Bi-harmonically excited pendulum: shifted resonances and quenching the low frequency excitation

The effect of the harmonic high-frequency vibration of the suspension point on a mathematical pendulum is well known [1]. It can be described as stiffening/softening or stabilization/destabilization of the up-pointing and down-pointing equilibriums for pure vertical or pure horizontal excitation. If the excitation is tilted the effect of biasing appears in addition [2]. The effects of bi-harmonic excitation are more complex. Two of them are discussed in the recent paper. The first one occurs if one of the excitation frequencies is high and another one is low. Then the so called shifted or conjugated resonances can be observed [3]. The second one takes place if the two excitation frequencies are high but their difference is small (slowly modulated high-frequency excitation according to [4]). It is shown that in that case it is possible to choose the bi-harmonic excitation in order to quench the resonance of the pendulum without changing its basic frequency. The analysis is fulfilled both for the external and parametric excitations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Locating damaged storeys in a structure based on its identified modal parameters in Cauchy wavelet domain

Structural damage detection based on the changes of dynamic properties is a major topic for structural health monitoring. In this paper, efforts are made to extend the flexibility-based damage localization methods, especially the damage locating vectors (DLVs) method, to the case of earthquake vibration, where the finite element model and mass matrices are not available. First, a new method using continuous Cauchy wavelet transform (CCWT) and state-variable time series model is proposed to identify the modal parameters of a structure. Then the flexibility matrix can be constructed from the identified modal parameters. Second, a modified DLVs damage assessment approach is also proposed to locate damage positions in the structure through a weighted relative displacement index (WRDI). This index is calculated by using DLVs vectors determined from the change of flexibility matrix before and after damage of the structure. Numerical analyses demonstrate that the proposed process can indeed monitor the variation of stiffness for each storey. These two approaches are further applied to process the dynamic responses of three-storey and eight-storey steel frames in shaking table tests. The proposed scheme is also proved to be superior to mode shape based methods (CMS, COMAC) in monitoring the variation of stiffness for each storey.     

A Contribution to Jerk Detection

In technical applications the jerk information will be used for i.a. motion control, comfort evaluation or prediction of acceleration. In the majority of cases the jerk will be determined indirectly by differentiation of measured acceleration signals and depends consequently on the acceleration signals' quality and the differentiation's algorithms. An accurate jerk determination can only be realized by using an appropriate filter with respect to the relevant frequency range. In order to avoid such limitation a method of direct jerk detection will be required. Based on a 2 DOF mass system with viscous coupling a possible method was presented in [1] to detect directly the jerk. Thereby, in certain conditions the jerk is proportional to the displacement of one mass. Another method of direct jerk detection is given implicitly in [2]. With this method the jerk information will be generated by an additional inner variable of a damped single mass system based on the fundamental idea of the Mesoscopic Particle Method [3]. Both presented methods will be investigated and evaluated regarding its limits of applicability as a result of arbitrary periodical and impact-like excitations. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Localization of a delamination and estimation of its length in a composite laminate beam by the VSHM and pattern recognition methods

The purpose of this study was to investigate the delamination damage in laminate composite beams in order to adapt the vibration-based structural health monitoring (VSHM) method for laminated structures. The analysis was concentrated on the vibration characteristics of laminated specimens, in particular, on the first several natural frequencies of a composite laminate beam with a delamination damage. The core of this work is an experimental investigation into the vibration response of a composite laminate beam and its changes caused by delaminations of different sizes and different location in the beam. The aim was to determine how the first six harmonic frequencies are changed by a delamination, and the results show that they can be successfully used to clarify the presence, location, and dimensions of delaminations in a composite beam. A pattern recognition analysis was used to locate the damage, while its detection and evaluation were performed by using changes in the harmonic frequencies. A finite-element analysis was carried out, and the variations in the natural frequencies due to delamination are found to be in good agreement with experimental results.     

Transient amplification of maximum vibration amplitudes

Many low damped structures as turbine blades or drill strings are exposed to high dynamical loads causing high vibration amplitudes. These applications comprise sub-critical eigenfrequencies. Hereby, the lower eigenfrequencies have to be passed before reaching the operating point. Most investigations of vibration amplitudes caused by a resonance passage deal with the computation of single degree of freedom systems. Thereby, it has been shown that the stationary vibration response provides the highest possible amplitude. Further it can be stated that the maximum vibration response of the resonance passage decreases with an increasing sweep velocity [3]. Isolated modes of linear systems can be represented by single degree of freedom systems. Subsequently a mode shape can be described by the multiplication of the amplification function of the mode and the belonging eigenvector. There are only some recent works that deal with resonance passages of vicinal modes, e. g. [1]. In this paper the resonance passage of a three dimensional system with nearby modes is studied. To calculate the transient vibration response an analytical approach is used. It is shown that the maximum amplitude of the stationary vibration response is not the upper limit for the maximum amplitude of the resonance passage. Thus, the maximum amplitude may rise while the sweep velocity increases. Hence, regarding a multi degree of freedom system the maximum amplitude of the resonance passage can exceed the maximum amplitude of the stationary vibration response. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of microscopic failure in heterogeneous materials

The proper modeling of state-of-the-art engineering materials requires a profound understanding of the nonlinear macroscopic material behavior. Especially for heterogeneous materials the effective macroscopic response is amongst others driven by damage effects and the inelastic material behavior of the individual constituents [1]. Since the macroscopic length scale of such materials is significantly larger than the fine-scale structure, a direct modeling of the local structure in a component model is not convenient. Multiscale techniques can be used to predict the effective material behavior. To this end, the authors developed a modeling technique based on representative volume elements (RVE) to predict the effective material behavior on different length scales. The extended finite element method (XFEM) is used to model discontinuities within the material structure independent of the underlying FE mesh. A dual enrichment strategy allows for the combined modeling of kinks (material interfaces) and jumps (cracks) within the displacement field [2]. The gradual degradation of the interface is thereby controlled by a cohesive zone model. In addition to interface failure, a non-local strain driven continuum damage model has been formulated to efficiently detect localization zones within the material phases. An integral formulation introduces a characteristic length scale and assures the convergence of the approach upon mesh refinement [3]. The proposed method allows for an efficient modeling of substantial failure mechanisms within a heterogeneous structure without the need of remeshing or element substitution. Due to the generality of the approach it can be used on different length scales. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of non-stationary vibration signals based on the modified Kronecker sequences

The paper establishes a representation model for non-stationary random vibration signals based on the modified Kronecker sequences. The modified Kronecker sequence constructed via generalizing golden ratio is one of the special types of low discrepancy sequences which have better dimensional projections [1]. The actual modeling and simulation of non-stationary random data is more suitable for seismological signals and not for the vehicle vibrations [2, 3]. Under these circumstances, this paper presents a new algorithm for finding the modified Kronecker sequences in order to generate non-stationary vehicle vibration signals which mostly withhold the amplitude-frequency-time distribution of the sample signal. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermoactive vibration control of shafts

Flexible long‐span rotating shafts exhibit flutter instability conditioned by internal friction in bending at high rotation speeds. Under usual working conditions a shaft may be additionally subjected to external excitations related to unbalance forcing or edge bearing movements. Flutter occurs at angular speeds exceeding the lowest natural frequency of the shaft as a nonrotating beam. Thus, externally excited resonances mostly appear in the subcritical speed zone although they can interact with flutter vibration as well. The present paper is concerned with resonant vibration control of shafts based on application of thermoactive SMA components in composite shaft structures, as conceptually shown in [1]. The well known unique properties of SMAs consisting in huge changes of the elastic modulus and its loss factor as results of a reversible martensitic phase transformation under slight temperature variations [2] promise to control shaft vibrations through temperature‐induced modal modifications of the structure. The main resonance of a simply supported rotating shaft is considered to be controlled by open‐loop SMA activation. Efficiency of thermoactive vibration control is analysed and a concept of an intelligent self‐controlled shaft structure is introduced. Geometric nonlinearity is assumed in modelling and computer simulations to show the thermoactive resonance suppression including the case when both externally excited and flutter vibrations interact.     

The Cyclic Thermomechanical Coupled Problem of Thermal Gradients in Friction Railway Disc Brakes

The emergency braking distance of a TGV train at a speed of 320 km/h is almost 3000 m. Dry running brakes are reliable due to their predictable response to external stress and are thus used in such applications. The kinetic energy is dissipated proportionately into the brake disc and brake pad. This induced dissipation of energy and the high frequency of brake application cause high temperatures. These immense temperature changes could cause macroscopic cracks leading to failure of discs and accidents [1]. Generally, hot spotting describes the development of thermal localizations and can lead to early damage, early wear, pad performance loss, and squeal noise [2]. The aim of the present study is to improve a disc-pad transient numerical model by use of a coupled thermomechanical method. It is based on full 3-d thermomechanical calculations taking disc rotation into account. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear dynamics of high-dimensional models of in-plane and out-of-plane vibration in an axially moving viscoelastic beam

Nonlinear dynamics of high-dimensional models of an axially moving viscoelastic beam with in-plane and out-of-plane vibration with combined parametric and forcing excitations are investigated by the incremental harmonic balance (IHB) method in this paper. Governing equations of transverse in-plane and out-of-plane and longitudinal vibration are obtained basing on the Hamilton's principle. The Galerkin method is used to separate time variable and spatial variable to obtain a set of multi-order differential equations. The IHB method with the fast Fourier transform (FFT) is used to solve periodic response of high-dimensional models of the beam for which convergent mode is reached. Stability of the steady-state periodic solutions is analyzed using the multivariable Floquet theory. Particular attention is paid to in-plane and out-of-plane vibration on convergent mode of the beam with combined parametric and forcing excitations. Multiple solutions are observed, and jump phenomena between in-plane and out-of-plane vibration with different transverse cross sections are discovered.     

A semi-analytical direct optimal control solution for strongly excited and dissipative Hamiltonian systems

A semi-analytical direct optimal control solution for strongly excited and dissipative Hamiltonian systems is proposed based on the extended Hamiltonian principle, the Hamilton-Jacobi-Bellman (HJB) equation and its variational integral equation, and the finite time element approximation. The differential extended Hamiltonian equations for structural vibration systems are replaced by the variational integral equation, which can preserve intrinsic system structure. The optimal control law dependent on the value function is determined by the HJB equation so as to satisfy the overall optimality principle. The partial differential equation for the value function is converted into the integral equation with variational weighting. Then the successive solution of optimal control with system state is designed. The two variational integral equations are applied to sequential time elements and transformed into the algebraic equations by using the finite time element approximation. The direct optimal control on each time element is obtained respectively by solving the algebraic equations, which is unconstrained by the system state observed. The proposed control algorithm is applicable to linear and nonlinear systems with the quadratic performance index, and takes into account the effects of external excitations measured on control. Numerical examples are given to illustrate the optimal control effectiveness.     

An accelerated differential evolution algorithm with new operators for multi-damage detection in plate-like structures

This paper proposes an Accelerated Differential Evolution (ADE) algorithm for damage localization and quantification in plate-like structures. In this study, the inverse damage detection problem is formulated as a nonlinear optimization problem. The objective function is established through the alterations of the structure flexibility matrix weighted with a penalty-function, used specifically to prevent the detection of false alarms. The ADE algorithm is designed via the introduction of three modifications in the standard differential evolution algorithm. Firstly, the initial population is created using knowledge we usually have about the damage scenario of a structure. Such initialization technique assists the algorithm to converge promptly. Secondly, in the mutation phase, a new difference vector, created based on the dispersion of individuals through the search space, is used to ensure the automatic balance between global and local searching abilities. Thirdly, a new exchange operator is designed and used to avoid the untimely convergence to local optima. Finite-element models of isotropic and laminated composite plates are considered as numerical examples to test the efficiency of the proposed approach. Numerical results validate the performance of the ADE method, in terms of both solution accuracy and computational cost and highlight its ability to locate and assess damage, even for large-scale problems and noise-contaminated data.     

An efficient indicator for structural damage localization using the change of strain energy based on static noisy data

An efficient method is proposed to find multiple damage locations in structural systems. The change of static strain energy (SSE) due to damage is used to establish an indicator for determining the damage location. The SSE is determined using the static analysis information extracted from a finite element modeling. In order to assess the performance of the proposed method for structural damage detection, some benchmark structures having a number of damage scenarios are considered. Numerical results demonstrate that the method can accurately locate the structural damage when considering the measurement noise. The efficiency of the proposed indicator for finding the damage site is also compared with a modal strain energy based index (MSEBI) provided in the literature.     

Main frequency band of blast vibration signal based on wavelet packet transform

As a key parameter in blasting safety criteria, accurately describing the frequency's characteristics is of practical significance. Due to the deficiency of Fourier transform in the analysis of non-periodic and non-stationary signals, this study defined a wavelet frequency domain parameter, referred to as a main frequency band. A computational method associated with the wavelet packet transform is also proposed. To verify the feasibility of main frequency band and the proposed computational method in describing blasting frequency characteristics, an application is exemplified with field blasting vibration signals monitored in a mine. The effects of explosive charge and distance on main frequency band distribution characteristics are also studied. Results show that the main frequency band based on the computational method is a sensitive, accurate and efficient frequency parameter; it can accurately describe the frequency characteristics of blasting signals and effectively overcome the drawbacks in Fourier transform. When the explosive charge is constant, the span of main frequency reduces as a whole as the distance increases, and the frequency domain energy of blast vibration signals are concentrated mainly in the low-frequency range. When the distance is constant, the peak energy of blast vibration signals increase with the increase of explosive charge, without obvious change in main frequency band. To avoid the effects of interferences on frequency characteristics, the least square method is employed to eliminate signal trend components, and the wavelet threshold method with a hard thresholding function and the Birge–Massart strategy is applied in denoising.     

Excitation strategies for vibration based damage detection using piezoelectric transducers and machine learning

Damage detection methods of structural components have been extensively evaluated in theoretical and experimental research studies in the last few years. In this context, machine learning algorithms are used to evaluate the health state of structures. This work assesses the dependency of various excitation frequencies in guided-wave based structural health monitoring (SHM) systems and the performance of damage detection, which are barely investigated, in particular in SHM technologies using machine learning approaches. Machine learning can be directly used in SHM applications including environmental effects (noise, imperfection, statistical tests, etc.) to train a new system and to solve the inverse problem. Thereby, the piezoelectric effect is used to apply guided-waves through the structure or to measure the vibration response of flexible structures. The important outcome of this study is to improve the efficiency and performance of SHM systems by optimising the excitation frequency using machine learning approaches. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

非线性系统动力分析的模态综合技术

各种模态综合方法已广泛应用于线性结构的动力分析,但是,一般都不适用于非线性系统. 本文基于[20][21]提出的方法,将一种模态综合技术推广到非线性系统的动力分析.该法应用于具有连接件耦合的复杂结构系统,以往把连接件简化为线性弹簧和阻尼器.事实上,这些连接件通常具有非线性弹性和非线性阻尼特性.例如,分段线性弹簧、软特性或硬特性弹簧、库伦阻尼、弹塑性滞后阻尼等.但就各部件而言,仍属线性系统.可以通过计算或试验或兼由两者得到一组各部件的独立的自由界面主模态信息,且只保留低阶主模态.通过连接件的非线性耦合力,集合各部件运动方程而建立成总体的非线性振动方程.这样问题就成为缩减了自由度的非线性求解方程,可以达到节省计算机的存贮和运行时间的目的.对于阶次很高的非线性系统,若能缩减足够的自由度,那么问题就可在普通的计算机上得以解决. 由于一般多自由度非线性振动系统的复杂性,一般而言,这种非线性方程很难找到精确解.因此,对于任意激励下系统的瞬态响应,可以采用数值计算方法求解缩减的非线性方程.     

Further development of the mathematical model of a snakeboard

This paper gives the further development for the mathematical model of a derivative of a skateboard known as the snakeboard. As against to the model, proposed by Lewis et al. [1] and investigated by various methods in [1–13], our model takes into account an opportunity that platforms of a snakeboard can rotate independently from each other. This assumption has been made earlier only by Golubev [13]. Equations of motion of the model are derived in the Gibbs-Appell form. Analytical and numerical investigations of these equations are fulfilled assuming harmonic excitations of the rotor and platforms angles. The basic snakeboard gaits are analyzed and shown to result from certain resonances in the rotor and platforms angle frequencies. All the obtained theoretical results are confirmed by numerical experiments.      

Localization of vibration propagation in two-dimensional systems

In this paper, a method of regular perturbation for a linear algebraic system is applied to study localization of vibration propagation in randomly disordered weakly coupled two-dimensional cantilever-spring arrays under external harmonic excitations. Localization factors, which characterize the average exponential rates of decay of the amplitudes of vibration, are defined in terms of the angles of orientation. First-order approximate results of the localization factors are obtained using a combined analytical–numerical approach.     

线性空间C[a,b]上的线性相关性研究

研究了线性空间C[a,b]上的线性相关性,给出了衡量C[a,b]上n个函数线性相关性程度的量以及线性相关的充分必要条件.