a sphere are performed with different system rotation rates, where a large-scale forcing is employed. For the case without system rotation, the intense vortex structures are tube-like. When a weak rotation is introduced, small-scale structures are reduced and vortex tubes tend to align with the rotation axis. As the rotation rate increases, a large-scale anticyclonic vortex structure is formed near the rotation axis. The structure is shown to be led by certain geostrophic modes. When the rotation rate further increases, a cyclone and an anticyclone emerge from the top and bottom of the boundary, respectively, where two quasi-geostrophic equatorially symmetric inertial waves dominate the flow. Based on HWD, effects of spherical confinement on rotating turbulence are systematically studied. It is found that the forward cascade becomes weaker as the rotation increases. When the rotation rate becomes larger than some critical value, dual energy cascades emerge, with an inverse cascade at large scales and a forward cascade at small scales. Finally, the flow behavior near the boundary is studied, where the average boundary layer thickness gets smaller when system rotation increases. The flow behavior in the boundary layer is closely related to the interior flow structures, which create significant mass flux between the boundary layer and the interior fluid through Ekman pumping.     

Three-phase plane composites of minimal elastic stress energy: High-porosity structures

The paper establishes exact lower bound on the effective elastic energy of two-dimensional, three-material composite subjected to the homogeneous, anisotropic stress. It is assumed that the materials are mixed with given volume fractions and that one of the phases is degenerated to void, i.e., the effective composite is porous. Explicit formula for the energy bound is obtained using the translation method enhanced with additional inequality expressing certain property of stresses. Sufficient optimality conditions of the energy bound are used to set the requirements which have to be met by the stress fields in each phase of optimal effective material regardless of the complexity of its microstructural geometry. We show that these requirements are fulfilled in a special class of microgeometries, so-called laminates of a rank. Their optimality is elaborated in detail for structures with significant amount of void, also referred to as high-porosity structures. It is shown that geometrical parameters of optimal multi-rank, high-porosity laminates are different in various ranges of volume fractions and anisotropy level of external stress. Non-laminate, three-phase microstructures introduced by other authors and their optimality in high-porosity regions is also discussed by means of the sufficient conditions technique. Conjectures regarding low-porosity regions are presented, but full treatment of this issue is postponed to a separate publication. The corresponding “G-closure problem” of a three-phase isotropic composite is also addressed and exact bounds on effective isotropic properties are explicitly determined in these regions where the stress energy bound is optimal.     

Random Vibrations with Impacts: A Review

Analytical methods and specific results are presented for random vibrations of systems with lumped parameters and “classical” impacts whereby finite relations between impact/rebound velocities are imposed at the impact instants that are not known in advance but rather governed by the equations of motion. Emphasis is placed on the procedures using special piecewise-linear transformation of state variables that exclude the velocity jumps at impacts or makes them small if impact losses are present. In the former case, exact analyses for stationary probability densities of the response to white-noise excitation are possible, whereas the stochastic averaging method is applied in the latter case. Furthermore, the special case of an isochronous system permits a more profound response analysis, such as predicting the spectral density of the response or subharmonic response to narrow-band excitation. The method of direct energy balance is also illustrated, based on direct application of the stochastic differential equation calculus between impacts. Certain two-degree-of-freedom impacting systems are considered, with application to moored systems, as used in ocean engineering.     

弧形折纸模式薄壁结构的压缩变形与能量吸收

选用PolyMax^TM PLA为试样材料,利用3D打印技术制备了弧形折纸薄壁管件。基于准静态轴向压缩实验,运用ABAQUS软件对弧形折纸薄壁管件轴向准静态压缩和冲击行为进行了有限元计算,探讨了其变形模式和能量吸收特性,分析了预折角和薄壁单胞管件阵列数量对其压溃模式及能量吸收的影响。有限元计算结果与实验结果吻合较好。薄壁管件的变形过程可分为4个阶段：初始压溃阶段、预折角塑性旋转阶段、腹板塑性屈曲阶段和完全压溃密实化阶段。弧形折痕的引入能够有效地降低薄壁管件在压缩过程中的初始压溃载荷峰值,减小冲击载荷的振荡幅值。对比了高度相等、质量近似相等的方管与弧形折纸薄壁管在不同冲击速度下的压缩变形与能量吸收。在准静态压缩作用下,对于单胞模型,仅有折痕倾角为70°的模型的比吸能优于方管;对于多胞管件阵列模型,方管的比吸能均优于折纸管。折纸管的压缩力效率和比总体效率均优于方管,其中折痕倾角为50°的模型的压缩力效率和比总体效率最高。在动态冲击压缩下,阵列方管的比吸能均优于阵列折纸管。当冲击速度为10 m/s时,折纸管的压缩力效率和比总体效率均优于方管,其中折痕倾角为50°的模型的压缩力效率和比总体效率最高。当冲击速度为20 m/s时,仅有折痕倾角为50°的模型的压缩力效率和比总体效率优于方管。

     

Nonlinear dynamic formulation for flexible origami-based deployable structures considering self-contact and friction

Nonlinear Dynamics - Compared with the conventional rigid origami, the flexible origami has larger deformation and more complicated mechanical property and nonlinear problems due to self-contact...     

Formation of heterogeneous spatial structures in a boundary lubrication layer during friction

This paper presents a synergetic model describing the boundary friction of two atomically smooth solid surfaces separated by an ultrathin lubricant layer. The model is constructed using the Lorenz system of equations, which is parameterized by shear stresses, shear strains, and the lubricant temperature. Given the spatial inhomogeneity of these parameters, it is shown that a structure with two types of domains is formed during friction on the contact plane. Time dependences of the fractal dimensions of the domain distributions over the contact plane are calculated, and it is shown that there exists a time when the fractal dimensions take minimum values. During the evolution, the system tends to a homogeneous state in which the shear stresses over entire contact area have a constant value which determines the relative velocity of motion of the friction blocks.