A hybrid formulation for mid-frequency analysis of assembled structures

A new formulation able to predict the behaviour of structures in the mid-frequency range is presented in this paper. The mid-frequency field is a hybrid domain for which assembled structures exhibit simultaneously low- and high-frequency behaviours, depending on the material and geometrical properties of different subsystems. Thus, dealing with the mid-frequency field requires simulation methods which are able to account the differences in behaviour of different subsystems. The hybrid formulation is based on the coupling of two different formulations, the finite elements for the low-frequency behaving subparts and a probabilistic formulation, the smooth integral formulation, applied to the high-frequency subsystems. The hybrid method enables to correctly predict the deterministic response of the low-frequency parts which is not affected by randomness, and the smooth trend of the contributions of the high-frequency parts. The paper is concluded with several numerical examples computed for coupled one- and two-dimensional structures.     

A numerical approach for flow-induced vibration of pipe structures

A structural impedance approach is extended for the dynamic analysis of pipe structures conveying fluid flow. The method is efficient in computation and convenient for studying transient responses. Thus, it is possible to study the transition from a stable condition to an unstable condition of the pipe structure as the flow speed increases. The structure may also exhibit different modes of instability. The present approach predicts the mode without prior assumption. Numerical examples are given for a hanging cantilever and a simply supported pipe. The critical speed associated with the dynamic stability is calculated and compared with available analytical and experimental results.     

A model for vibration transmission of light-heavy structures

The vibration transmission of light-heavy structures is investigated in this paper. The light-heavy structure consists of a thin beam and a mass block. Based on numerical simulations with the finite element method and experiments, the block's effect on the thin beam is defined. A theoretical model for this beam-block structure is successfully developed, which is validated and agrees very well with the numerical and experimental models. Two kinds of transfer functions of velocities between any two points on the beam-block structure are studied experimentally and theoretically. The theoretical transfer functions agree well with the experimental results. There are peaks and valleys in the transfer functions, where the peaks occur at the anti-resonant frequencies of the second point and the valleys at the anti-resonant frequencies of the first point. Away from these peaks and valleys the magnitude of the transfer functions are about 0 dB for two points on the beam, and about 20 dB in our experiments for a point on the beam and another point on the block (close to the theoretical prediction of 18 dB determined by the mass ratio of the beam and the block). With these transfer functions, new techniques might be developed for indirect measurement of the vibration of the thin beam by measuring the vibration of the block.     

A combined finite element-stiffness equation transfer method for steady state vibration response analysis of structures

An extended finite element transfer matrix method, in combination with stiffness equation transfer, is applied to dynamic response analysis of the structures under periodic excitations. In the present method, the transfer of state vectors from left to right in a combined finite element-transfer matrix (FE-TM) method is changed into the transfer of general stiffness equations of every section from left to right. This method has the advantages of reducing the order of standard transfer equation systems, and minimizing the propagation of round-off errors occurring in recursive multiplication of transfer and point matrices. Furthermore, the drawback that in the ordinary FE-TM method, the number of degrees of freedom on the left boundary be the same on the right boundary, is now avoided. A FESET program based on this method using microcomputers is developed. Finally, numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for steady state vibration response analysis of structures.     

Symplectic analysis of vertical random vibration for coupled vehicle–track systems

A computational model for random vibration analysis of vehicle–track systems is proposed and solutions use the pseudo excitation method (PEM) and the symplectic method. The vehicle is modelled as a mass, spring and damping system with 10 degrees of freedom (dofs) which consist of vertical and pitching motion for the vehicle body and its two bogies and vertical motion for the four wheelsets. The track is treated as an infinite Bernoulli–Euler beam connected to sleepers and hence to ballast and is regarded as a periodic structure. Linear springs couple the vehicle and the track. Hence, the coupled vehicle–track system has only 26 dofs. A fixed excitation model is used, i.e. the vehicle does not move along the track but instead the track irregularity profile moves backwards at the vehicle velocity. This irregularity is assumed to be a stationary random process. Random vibration theory is used to obtain the response power spectral densities (PSDs), by using PEM to transform this random multiexcitation problem into a deterministic harmonic excitation one and then applying symplectic solution methodology. Numerical results for an example include verification of the proposed method by comparing with finite element method (FEM) results; comparison between the present model and the traditional rigid track model and; discussion of the influences of track damping and vehicle velocity.     

Mechanical analysis of active vibration damping in continuous structures

The aim of this work is to solve problems of active damping of vibrations in some given domain of a continuous viscoelastic structure. A mathematical model of the mechanical system, the sources of perturbing vibrations, the control system, and the different absorption criteria to be compared are defined. The problems are set in infinite dimension spaces, and the approximate problems are derived in finite dimension spaces. Two methods of resolution are proposed and the solutions are compared. Numerical results simulating the response of a square plate submitted to flexural vibrations are presented for three different absorption criteria, thus permitting a quick evaluation of the comparative effectiveness of the chosen criteria.     

Analysis of the coupled thermoelastic vibration for axially moving beam

The coupled thermoelstic vibration characteristics of the axially moving beam are investigated. The differential equation of motion of the axially moving beam under the thermoelastic coupling is established based to the equilibrium equation and the thermal conduction equation involving deformation term. The eigenequation is deduced and the dimensionless complex frequencies of the axially moving beam with different boundary conditions under the coupled thermoelastic case are calculated by the differential quadrature method. The curves of the real parts and imaginary parts of the first three-order dimensionless complex frequencies versus the dimensionless axially moving speed are obtained. The effects of the dimensionless coupled thermoelastic factor, the ratio of length to height, the dimensionless moving speed on the stability of the beam are analyzed.     

二维振动方向变换器的耦合振动及其等效电路

二维振动方向变换器集功率合成和二维超声输出的功能于一体,在功率超声技术中具有重要的应用价值。然而,对于二维振动方向变换器的设计分析只有一种较为复杂的波动方程法。为此,本文研究了二维振动方向变换器的另外一种简明的设计分析方法——等效电路法。通过引入二维机械耦合系数和纵向力转换系数,利用力电类比原理建立了二维振动方向变换器的同相及反相二维耦合振动的统一等效电路模型。利用本文提出的设计方法,计算了两种不同材料的二维振动方向变换器的谐振频率,与有限元计算结果及实验测试结果一致,为该类超声振动系统的工程应用提供了一种简洁直观的设计分析方法。     

Free vibration analysis of piezoelectric coupled circular plate with open circuit

A vibration analysis of a circular steel substrate surface bonded by a piezoelectric layer with open circuit is presented. A solution for the electrical potential along the thickness direction of the piezoelectric layer satisfying the open circuit electric boundary condition is developed for the first time. The mechanical model and solutions for the vibration analysis of the piezoelectric coupled circular plate are then established based on the developed electrical potential, the Kirchhoff plate model, and the Maxwell equation. The first four mode shapes and the corresponding resonant frequencies of the plate with two standard boundary conditions are presented in numerical simulations and compared with those of a piezoelectric coupled plate with the closed circuit condition. The simulations show that the resonant frequencies of the open circuit piezoelectric coupled plate are higher than those of the closed circuit piezoelectric coupled plate. Corresponding discussions are thus provided for the higher piezoelectric effect from the open circuit piezoelectric layer.     

超声耦合振动与“局部共振”现象

本文从耦合振动的角度出发，对超声加工系统中出现的“局部共振”现象进行了研究，通过对振动系统的分析用计算，指出“局部共振”流言是耦合振动的一种表现。     

A basic hybrid finite element formulation for mid-frequency analysis of beams connected at an arbitrary angle

When beams are connected at an arbitrary angle and subjected to an external excitation, both longitudinal and bending waves are generated in the system. Since longitudinal wavelengths are considerably longer than bending wavelengths in the mid-frequency region, the number of bending wavelengths in the beams is considerably larger than the number of longitudinal wavelengths. In this paper, plannar beams connected at arbitrary angles are considered. The energy finite element analysis (EFEA) is employed for modelling the bending behavior of the beams and the conventional finite element analysis (FEA) is utilized for modelling the longitudinal vibration in the beams. Thus, a basic hybrid FEA formulation is presented for mid-frequency analysis of systems that contain two types of energy. The bending vibration is associated with the long members in the system and the longitudinal vibration is associated with the short members. The long members are considered to have high modal overlap and to contain several wavelengths within their dimension, and uncertainty effects are present. The short members contain a small number of wavelengths, and exhibit a low modal overlap. Due to the low modal overlap the resonant frequencies are spaced far apart in the frequency domain, therefore the short members exhibit resonant or non-resonant behavior depending on the frequency of the excitation.In this work, the bending and the longitudinal vibration within the same beam member are treated as a long and as a short member, respectively. A hybrid joint formulation is developed between long and short members. Power reflection and transmission coefficients are derived for each joint. The distribution of the energy throughout the system demonstrates a strong dependency on the power transfer coefficients. Several systems are analyzed by the hybrid FEA and by analytical solutions, and good correlation between them is observed.     

Free vibration analysis of civil engineering structures by component-wise models

Higher-order beam models are used in this paper to carry out free vibration analysis of civil engineering structures. Refined kinematic fields are developed using the Carrera Unified Formulation (CUF), which allows for the implementation of any-order theory without the need for ad hoc formulations. The principle of virtual displacements in conjunction with the finite element method (FEM) is used to formulate stiffness and mass matrices in terms of fundamental nuclei. The nuclei depend neither on the adopted class of beam theory nor on the FEM approximation along the beam axis. This paper focuses on a particular class of CUF models that makes use of Lagrange polynomials to discretize cross-sectional displacement variables. This class of models are referred to as component-wise (CW) in recent works. According to the CW approach, each structural component (e.g. columns, walls, frame members, and floors) can be modeled by means of the same 1D formulation. A number of typical civil engineering structures (e.g. simple beams, arches, truss structures, and complete industrial and civil buildings) are analyzed and CW results are compared to classical beam theories (Euler–Bernoulli and Timoshenko), refined beam models based on Taylor-like expansions of the displacements on the cross-section, and classical solid/shell FEM solutions from the commercial code MSC Nastran. The results highlight the enhanced capabilities of the proposed formulation. It is in fact demonstrated that CW models are able to replicate 3D solid results with very low computational efforts.     

The use of asymptotic modelling in vibration and stability analysis of structures

The use of springs with very large stiffness to model constraints in vibratory systems has been a popular approach to overcome the limitations on the choice of admissible functions in the Rayleigh-Ritz method. The maximum possible error resulting from this asymptotic modelling can be determined by using positive and negative stiffness values, or in general terms using positive and negative penalty functions. This paper illustrates how this method could be used to determine the critical loads of structures.     

A modal disturbance estimator for vibration suppression in nonlinear flexible structures

This paper presents a control strategy for the suppression of vibration due to unknown disturbance forces in large, nonlinear flexible structures. The control action proposed, based on the modal approach, consists of two contributions. The first is the well-known Independent Modal-Space Control, which increases system damping and improves its behavior close to the resonance frequencies. The second is a disturbance estimator, which calculates the modal components of the external forces acting on the system and compensates for them using actuator forces. The system modal coordinates, required by both logics, are estimated through a modal state observer.The proposed control logic is tested on a flexible boom. The paper reports the numerical and experimental results both for the linear and nonlinear (large motion) boom configuration.     

A finite element for the vibration analysis of Timoshenko beams

A Timoshenko beam finite element is presented which has three nodes and two degrees of freedom per node, namely the values of the lateral deflection and the cross-sectional rotation. The element properties are based on a coupled displacement field; the lateral deflection is interpolated as a quintic polynomial function and the cross-sectional rotation is linked to the deflection by specifying satisfaction of the governing differential equation of moment equilibrium in the absence of the rotary inertia term. Numerical results confirm that this procedure does not preclude convergence to true Timoshenko theory solutions since rotary inertia is included in lumped form at element ends. The new Timoshenko beam element has good convergence characteristics and where comparison can be made in numerical studies it is shown to be generally more efficient than previous elements.     

A study on the short—wavelength and high—numerical—aperture phase—change recording

In this paper, we discuss the phase-change recording at a short-wavelength (514nm) and a high numerical aperture (0.85). Effects of recording power and pulse width on the size of the recording marks are studied. The minimum recording mark with a length of approximately 220nm has been observed. The capacity of about 17GB for a single-layer disc of a 12cm diameter can be obtained. The maximum carrier-to-noise ratio reaches 45dB at a writing power of 13--14mW.     

A time-domain approach for damage detection in beam structures using vibration data with a moving oscillator as an excitation source

The problem of detecting local/distributed change of stiffness in bridge structures using ambient vibration data is considered. The vibration induced by a vehicle moving on the bridge is taken to be the excitation source. A validated finite element model for the bridge structure in its undamaged state is assumed to be available. Alterations to be made to this initial model, to reflect the changes in bridge behaviour due to occurrence of damage, are determined using a time-domain approach. The study takes into account complicating features arising out of dynamic interactions between vehicle and the bridge, bridge deck unevenness, spatial incompleteness of measured data and presence of measurement noise. The inclusion of vehicle inertia, stiffness and damping characteristics into the analysis makes the system time variant, which, in turn, necessitates treatment of the damage detection problem in time domain. The efficacy of the procedures developed is demonstrated by considering detection of localized/distributed damages in a beam-moving oscillator model using synthetically generated vibration data.