Showing papers on "Random vibration published in 2004"

Duality system in applied mechanics and optimal control

Abstract: Contents Preface Introduction 0.1. Introduction to Precise integration method 1: Introduction to analytical dynamics 1.1. Holonomic and nonholonomic constraints 1.2. Generalized displacement, degrees of freedom and virtual displacement 1.3. Principle of virtual displacement and the D'Alembert principle 1.4. Lagrange equation 1.5. Hamilton variational principle 1.6. Hamiltonian canonical equations 1.7. Canonical transformation 1.8. Symplectic description of the canonical transformation 1.9. Poisson bracket 1.10. Action 1.11. Hamilton-Jacobi equation 2: Vibration theory 2.1. Single degree of freedom vibration 2.2. Vibration of multi-degrees of freedom system 2.3. Small vibration of gyroscopic systems 2.4. Non-linear vibration of multi-degrees of freedom system 2.5. Discussion on the stability of gyroscopic system 3: Probability and stochastic process 3.1. Preliminary of probability theory 3.2. Preliminary of stochastic process 3.3. Quadratic moment stochastic process (regular process) 3.4. Normal stochastic process 3.5. Markoff process 3.6. Spectral density of stationary stochastic process 4: Random vibration of structures 4.1. Models of random excitation 4.2. Response of structures under stationary excitations 4.3. Response under excitation of non-stationary stochastic process 5: Elastic system with single continuous coordinate 5.1. Fundamental equations of Timoshenco beam theory 5.2. Potential energy density and mixed energy density 5.3. Separation of variables, Adjoint symplectic ortho-normality 5.4. Multiple eigenvalues and the Jordan normal form 5.5. Expansion solution of the inhomogeneous equation 5.6. Two end boundary conditions 5.7. Interval mixed energy and precise integration method 5.8. Eigenvector based solution of Riccati equations 5.9. Stepwise integrationmethod by means of sub-structural combination 5.10. Influence function of single continuous coordinate system 5.11. Power flow 5.12. Wave scattering analysis 5.13. Wave induced resonance 5.14. Wave propagation along periodical structures 6: Linear optimal control, theory and computation 6.1. State space of linear system 6.2. Theory of stability 6.3. Prediction, filtering and smoothing 6.4. Prediction and its computation 6.5. Kalman filter 6.6. Optimal smoothing and computations 6.7. Optimal control 6.8. Robust control Concluding remarks

Random Vibrations with Impacts: A Review

Abstract: 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.

Structural damage detection using empirical mode decomposition: experimental investigation

Abstract: This paper presents an experimental investigation on the applicability of the empirical mode decomposition (EMD) for identifying structural damage caused by a sudden change of structural stiffness. A three-story shear building model was constructed and installed on a shaking table with two springs horizontally connected to the first floor of the building to provide additional structural stiffness. Structural damage was simulated by suddenly releasing two pretensioned springs either simultaneously or successively. Various damage severities were produced using springs of different stiffness. A series of free vibration, random vibration, and earthquake simulation tests were performed on the building with sudden stiffness changes. Dynamic responses including floor accelerations and displacements, column strains, and spring releasing time instants were measured. The EMD was then applied to measured time histories to identify damage time instant and damage location for various test cases. The comparison of identified results with measured ones showed that damage time instants could be accurately detected in terms of damage spikes extracted directly from the measurement data by EMD. The damage location could be determined by the spatial distribution of the spikes along the building. The influence of damage severity, sampling frequency, and measured quantities on the performance of EMD for damage detection was also discussed.

The precise computation for wave propagation in stratified materials

Abstract: The problem of random wave travelling along stratified materials is important for earthquake engineering. The soil is considered multi-layered and located above the base-rock, whose material property is assumed to be much stiffer than the soil, and the power spectrum density of the random excitation is given at the base rock. The soils can be arbitrarily anisotropic for each layer. The governing differential equations are derived in frequency and wavenumber domain and only a set of ordinary differential equations must then be solved. The eigensolution expansion method is used to solve for the responses of the layers. The precise integration algorithm in combination with the extended W–W algorithm is applied to obtain all the eigensolutions of the ODE (ordinary differential equation). Thereafter, the recently developed pseudo-excitation method for structural random vibration is transplanted to the solution of the layered soil responses. Numerical results are given and compared with some classical results. This shows the relevance of the presented method. Copyright © 2004 John Wiley & Sons, Ltd.

Description and simulation of nonstationary processes based on hilbert spectra

Abstract: A new method is proposed for the description and simulation of nonstationary random processes based on Hilbert spectra of their sample observations. A sample of a random process is first decomposed into intrinsic mode functions (IMFs) by the method of empirical mode decomposition. The Hilbert transforms of the IMFs yield the instantaneous amplitude and frequency, from which the Hilbert spectrum can be obtained as a function of time and frequency. The average of the Hilbert spectra over the samples is then defined as the Hilbert spectrum of the process and used as the target in the simulation of the process. The method is also extended to vector random processes. Unlike current procedures such as those based on the evolutionary process, no assumptions of functional forms for the spectra are necessary which are unknown a priori; and no assumptions of piecewise stationarity and egodicity of the process are required in parameter estimation. Applications to spectral characterization and simulation of multivariate earthquake ground motions show that the Hilbert spectra give a clear description of the time-varying spectral content of the motions and the simulated samples represent an accurate statistical image of the records. The response spectra compare well with those of the records and retain the jagged look. The method has great potential for engineering applications when dealing with nonstationary, nonlinear random processes.

Reliability of uncertain inelastic structures under earthquake excitation

Abstract: The assessment of safety for structures subjected to earthquake excitation is a time-variant reliability problem whose practical solution, when the structure behaves inelastically and uncertainty in the mechanical parameters is taken into account, is traditionally sought by means of simulation. In this paper the feasibility of an alternative solution based on the first order reliability method is explored. The problem is expressed in terms of first-excursion event within a conceptual framework, established in recent years, in which random vibration problems are discretized to make them tractable by the well-established methods of time-invariant structural reliability. The necessary extensions to apply the methodology to reinforced concrete frame structures are presented. Applications to a simple spring-mass system and to a complete three-dimensional bridge structure are presented.

Biodynamic response of human fingers in a power grip subjected to a random vibration.

Abstract: Background. Knowledge of the biodynamic response (BR) of the human hand-arm system is an important part of the foundation for the measurement and assessment of hand-transmitted vibration exposure. This study investigated the BR of human fingers in a power grip subjected to a random vibration. Method. Ten male subjects were used in the experiment. Each subject applied three coupling actions to a simulated tool handle at three different finger grip force levels. Results and Conclusions. The BR is practically independent of the hand coupling actions for frequencies at or above 100 Hz. Above 50 Hz, the BR is correlated to finger and hand sizes. Increasing the finger coupling force significantly increases the BR. Therefore, hand forces should be measured and used when assessing hand-transmitted vibration exposure. The results also show that under a constant-velocity vibration, the finger vibration power absorption at frequencies above 200 Hz is approximately twice that at frequencies below 100 Hz. This suggests that the frequency weighting specified in the current ISO 5349-1 (2001) may underestimate the high frequency effect on vibration-induced finger disorders.

Stochastic Averaging of Preisach Hysteretic Systems

Abstract: The sustained progress in the study of the hysteretic behavior of structural and mechanical systems has led to the adoption of increasingly sophisticated and reliable mathematical representations. Models based on the distributed elements (hysterons) appear to be quite versatile. Among these, the Preisach hysteretic model has received considerable attention in the field of engineering mechanics. In this paper, the stochastic response of a Preisach hysteretic system driven by a white noise process is investigated. In this regard, the method of stochastic averaging is modified to be applicable for the determination of the probability density of the stationary system response envelope. Remarkably, this probability density expression in conjunction with the response of an auxiliary linear system can also be used to determine the power spectrum of the system response. The approximate theoretical solutions are validated by data derived by a pertinent Monte Carlo study.

Identification of the head-neck complex in response to trunk horizontal vibration

Abstract: A method is proposed for identifying the head-neck complex (HNC) in the seated human body when it is exposed to the trunk horizontal (fore-and-aft) vibration. It is assumed that the HNC only has the anteroposterior (flexion/extension) motion in the sagittal plane. An electrohydraulic vibrator is used as a source of vibration. To generate the trunk horizontal vibration, the trunk of the seated subject is fixed to the seatback. The subjects are exposed to the random vibration at a magnitude of 1.60 ms-2 rms (root-mean-square) for 50 s. The coherence and frequency response function are then obtained in the frequency range 0.5–3 Hz. The results show that the HNC behavior is quasilinear with a resonance frequency between 1 and 1.4 Hz. Accordingly, a two-dimensional single-inverted pendulum is considered as a model for the HNC. The frequency domain identification method is then used to estimate the unknown parameters, including the HNC viscoelastic and inertia parameters. The model is examined in a time domain using the random vibration. Good agreement is obtained between experimental and simulation results, indicating the reliability of the proposed method.

Transverse vibration of train-bridge and train-track time varying system and the theory of random energy analysis for train derailment.

Abstract: Summary In this paper, the fundamental problems in the calculation of transverse vibration of train-bridge and train-track time-varying system (hereinafter referred to as the system) are expounded. That is, (1) Proper solution to transverse vibration of the system cannot be obtained by establishing separate transverse vibration equation groups for the car and the bridge (or track); (2) The exciting source of transverse vibration of the system has not been made definite; (3) It is difficult to carry out the random analysis of vibration of the time varying system as the theory of the random vibration analysis for the time varying system has not been established. Our thinking and methods to solve these problems are introduced. On the above-mentioned basis, the theory of random energy analysis for train derailment is presented. The main contents of this theory are as follows: method of random energy analysis of transverse vibration of the system; geometric criterion of derailment; mechanism of derailment caus...

Dynamic Response Analysis of Stochastic Frame Structures Under Nonstationary Random Excitation

Abstract: A new method (random factor method) for the dynamic response analysis of linear stochastic frame structures under nonstationary random excitation is presented. From the expressions of structural random response of the frequency domain, the computational expressions of the mean value, variance, and variation coefficient of the mean square value of the structural nonstationary random displacement and stress response are developed by means of the random variable's functional moment method and the algebra synthesis method, in which the randomness of the structural physical parameters is considered. The influences of the randomness of the structural physical parameters on the randomness of the mean square value of the structural displacement and stress response are inspected via an engineering example.

Random Vibration of SMA Systems via Preisach Formalism

Abstract: Interest in shape memory alloys (SMA) applications has increased dramatically in recent years. The primary problem in studying systems endowed with SMA devices involves quantifying their mechanical behavior. A most promising tool for this task is the Preisach model, which, due to its abstract nature, is extremely versatile for capturing various hysteretic phenomena present in SMA. In this paper a procedure to calibrate the Preisach model to fit available experimental data is employed first. Then the random responses of SMA systems are investigated by focusing on the numerical implementation of the Preisach model. A version of the stochastic averaging technique is used for this purpose. The probability density function of the amplitude and the power spectral density of the response are determined. Also, the probability density function of the response process is estimated. The analytical results are found in good agreement with those derived by a pertinent Monte Carlo study. Obviously, the methodology described herein can be applied for the study of other hysteretic systems, such as mechanical joints, provided that adequate calibration of the Preisach model has been performed a priori.

Effects of excitation probability distribution on system responses

Abstract: For a system subjected to a random excitation, the probability distribution of the excitation may affect behaviors of the system responses. Such effects are investigated for a variety of dynamical systems, including a linear oscillator, an oscillator of cubic non-linearity in both damping and stiffness, and a non-linear oscillator of the van der Pol type. The random excitations are assumed to be stationary stochastic processes, sharing the same spectral density, but with different probability distributions. Each excitation process is generated by passing a Brownian motion process through a non-linear filter, which is governed by an Ito stochastic differential equation. Monte Carlo simulations are carried out to obtain the transient and stationary properties of the system response in each case. It is shown that, under different excitations, the transient behaviors of the system response can be markedly different. The differences tend to reduce, however, as time of exposure to the excitations increases and the system reaches the stationary state.

Application of Operational Modal Analysis to a Machine Tool Testing

Abstract: Modal analysis testing of a mechanical structure is performed usually by artificial excitation of a structure and measuring input forces and output responses of a mechanical system. The excitation is either transient (impact hammer testing), random, burst-random or sinusoidal (shaker testing). The modern signal processing tools enable to determine properties of a mechanical structure such as resonance frequencies, damping ratios, and mode patterns by measuring the response of the structure without using an artificial excitation. The advantage of this technique is that modal parameters of a structure may be evaluated while the structure is under actual operating conditions. That will allow developing a model within true boundary conditions and actual force and vibration levels. The machine tool structure characteristics that effect productivity and quality have to be evaluated by testing. These characteristics include natural frequencies, modes of vibration, and external sources of high level vibration. Not all modes of machine tool structure effect machine quality. As a result only the modes that are excited during cutting have to be taken in the account. This approach narrowed the frequency range, which has to be considered in test. The machine tool during cutting and/or idling is loaded by a set of external and internal exciting forces. Spectrum, frequency range and application points of these forces are unknown in many cases. Under these exciting forces the vibration between the tool and workpiece, and vibration of machine tool components are sums of many independent vibrations and may be considered as stationary random processes. This assumption allows applying the theory of stationary random processes to machine tool dynamic testing during cutting. Several characteristics of random processes are used to separate harmonic vibration from narrow-band random vibration at natural frequencies. The spectral analysis of machined surface profiles and its correlation with observed vibration allows choosing modes that have to be developed. The analysis of these modes provides a basis for machine tool structure improvement. The proposed experimental approach was verified by experiments at different machine tools. Results of these tests are presented in the paper.Copyright © 2004 by ASME

Random Vibration of Systems with Viscoelastic Memory

Abstract: The equation of motion of linear dynamic systems with viscoelastic memory is usually expressed in a integrodifferential form, and its numerical solution is computationally heavy. In two recent papers, the writers suggested that the system memory be accounted for through the introduction of a number of additional internal variables. Following this approach, the motion of the system is governed by a set of first-order, linear differential equations, whose solution is quite easy. In this paper, the approach is extended to single-degree-of-freedom systems subjected to random, nonstationary excitation. The equations governing the time variation of the second-order statistics are derived, and an effective step-by-step solution procedure is proposed. Numerical example shows the accuracy of the procedure for white and nonwhite excitations.

Boundary element modeling of multidirectional random wave diffraction by multiple rectangular submarine pits

Abstract: The diffraction of multidirectional random surface waves by one or more rectangular submarine pits is investigated theoretically. The present method is based on the principle of cumulative superposition of diffraction solutions for linear Airy wave theory obtained by a two-dimensional boundary integral equation in water of uniform depth. The constant segment mode has been utilized to obtain the velocity potentials on the interface of each pit, and a specified discrete form of the Mitsuyasu directional spectrum is used for the incident wave conditions. The results of the present model have been validated through the comparison with those obtained by previous works ( kh kh >1. In accordance with reasonable agreement from these comparisons, it is concluded that the present BEM numerical model may accurately be utilized to predict the wave field around multiple submarine pits or navigation channels in many practical applications.

Random vibration and deterministic analyses of cable-stayed bridges to asynchronous ground motion

Abstract: In this paper, a comparison of various random vibration and deterministic dynamic analyses of cable-stayed bridges subjected to asynchronous ground motion is presented. Different random vibration methods are included to determine the dynamic behaviour of a cable-stayed bridge for various ground motion wave velocities. As a numerical example the Jindo Bridge located in South Korea is chosen and a 413 DOF mathematical model is employed for this bridge. The results obtained from a spectral analysis approach are compared with those of two random vibration based response spectrum methods and a deterministic method. The analyses suggest that the structural responses usually show important amplifications depending on the decreasing ground motion wave velocities.

Wavelet analysis of vehicle nonstationary vibration under correlated four-wheel random excitation

Abstract: The wavelet analysis method is introduced in this paper to study the nonstationary vibration of vehicles. A new road model, a so-called time domain correlated four-wheel road roughness, which considers the coherence relationships between the four wheels of a vehicle, has been newly developed. Based on a vehicle model with eight degrees of freedom, the analysis of nonstationary random vibration responses was carried out in a time domain on a computer. Verification of the simulation results show that the proposed road model is more accurate than previous ones and that the simulated responses are credible enough when compared with some references. Furthermore, by taking wavelet analysis on simulated signals. some substantial rules of vehicle nonstationary vibration, such as the relationship between each vibration level, and how the vibration energy flows on a time-frequency map, beyond those from conventional spectral analysis, were revealed, and these will be of much benefit to vehicle design.

Random vibration movements of liquid nanosized Pb inclusions in Al

Abstract: Transmission electron microscopy has been used to study the behavior of liquid nanosized Pb inclusions in Al ribbons made by rapid solidification. In situ heating experiments carried out in the temperature range from around 375 to 450 ◦ C have shown that liquid inclusions with sizes from around 10–50 nm, that are trapped on dislocations, perform random vibrations around their positions of attachment with vibration periods of some fractions of seconds. The amplitudes of the vibrations in directions perpendicular to the dislocations are a few nanometers, while the motion in directions parallel to the dislocations can be more than an order of magnitude larger. Under conditions where two or more inclusions, attached to a dislocation line, display one-dimensional random motion the inclusions are rarely seen to coalesce. Movement of the inclusions has been monitored by video and shorter sequences have been digitized and analyzed frame-by-frame. The analysis shows that the step lengths have Gaussian distributions indicative of random walks. Fractal analysis of the paths shows that the fractal dimension is close to two which agrees well with the observations that the inclusions carry out linear random walks in a confined space. © 2003 Elsevier B.V. All rights reserved.