Fractional calculus applied to radiation damping

Separate treatment of the low– and high–frequency part of the dynamic stiffness is essential when approximating the latter in the frequency–domain. In this paper, a doubly–asymptotic rational approximation of the low–frequency part is combined with an analytical interpretation of the asymptotic part leading to a system of fractional differential equations to represent the force–displacement relationship. Here, an analogy between fading memory of viscoelastic materials and radiation damping of unbounded domains is visible.     

新型轻质复合材料夹芯结构振动阻尼性能研究进展

作为新一代先进轻质超强韧结构材料,复合材料格栅和点阵夹芯结构受到了国内外学者的广泛关注.目前关于该类结构材料的设计制备以及相关力学性能研究已取得了大量的研究成果.然而对该类结构振动阻尼性能的研究则处于起步阶段.该文综述了纤维增强树脂基复合材料简单层合结构以及各类夹芯结构振动阻尼性能的研究现状.首先阐述其阻尼机理, 然后分别概述了复合材料简单层合板的微观和宏观阻尼模型、复合材料粘弹性阻尼夹层结构和新型夹层结构的阻尼预报工作,最后总结归纳现有关于该类结构阻尼特性研究工作中已取得的成果和不足之处,并对其未来发展进行了展望.     

Active Vibration Damping and Model-Based Control for an Adaptronic Actuator

The static and dynamic flexibility of a machine tool is often the major limiting factor for the machining quality, especially if high processing speeds as well as high accuracies are desired. Particularly parallel kinematic machines, which have been developed for high processing speeds and accuracy and which often use lightweight structures, can suffer from severe problems with vibrations of system components and the loss of accuracy due to deformations of machine parts. Introducing so–called adaptronic or smart components into the machine tool structure opens up new and interesting possibilities to actively control the deformations and vibrations of flexible machine parts. They allow to specifically target such undesired properties and to significantly reduce or even eliminate their influence on the system performance. Concepts of active vibration damping and model–based control are presented here for such an adaptronic actuator implemented in a machine tool with parallel kinematics. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The vibrational behaviour of bladed disks with multiple coupling devices

In turbomachinery applications turbine blades are subjected to high static and dynamic loads. Static loads are due to centrifugal stresses and thermal strains. Especially the dynamic excitation caused by fluctuating gas forces results in high vibration amplitudes which can lead to high cycle fatigue failures (HCF). Therefore, in practical applications, coupling devices like underplatform dampers, lacing wires and tip shrouds are installed to the structure. In case of blade vibrations the relative displacements between these coupling devices and the blades generate friction forces. The resulting energy dissipation provides additional damping to the structure. Furthermore, coupling devices, in particular tip shrouds, snubbers and lacing wires, increase the stiffness of the structure. Hence, they lead to a shift of the resonance frequencies. So far, only effects of single coupling devices and the influencing properties have been examined. Within this paper the effect of multiple couplings is determined and compared with single couplings. The forced response of turbine bladings with multiple couplings is calculated under consideration of geometrical and mechanical parameters of the blading and contacts, respectively. The results are compared with the single coupled blading. Furthermore, a multiple coupled device with under-platform damper and connecting pin is compared with respect to his effectiveness. Especially the influence on the resonance frequency and the achievable damping is analysed. The results of the simulation are verified by measurements at a two-blade non-rotating test rig with an underplatform damper and connecting pin. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vibrations of linear structures with spatial local nonlinearities

Classical Modal Analysis can be applied to linear systems if the corresponding damping matrix is proportional to the mass or/and stiffness matrices. Otherwise, e.g., in case of structures with single external damping devices, an alternative or approximate solution procedure for determining the dynamic response has to be chosen, compare [1]–[3]. Vibration problems of linear structures with spatially localized nonlinearities are related to those non-classically damped systems. Such systems are characterized by the fact that their nonlinear behavior is largely restricted to a limited number of single points in the structure. The objective of this paper is to present an approximate semi-analytical procedure for analyzing the steady-state harmonic response of those locally nonlinear structures, where special emphasis is laid on beams with single nonlinear devices. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Homogenization of thin structured sheet metals by using FEM

Thin structured sheet metals promise high potential concerning lightweight design in industrial applications regarding the classical mechanical engineering and vehicle construction as well as the aeronautics. Compared to flat, unstructured sheet metals the component stiffness and buckling behavior can significantly be improved by structuring especially in out of plane direction. To be able to calculate the elastic behavior of large structures from structured sheet metals a mechanical surrogate model is developed which describes effectively average material parameters based on processes of homogenization. For the surrogate properties symmetry and antisymmetry boundaries and periodic boundaries respectively are contemplated on elementary cells whose structural mechanical behavior is decisive. By using an energetic approach [3] the stiffnesses of large plate and shell structures can be determined by a cooperatively small amount of finite elements. By means of these material properties elastic behavior can easily be calculated. With it an efficient numerical design is guaranteed. This explained analysis can be applied to other periodically built up plate structures. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A novel analysis method for damping characteristic of a type of double-beam systems with viscoelastic layer

The double-beam system with a viscoelastic layer is a classical mechanical model for many beam-type composite structures. However, few studies have been able to optimize the structure from the perspective of structural damping characteristics. To fully understand the damping characteristics of the viscoelastic double-beam system, an analysis method based on dynamic stiffness method and Wittrick-Williams algorithm is presented in this paper. Through numerical case studies, five typical parameters of the viscoelastic double-beam system are discussed to investigate their influence on the damping characteristic of the system. Finally, the conclusions are used to parametric analysis for a kind of double-sheathing cable systems. Results show that the damping coefficient of the connection layer have a significant effect on the damping characteristic of the double-sheathing cable system compared with other design parameters. The proposed methods and conclusions obtained in this paper are helpful to design and optimize the structural parameters of engineering structures, thus having certain application and promotional value.     

Control Strategies for a Hybrid Articulated Robot

Due to higher requirements in productivity and cost efficiency of production lines, robots and other manipulators have to move faster. One possibility to fulfill the mentioned goals is to build lightweight constructions having elastic deformations in joints and links. The elastic components tend to vibrations and static deflections. Methods that compensate or minimize these drawbacks are the focus of this paper. An articulated robot with 6 joints and flexibility in joints and links is under consideration. The joints are actuated by DC motors combined with Harmonic Drive gears which offer high gear ratios but undergo elastic deformations. The links are flexible in two bending directions and in torsional sense. To achieve ordinary differential equations, a Ritz approach together with the projection equation is used. The obtained model is used for feedforward and feedback control design. Based on reference trajectories and on a rigid body model, estimations for the elastic deflections are calculated. These deflections are used to alter the reference trajectory in order to minimize the error of the tool center point. For basic active damping, non-local curvature feedback is used. Together with PD joint control and the feedforward control, satisfying results are obtained. Additionally, a sliding control approach is presented. The stiffness of the tool center point is enhanced with the drawback of less active damping. Simulation results and measured data are presented and compared. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On some regularities in dynamic response of cyclic periodic structures

The paper deals with cyclic periodic structures modelling bladed disk assemblies of blades with friction elements for vibration damping. These elements placed between adjacent blades reduce the vibration amplitudes by means of dry friction resulting from centrifugal forces acting on the elements and relative displacements of the blades. However, the application of these friction elements results in an additional dynamical coupling which together with mistuning of some system parameters (e.g., blade eigenfrequency or contact parameters) may cause localization of vibration. In the present paper a linear approximation of such a system is investigated. The structure composed of cyclic periodic cells modelled each as a clamped-free beam interacting with each other by means of viscoelastic elements of complex stiffness is applied for dynamic system analysis. In case of free vibrations as well as in case of steady-state dynamic response to a harmonic pressure field, a perfect periodic structure and the structures with periodically mistuned parameters (blade eigenfrequencies and contact parameters) are studied. Some regularities in the dynamic response of the systems with mistuning have been noticed. Despite the fact that only a linear approximation has been used, the results and conclusions can be applied for models which describe the blade interaction in a nonlinear way.     

Numerical and experimental investigations of dynamic contact phenomena in jointed structures

Structural dynamic properties like stiffness and damping are strongly influenced by contact phenomena in jointed structures. Therefore numerical and experimental investigations are presented, in order to understand and predict the behaviour of such mechanical devices. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

超轻碳气凝胶的机械鲁棒性增强策略及其应用北大核心CSCD

作为一种轻质多孔材料,碳气凝胶是一类具有高孔隙率、低密度和优异环境稳定性的碳质多功能固体材料,这些独特性能的结合使得它们在柔性传感器、能源设备、声学设备和环境保护等领域得到广泛应用.然而,在现有多孔材料中普遍存在着机械鲁棒性和稀疏三维网络结构间的矛盾.良好的鲁棒性可以确保气凝胶在应用过程中的结构完整性和性能稳定性,而稀疏三维网络结构则是确保气凝胶材料轻质多孔的结构前提,这一矛盾是材料科学、固体力学和设计应用等诸多领域研究者面临的共同挑战.该文综述了常见的国内外超轻碳气凝胶的鲁棒性增强策略,包括细胞壁(cell wall)增强、细胞壁取向调控、细胞壁拓扑结构设计和结点强化(joint reinforcement).此外,该文总结了在不引入高分子弹性体的情况下实现超轻全碳气凝胶的拉伸弹性的设计原则,简要概述了高鲁棒性碳气凝胶的新应用,并对该领域尚待解决的问题提出了展望.     

Stiffness and damping models for the oil film in line contact elastohydrodynamic lubrication and applications in the gear drive

Innovative stiffness and damping models for oil films are developed to account for the impacts in both normal and tangential directions. Given that these models are applied to a gear drive in line contact elastohydrodynamic lubrication (EHL), the combined stiffness is derived from the stiffness of both the oil film and gear tooth while the combined damping is established from the damping of these parts. The effects of three fundamental parameters (contact force, rotation speed, and tooth numbers) of the gear drive in line contact EHL on the combined stiffness and damping are then investigated. The results reveal that the small normal and tangential stiffness of the lubricant can alleviate meshing impact and shear vibration, while the impact and friction heat can be reduced by using an oil film with either a large normal damping or small tangential damping. Given that its amplitude and fluctuation are closely related to shear rate, effective viscosity, entrainment velocity, and curvature radii, the improved combined stiffness and damping can be obtained by rationally matching the geometric and operating parameters.     

Formulação numérica de estruturas compósitas amortecidas utilizando as teorias da Deformação Cisalhante de Primeira Ordem e de Alta Ordem

Composite materials have been used in the design of the aircrafts structures because their low weight and high mechanical strength. However, structures made in composite material are exposed to dynamical and/or static loading environments. Therefore, a major research effort is undertaken in the development of tools numerical for analysis and design of composite structures. This paper presents a numerical formulation of the composite structures using the Finite Element Method (FEM). The damped composite structures, using inserted viscoelastic devices, and undamped composite structures are formulated by FEM. Viscoelastic materials are applied as continuous layers inserted on composite structures. The intrinsic damping of the composite material is included in the studies, too. The First‐order (FSDT) and Higher‐order Shear Deformation (HSDT) theories are formulated. They are distinguished by order of the approximation functions used in the mechanical displacements field. Both theories are computationally implemented using the Serendipity finite element. This is a rectangular finite element with 8 nodes, 5 or 11 degrees of freedom per node. The results are compared with papers predictions. The advantages and disadvantages of using each theory in the modeling of composite (thin or thick) and thick sandwiches structures, including the intrinsic and the viscoelastic damping, are discusses.     

An equivalent moving force model for consideration of human-structure interaction

To predict the vibration response of footbridges, many codes of practice use a deterministic moving force (MF) model. This approach may not be well suited for the design of slender, lightweight, low-damping, and low-frequency footbridges because it ignores the pedestrian interaction with the vibrating footbridge. On the other hand, a spring-mass-damper (SMD) model is able to incorporate human mass, stiffness, and damping into the vibration response prediction. However, the SMD model is computationally demanding and not commonly available in engineering practice. To address this shortfall, a framework is proposed to derive a computationally-efficient equivalent MF-structure system to the reference SMD-structure system such that both systems give a similar vibration response metric. Analytical and numerical approaches to the equivalent MF (EMF) system are described in detail and applied to bridges with approximately simply-supported mode shapes. A sensitivity analysis is carried out to show the effects of different pedestrian parameters on the equivalent damping of the EMF system. The effects of pedestrian damping, frequency, and weight are found to be pronounced, while those of dynamic load factors and pedestrian step length are insignificant. Finally, empirical expressions are proposed in a probabilistic framework to determine the equivalent damping for simply-supported low-frequency footbridges as a function of bridge frequency. This work should find use in the serviceability assessment of low-frequency footbridges in engineering practice.     

井下钻柱纵向横向耦合振动模型建立与数值分析

针对井下钻柱运动的复杂性,基于动力学理论,建立了井下钻柱纵向和横向耦合振动的数学模型,并进行数值求解及分析.根据井下钻柱的实际工况,以整个井下钻柱为研究对象,提出了钻柱纵向和横向耦合振动的动力方程,并利用解析法和无量纲法分别求解出其动刚度和动阻尼的表达式,以及钻柱前两阶振动的固有频率.分析结果表明:当井下钻柱振动频率增大时,其动刚度呈幅值衰减的周期性变化,而其动阻尼呈幅值增强的周期性变化;井下钻柱长度和横截面面积越大,其动刚度和动阻尼的幅值越小;井下钻柱的Poisson(泊松)比对其振动的动刚度、动阻尼和前两阶固有频率没有影响;同时,井下钻柱的第二阶固有频率始终大于第一阶固有频率.该文的研究方法和模型为井下钻柱钻具分析和结果优化提供了理论参考和实际意义.     

A nonlinear model for rotor-shaft joints of high speed rotor systems with internal damping

Viscous internal damping in joints of high speed rotor systems causes instabilities above a certain frequency of revolution. In the majority of cases a nonlinearity adjusts the stability margin towards higher frequencies. In this paper an analytical solution of a nonlinear four degrees of freedom rotor model with internal damping is proposed, which enables to clearly analyse the influence of shaft stiffness, connection stiffness, rotor mass and shaft mass. The steady state solution of the unbalance case and the stability boundaries are deduced analytically. The stabilizing effect of the nonlinearity is shown. The analytical solutions are in good agreement with numerical results obtained by FERAN, a rotor dynamic simulation tool. A model, representing the rotor–shaft connection with an o–ring has been analyzed by a hydro pulse rig. Beneath the linear way, two further approaches to describe the measured hysteresis, a cubic and a bilinear force law are shown in the paper. The different analytical and numerical results for the whole rotor system with these three approaches are compared. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The variability of dynamic responses of beams resting on elastic foundation subjected to vehicle with random system parameters

This paper investigates the variability of dynamic responses of a beam resting on an elastic foundation, which is subjected to a vehicle with uncertain parameters, such as random mass, stiffness, damping of the vehicle and random fields of mass density, and the elastic modulus of the beam and stiffness of elastic foundation. The vehicle is modeled as a two-degree-of-freedom spring-damper-mass system. The equations of motion of the beam was constructed using a finite element method. The mass and elastic properties of the beam, and the stiffness of foundation are assumed to be Gaussian random fields and were simulated by the spectral represent method. Masses, stiffness of the spring, and the damping coefficient of the vehicle are assumed as Gaussian random variables. The numerical analyses were performed using the finite element method (FEM) in conjunction with the Monte Carlo simulation (MCS). The variability of dynamic responses of the beam were investigated with various cases of random parameters. For each sample, the equations of motions were solved with the Wilson-q integral method to find dynamic responses. The influence of random system parameters and their correlation on the response variability is discussed in detail.     

粘弹性Timoshenko梁的动力学普遍方程及其动态特性分析

本文用直接力法在时域内推导了粘弹性Timoshenko梁的控制微分方程,它同时计及了材料的拉伸粘性和剪切粘性.为了测定标准线性固体的复模量和三参数,对有机玻璃(PMMA)和尼龙6(PCL)试件成功地应用了强迫振动梁技术.通过大量数值计算,对粘弹性Timoshenko梁的动力特性,特别是阻尼特性进行了分析.结果表明,材料粘性对结构的动力特性,尤其是对阻尼有较大影响。对于高粘性材料,其动力学性质用标准线性固体模型来描写是合适的.     

Hybrid computational aeroacoustics based on compressible flow data at low Mach numbers

In some practical applications (e.g. cavity with a lip), even at low Mach numbers, acoustic feedback mechanisms excite flow structures. The compressible flow simulation cannot distinguish between a pure fluid dynamic part and acoustic phenomena. With this in mind, we propose a workflow based on Helmholtz-Hodge decomposition, to extract pure source terms of the compressible flow simulation, to model the sound radiation. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic analysis and passive control of viscoelastically damped nonlinear dynamic contacts

This paper presents an analytical and finite element study on nonlinear contact dynamics and controls. Nonlinear dynamic contacts between eccentrically supported masses and simply supported beams are studied. Passive control of the dynamic contacts using viscoelastic dampers is also proposed and evaluated. A nonlinear contact finite element is modeled by a set of nonlinear stiffness and damping polynomial functions; and a nonlinear viscoelastic finite element is modeled by a Standard Linear Model with frequency-dependent nonlinear stiffness and damping functions. Analyses show that the dynamic contact force increases as the initial gap increases. Application of viscoelastic dampers can effectively reduce contact loads and prevent dynamic contacts. A simple design equation is also proposed.