Modal Parameters Of System Research Articles

Uninterrupted and accelerated vibrational fatigue testing with simultaneous monitoring of the natural frequency and damping

A mechanical system's modal parameters change when fatigue loading is applied to the system. In order to perform an accelerated vibration-based fatigue test these changes must be taken into account in order to maintain constant-stress loading. This paper presents an improved accelerated fatigue-testing methodology based on the dynamic response of the test specimen to the harmonic excitation in the near-resonant area with simultaneous monitoring of the modal parameters. The measurements of the phase angle and the stress amplitude in the fatigue zone are used for the real-time adjustment of the excitation signal according to the changes in the specimen's modal parameters. The presented methodology ensures a constant load level throughout the fatigue process until the final failure occurs. With the proposed testing methodology it is possible to obtain a S-N point of the Woehler curve relatively quickly and to simultaneously monitor the changes of the specimen's natural frequency and damping loss factor. The presented methodology with real-time control is verified on an aluminum Y-shaped specimen (106 load cycles are achieved in 21min) and is applicable to a specimen with arbitrary geometry. Besides the faster completion of the fatigue test the methodology can be adopted for the validation of the vibrational fatigue analysis.

Identification of linear time-varying systems using a wavelet-based state-space method

In this paper a new wavelet-based state-space method for the identification of dynamic parameters in linear time-varying systems is presented using free vibration response data and forced vibration response data. For an arbitrarily linear time-varying system, the second-order vibration differential equations are first rewritten as the first-order state equations using the state-space theory. The excitation and response signals are projected using the Daubechies wavelet scaling functions and the first-order state-space equations are transformed into simple linear equations using the orthogonality of the scaling functions. This allows the time-varying equivalent state-space system matrices at each moment to be identified directly via solving the linear equations. The system modal parameters are extracted though eigenvalue decomposition of the state-space system matrices. The stiffness and damping matrices are determined by comparing the identified equivalent system matrices with the physical system matrices. The proposed algorithm is investigated with a two-degree of freedom spring–mass–damper system and a cantilever beam. Numerical results demonstrate that the proposed method is robust and effective with regards to the identification of abruptly, smoothly and periodically time-varying parameters.

Optimal FIR Input Shaper Designs for Motion Control With Zero Residual Vibration

This paper considers the design of input shaping filters used in motion control of vibratory systems. The filters preshape a command or actuation signal in order to negate the effect of vibratory modes. A class of finite impulse response filter satisfying a set of orthogonality conditions that ensure zero residual vibration is introduced. Filter solutions having minimum quadratic gain, both with and without the inclusion of non-negativity (peak gain) constraints, are presented. Unlike impulse-based shapers, the filters have impulse responses with no singularities and therefore automatically remove discontinuities from an input signal. Minimum duration impulse response solutions are also presented. These contain singularities but may also have smooth components. Discrete-time designs can be obtained numerically from system modal parameters, accounting for all modes simultaneously so that convolving single-mode solutions, which leads to suboptimality of the final design, is not required. Selected designs are demonstrated experimentally on a flexible link planar manipulator.

A System Characteristic Parameters Identification Method by Wavelet Transform Image Ridge

Dynamic characteristic of a system have to be obtained so as to offer the reliable data for the system dynamic modification and dynamic optimum design. The system modal parameters identification can be changed into the global optimization problem in wavelet plane because the wavelet ridges can carry much information of system characteristic parameters. Firstly, the paper will introduce the so-called PSO (Particle Swarm Optimization) technique into the modal analysis and propose the PSO wavelet ridge extraction algorithm. Furthermore, the formulas identifying modal parameters from a wavelet ridge are derived and computation steps were given. The simulation experiments are implemented in order to evaluate precision of this method and the robustness of noise. Finally, the proposed method applies to the modal parameters identification of a watermelon to explore the effectiveness. The experiment results prove the method is precision and insensitive to noise.

Efficient model updating and health monitoring methodology using incomplete modal data without mode matching

A methodology is presented for Bayesian structural model updating using noisy incomplete modal data corresponding to natural frequencies and partial mode shapes of some of the modes of a structural system. The procedure can be used to find the most probable model within a specified class of structural models, based on the incomplete modal data, as well as the most probable values of the system natural frequencies and the full system mode shapes. The method does not require matching measured modes with corresponding modes from the structural model, which is in contrast to many existing methods. To find the most probable values of the structural model parameters and system modal parameters, the method uses an iterative scheme involving a series of coupled linear optimization problems. Furthermore, it does not require solving the eigenvalue problem of any structural model; instead, the eigenvalue equations appear in the prior probability distribution to provide soft constraints. The method appears to be computationally efficient and robust, judging from its successful application to noisy simulated data for a ten-storey building model and for a three-dimensional braced-frame model. This latter example is also used to demonstrate an application to structural health monitoring. Copyright © 2005 John Wiley & Sons, Ltd.

A State Space Method for Modal Identification of Mechanical Systems from Time Domain Responses

A new state space method is presented for modal identification of a mechanical system from its time domain impulse or initial condition responses. A key step in this method is the identification of the characteristic polynomial coefficients of an adjoint system. Once these coefficients are determined, a canonical state space realization of the adjoint system and the system′s modal parameters are formulated straightforwardly. This method is conceptually and mathematically simple and is easy to be implemented. Detailed mathematical treatments are demonstrated and numerical examples are provided to illustrate the use and effectiveness of the method.

Equivalent linear modal parameter estimation for a nonlinear aeroelastic system

A nonlinear dynamic system modal analysis methodology is applied to a two degree-of-freedom, nonlinear aeroelastic system. Modal analysis is an essential tool in the flight flutter testing of new and modified aircraft structures, and is used to identify system modal parameters such as frequency and damping. Traditional spectral methods based on the fast Fourier transform, rely on the assumption of system linearity. It has been shown that even isolated nonlinearities in the aircraft structure can contribute to errors in the estimated values of frequency and damping obtained from such a modal analysis. The reverse multiple-input/single-output method, described by Bendat, is a spectral analysis technique applicable to the frequency response function obtained from a nonlinear dynamical system. The technique uses a band-limited random forcing input to obtain the system response and permits the separation of the linear and nonlinear portions of the frequency response function within the frequency domain. The linear portion of the frequency response may then be used to recover the values of frequency and damping for the equivalent linear system. Results are presented for the application of this method to the specific case of a two degree-of-freedom, structurally nonlinear, aeroelastic system. It is shown that the method may be used to successfully recover the linear frequency response function using the input and output data for the nonlinear system.

Optical measurement of discharge valve modal parameters for a rolling piston refrigeration compressor

In this paper we describe the methodology and results of an experiment to measure the fundamental undamped natural frequency and damping ratio for the discharge reed valve in a rolling piston rotary compressor. The small size and extreme flexibility of the valve assembly required the use of a non-contacting measurement technique; thus, an optical displacement follower was chosen as the primary transducer. The measurement system also incorporated a strain gage load cell and PC-based signal processing software. The sensitivity of the system modal parameters to design variables such as valve preload geometry, lubricant viscosity, and retaining screw torque was investigated. Eventually, the measured stiffness, fundamental natural frequency and equivalent viscous damping ratio were incorporated as valve model parameters in a comprehensive computer simulation program for the compressor. Results show that this reed valve design is lightly damped, and that the fundamental natural frequency is a strong function of preload geometry. Lubricant viscosity and retaining screw torque had little effect on the modal parameters.

Non-linear system vibration analysis using Hilbert transform--II. Forced vibration analysis method 'Forcevib'

A technique for non-linear system investigation based on the Hilbert transform enables us to identify system instantaneous modal parameters during free vibration analysis and various kinds of excitation of the dynamic system. The direct time domain approach allows the direct extraction of linear and non-linear systems parameters from a measured time signal of input and output. This paper describes forced vibration analysis, and the proposed method determines instantaneous system modal parameters even if an input signal is a high sweep frequency quasi-harmonic signal or random. Some examples of forced vibration analysis of a non-linear system are included.

Complex modal balancing of flexible rotors including residual bow

A balancing procedure utilizing the Complex Modal Method is presented for linear flexible rotor dynamic systems including the effect of residual shaft bow. The method does not require trial runs; however, a valid mathematical model of the system dynamics is required to obtain the system's modal parameters, which are used to relate the balance corrections to measured responses. Several balancing strategies based on the extension of previous work are suggested for single-speed balancing. Two applications are presented: 1) a gas turbine system with computergenerated response data, and 2) an operating steam turbine-generator system.