Identification of crack in a rotor system based on wavelet finite element method

The dynamics and diagnosis of cracked rotor have been gaining importance in recent years. In the present study a model-based crack identification method is proposed for estimating crack location and size in shafts. The rotor system has been modeled using finite element method of B-spline wavelet on the interval (FEM BSWI), while the crack is considered through local stiffness change. Based on Rayleigh beam theory, the influences of rotatory inertia on the flexural vibrations of the rotor system are examined to construct BSWI Rayleigh beam element. The slender shaft and stiffness disc are modeled by BSWI Rayleigh–Euler beam element and BSWI Rayleigh–Timoshenko beam element, respectively. Then the crack identification forward and inverse problems are solved by using surface-fitting technique and contour-plotting method. The experimental examples are given to verify the validity of the BSWI beam element for crack identification in a rotor system. From experimental results, the new method can be applied to prognosis and quantitative diagnosis of crack in a rotor system.     

Microstructural Model of a Closed-Cell Foam on the Basis of Image Analysis

The focus of this work is the identification of a unit cell that is able to represent the microstructure of a closed-cell solid foam to predict the effective behaviour of the foam numerically. For the investigation, a finite element model consisting of a repeating unit cell with periodical boundary conditions is implemented. A tetrakaidecahedral foam microstructure is considered as simplified cell geometry, and a strain-energy based homogenisation concept is utilized. On the basis of image analysis imperfections are applied to the cell. The obtained model is used as a representative volume element (RVE) for further investigations of the postbuckling behaviour of the foams. Different analyses are performed and the results are compared to literature and experimental data. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental and numerical investigation of metal foams undergoing large deformations

Open cell aluminum metal foams are a new kind of material that are used in composite structures to reduce their weight, to increase their sound or energy absorption capability or to decrease their thermal conductivity. The design and analysis of such structures requires a macroscopic constitutive model of the foam that has to be determined by various experiments under different loading conditions. We support this procedure by analyzing the microstructure of the metal foam numerically under large deformations. To this end, we employ the finite cell method that can deal with large deformations and allows for an automatic and efficient discretization of the CT-image of the foam. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic vibrations of a damageable viscoelastic beam in contact with two stops

A model for the material damage, due to dynamic vibrations of a Kelvin‐Voigt viscoelastic beam whose tip is constrained to move between two stops, is presented and numerically analyzed. The contact of the free tip with the stops is described by the normal compliance condition. The evolution of damage of the beam's material, which measures the reduction of its load carrying capacity, is modeled with a parabolic inclusion. The existence of the unique local solution is stated. A numerical algorithm is presented, in which spatially it is approximated by finite elements, and the time derivatives are discretized with the Euler scheme. Error estimates are derived for sufficiently regular solutions, and four numerical simulations are shown. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

On the stabilization mechanisms in liquid metallic foams

Metal foams are porous structures made up of conventional metals such as aluminium. Their advantageous density to stiffness ratio leads to a variety of applications especially in automotive industry, where they have gained interest as material used in shock absorbers and light weight construction parts. Solid metal foams are usually produced by solidification of a liquid metallic foam. The latter is generated by the introduction of gas into a melt analogous to aqueous foams. Depending on the parameters of the production process, porous structures with relative densities down to 10% of the original metal can be achieved. However, while the mechanisms leading to stable aqueous foams are quite well understood, this is not the case for metallic foams. In contrast for example to soap foams, no surface active or polar substances are present in liquid metals. It is merely known empirically that solid particles have a major influence on the stability of a liquid metallic foam. In this paper we present experimental observations showing that the stability and structure of metallic foams produced via a melt route are predominantly governed by interface rather than drainage effects. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

车路耦合非线性振动高阶Galerkin截断研究

将移动车辆模型化为运动的两自由度质量-弹簧-阻尼系统,道路模型化为立方非线性黏弹性地基上的弹性梁,并将路面不平度设定为简谐函数．通过受力分析,建立车路非线性耦合振动高阶偏微分方程．采用高阶Galerkin截断结合数值方法求解耦合系统的动态响应．首次研究不同截断阶数对车路耦合非线性振动动态响应的影响,确定Galerkin截断研究车路耦合振动的收敛性．研究结果表明,对于软土地基的沥青路面,耦合振动的动态响应,需要150阶以上的截断才能达到收敛效果．并通过高阶收敛的Galerkin截断研究了系统参数对车路耦合非线性振动动态响应的影响.     

Finite element method for the vibration of cracked beams with varying cross section

Vibration analysis of cracked beams having linearly varying cross-sections both in thickness and width was investigated. A computer program using the finite element method has been written to find the dynamical characteristics (natural frequencies and mode shapes) of the cracked beam. The cracked section in the beam has been modeled by a massless spring whose flexibility depens on the local flexibility induced by the crack. The stiffness of spring has been derived from the linear elastic fracture mechanics theory as the inverse of the compliance matrix calculated using stress intensity factors and strain energy release rate expression. Some examples have been given to explain the proposed method and investigate the effects of the depth and location of cracks on the natural frequencies and mode shapes. The results of current study and those in the literature are compared and good agreements have been found. Consequently it is showed that proposed method is reliable and simple. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Collapse criteria of foam cells under various loading

Recently porous materials are widely used in civil and mechanical engineering. In particular, such porous materials as metal and polymer foams have applications in lightweight structures. From mechanics point of view foams can demonstrate unusual behavior such as strain localization related to foam cells buckling under certain loads. The aim of this work is the elaboration of the model of foam material taking into account the cell collapse. We consider the cell collapse initiation during the elastic instability and its further evolution under loading. The geometrical structure of foam is generated with the use of the Voronoi algorithm. Based on stochastic distributions of cells we create various geometrical models of foams. The influence of the cell volume, wall thicknesses and material properties of the foam material on critical loads is obtained. The calculations are performed with the use of Abaqus CAD/CAE system. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flexible-link robots with combined trajectory tracking and vibration control

This work deals with asymptotic trajectory tracking and active damping injection on a flexible-link robot by application of Multiple Positive Position Feedback. The flexible-link robot is modeled and validated by using finite element methods and experimental modal analysis, and then a reduced order model of the flexible-link robot dynamics, up to the first dominant vibration modes, is employed for experimental evaluation on a test rig. Then, a combined control scheme is synthesized in two parts: first, a Sliding-Mode Control based on a cascaded Proportional-Integral-Derivative for regulation and trajectory tracking tasks, via a direct current motor torque as the control input for the overall system dynamics, and, second, a Multiple Positive Position Feedback for active vibration control and attenuation of residual vibrations on the tip position, via the input voltage applied to a piezoelectric patch actuator attached directly on the flexible beam. The results are evaluated on an experimental platform, where the dynamic performance of the overall active vibration control scheme leads to fast and effective tracking results, with damping ratios increased up to 300%.     

Stability analysis of nonlinear vibrations of a deploying flexible beam

Consider a rigid-flexible coupled system which consists of a central rigid body deploying a flexible appendage. The appendage is modeled as a finite deflection beam having linear constitutive equations. By taking the energy integral as Lyapunov function, it is proved that nonlinear transverse vibrations of the beam undergoing uniform extension or retrieval are stable when there are not controlling moment in the central rigid body and driving force on the beam, according to the partial stability theorem.     

Vibrations of Rotors Supported on Nonlinear Bearings

Rotors in electrical machines are supported by various types of bearings. In general, the rotor bearings have nonlinear stiffness properties and they influence the rotor vibrations significantly. In this work, this influence of these nonlinearities is investigated. A simplified finite element model using Timoshenko beam elements is set up for the heterogeneous structure of the rotor. A transversally isotropic material model is adopted for the rotor core stack. Imposing the nonlinear bearing stiffnesses on the model, the Newton-Raphson procedure is used to carry out a run up simulation. The spectral content of these results shows nonlinear effects due to the bearings. The rotor vibrations are further investigated in detail for various constant speeds. These results show non-harmonic vibrations of the rotor in a section of the investigated speed range. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Macroscopic mechanical properties of metal foam in dependence on the inhomogenities of the mesoscale

In this contribution, a way of simulating the influence of the mesoscopic irregular structure of metal foams on the macroscale is shown. To this end, mesoscopic periodic volume elements of a foam are derived in order to compute the mechanical properties including the effects of inhomogenities like imperfections, irregular structure and varying cell wall thicknesses. With the help of these volume elements, which are analysed via the finite element method, and their varying mechanical properties, a local varying stiffness can be computed and inserted into the macromechanical model. In this way the propagation of uncertainities from the mesoscale to the macroscale can be assessed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Piezoelectric energy harvesting from vibrations of a beam subjected to multi-moving loads

This study is intended to investigate piezoelectric energy harvesting from vibrations of a beam induced by multi-moving loads. Various multi-moving loads are analyzed by considering various parameters. The system of equations for electro-mechanical materials is derived by using the generalized Hamilton's principle under the assumptions of the Euler–Bernoulli beam theory. The electromechanical behavior of piezoelectric harvesters in a unimorph configuration is analyzed using finite element method. The Newmark's explicit integration technique is adopted for the transient analysis. The predictions of the results of the finite element models are verified by that of the available solutions. The effects of piezoelectric bonding location, velocity and number of moving loads as well as time lags between moving loads on the produced power are investigated. The numerical results show that the investigated parameters have significant effects on the energy harvesting from a vibration of beams under the action of multi-moving loads.     

Unilateral Constrained Bending Vibrations on a Torsional String

Vibrations in long torsional strings result in spatio‐temporal dynamics. In order to actively damp these vibrations the system has to be analysed analytically, numerically and experimentally. Stick‐slip‐effects result in torsional selfexcited vibrations of the string. These vibrations are coupled with bending vibrations which are constrained by the borehole. The straight string was modelled in an experimental setup. The control of the straight string and the unilateral constrained bending vibrations were treated seperately. The dynamics of straight strings were controlled using three different approaches: firstly, a simple PD‐controller with the parameters calculated based on a one‐degree‐of‐freedom oscillator, secondly, the parameters were optimized using a simplex‐method, thirdly, the Karhunen‐Loeve‐transformation was used in order to reduce the dimension of the system. A controller based on the reduced system was implemented and the parameters were optimized with the same simplex algorithm. The unilateral constrained bending motion were examined at a cantilever beam which was assumed to be constrained in one direction in the middle of the beam. First, the beam was modelled analytically as a continuous system. The two states (contact and no contact) were described separately. The transition between these states were modelled with energy assumptions. Second, the beam was modelled as a Finite‐Element‐System. The numerical results of both methods were compared with experimental data.     

A posteriori error analysis for the normal compliance problem

In this work, a contact problem between a linear elastic material and a deformable obstacle is numerically analyzed. The contact is modeled using the well-known normal compliance contact condition. The weak formulation leads to a nonlinear variational equation which is approximated by using the finite element method. A priori error estimates are recalled. Then, we define an a posteriori error estimator of residual type to evaluate the accuracy of the finite element approximation of the problem. Upper and lower bounds of the discretization error are proved for this estimator.     

Determination of the parameters of a system of bound beams from dynamical boundary measurements

The dynamical inverse problem for a two velocity system of a special kind is considered. The system describes vibrations of a composite beam formed by two bound beams, and we recover the shearing stiffness coefficient. Vibrations of the beam are generated by an impulse action applied to an end of the beam. Inverse data are the response operator and the dynamical measurement at the other end of the beam. Bibliography: 11 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 324, 2005, pp. 20–42.     

On the Excitation of Rolling Tires from the Road Surface Texture

Rolling tires are excited from the contact with the rough road surface to vibrations, which cause rolling noise. A two scale approach is suggested, where at the macro–scale the vibration of the rolling tire structure is modeled by quite detailed finite element methods. The road surface is described using measured textures. A fine resolution finite element discretization of the tread rubber is performed in order to resolve the asperity contact. The material properties are described by a non–linear viscoelastic rubber model. The tread patch is enforced to approach the rough surface in a transient dynamics manner. From these investigations an enveloping surface profile is reconstructed to be used for the excitation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

镍基定向结晶合金蠕变损伤的细观模型

针对镍基定向结晶合金的蠕变变形和损伤,本文建立了有限元和自洽两种晶体滑移细观模型。在这两种模型中同时考虑了晶粒滑移损伤和晶界损伤。通过一组镍基单晶合金和一组特殊结晶取向的定向结晶合金标定了模型参数。数值分析结果表明,这两种模型都可以比较准确地描述定向结晶合金的蠕变损伤变形和失效规律,尤其是定向结晶合金蠕变性能的结晶取向相关性。     

Free vibration analysis of a rigid bar supported by arbitrary elastic beams

For convenience, a two-node conventional elastic beam element (C beam element) with the displacements of its 2nd node replaced by those of center of gravity (c.g.) of the joined rigid bar is called the modified beam element (M beam element). The objective of this paper is to present a modified finite element method (modified FEM) such that the free vibration characteristics of a rigid bar supported by a number of elastic beams can be easily determined. First of all, the displacements for the 2nd node of a C beam element joined with the rigid bar are determined in terms of those for the c.g. of the joined rigid bar to establish the M beam element. Next, the mass and stiffness matrices for the M beam element are derived based on the displacements for the 1st node of the C beam element and those for the c.g. of the joined rigid bar. Then, the overall property matrices of the entire unconstrained vibrating system (i.e. a rigid bar supported by a number of elastic beams) can be determined by using the assembly technique of the conventional FEM and considering the effects of lumped mass and rotary inertia of the rigid bar. Finally, the boundary (supporting) conditions are imposed to produce the effective property matrices of the constrained vibrating system and then the free vibration characteristics are determined with the standard approach. In order to confirm the presented theory and the developed computer program, the rigid bar is modeled by a number of C beam elements with bigger Young’s modulus (E_R) and the conventional FEM is used to determine the natural frequencies and associated mode shapes of the vibrating system. It is found that the latter will converge to the corresponding ones obtained from the presented modified FEM when the magnitude of E_R increases to certain values.