Randall J. Allemang

Complex Mode Indication Function and its Applications to Spatial Domain Parameter Estimation

Abstract This paper introduces the concept of the Complex Mode Indication Function (CMIF) and its application in spatial domain parameter estimation. The concept of CMIF is developed by performing singular value decomposition (SVD) of the Frequency Response Function (FRF) matrix at each spectral line. The CMIF is defined as the eigenvalues, which are the square of the singular values, solved from the normal matrix formed from the FRF matrix, [H(jω)]H[H(jω)], at each spectral line. The CMIF appears to be a simple and efficient method for identifying the modes of the complex system. The CMIF identifies modes by showing the physical magnitude of each mode and the damped natural frequency for each root. Since multiple reference data is applied in CMIF, repeated roots can be detected. The CMIF also gives global modal parameters, such as damped natural frequencies, mode shapes and modal participation vectors. Since CMIF works in the spatial domain, uneven frequency spacing data such as data from spatial sine testing can be used. A second-stage procedure for accurate damped natural frequency and damping estimation as well as mode shape scaling is also discussed in this paper.

A frequency domain global parameter estimation method for multiple reference frequency response measurements

Abstract A method of using the matrix Auto-Regressive Moving Average (ARMA) model in the Laplace domain for multiple-reference global parameter identification is presented. This method is particularly applicable to the area of modal analysis where high modal density exists. The method is also applicable when multiple reference frequency response functions are used to characterise linear systems. In order to facilitate the mathematical solution, the Forsythe orthogonal polynomial is used to reduce the ill-conditioning of the formulated equations and to decouple the normal matrix into two reduced matrix blocks. A Complex Mode Indicator Function (CMIF) is introduced, which can be used to determine the proper order of the rational polynomials.

A MAGNETORHEOLOGICAL SEMI-ACTIVE ISOLATOR TO REDUCE NOISE AND VIBRATION TRANSMISSIBILITY IN AUTOMOBILES

The demand for low cost, quiet operation, and increased operator comfort in automobiles and other applications is requiring that new techniques be developed for noise and vibration isolation. One approach to reduce noise and vibration harshness is to develop a small low cost vibration isolator that can be used to mount components that generate vibration. To develop this isolator, passive, semi-active, and active control methods and different types of smart materials were studied. Based on this study, the most promising approach seems to be a semi-active magnetorheological isolator. An isolator of this type was designed to mount a compressor on an automobile body and to isolate the body from high frequency vibration produced by the compressor. This application is more difficult than the problem of isolating a component from vibration of a base because here vibration is also produced by the component. The new results that this study provides are: (i) a simulation model of a semi-active control system with a magnetorheological isolator, a low pass filter, and base and rotating unbalance excitations, (ii) detailed simulation studies showing the practical trade-offs between passive and semi-active isolator performance, and the effect of phase lag due to low pass filtering, and (iii) an electronically controlled isolator design that can turn filtering on or off to provide durability and isolation performance that cannot be achieved using a passive isolator alone. The isolator design proposed here can have several applications. These include engine mounts, pumps, and fans in automobiles, and the isolation of aviation and naval components where the isolator must be durable enough to withstand low frequency vibration and shock loading through its base, and at the same time prevent transmission of high-frequency vibration from the component to the mounting structure.

A Structural Neural System for Real-time Health Monitoring of Composite Materials

A prototype structural neural system (SNS) is tested for the first time and damage detection results are presented in this study. The SNS is a passive online structural health monitoring (SHM) system that mimics the synaptic parallel computation networks present in the human biological neural system. Piezoelectric ceramic sensors and analog electronics are used to form neurons that measure strain waves generated by damage. The sensing of strain waves is similar to the proven nondestructive evaluation (NDE) technique of acoustic emission (AE) monitoring. Fatigue testing of a composite specimen on a four-point bending fiXture is performed, and the SNS is used to monitor the specimen for damage in real time. The prototype SNS used four sensors as inputs, but the number of inputs can be in the tens or hundreds depending on the type of SNS processor used. This is an area of continuing development. The SNS has two channels of signal output that are digitized and processed in a computer. The first output channel tracks the propagation of waves due to damage, and the second output channel provides the combined AE responses of the sensors. The data from these two channels are used to predict the location of damage and to qualitatively indicate the severity of the damage. Overall, this study shows that the SNS can detect damage growth in composites during operation of the structure, and the SNS architecture has the potential to tremendously simplify the AE technique for use in on-board SHM. Ten or more input neurons can be used, and still only two output channels are needed. Two levels of monitoring are possible using the SNS; a coarser SHM approach, or an on-board NDE approach. The SHM approach uses the SNS with a coarse grid of neurons to monitor and detect damage occurring in a general area during operation of the structure. The SNS will indicate where and when a more sensitive inspection is needed which can be done using ground-based NDE techniques. The on-board NDE approach uses the SNS with a fine coverage of neurons for highly sensitive NDE which continuously listens for damage and provides real-time processing and information about any damage in the structure and the performance limits and safety of the vehicle.

Characterization of Nonlinear Vibrating Systems Using Internal Feedback and Frequency Response Modulation

The authors have developed a general frequency response function formulation in a previous article that relates the frequency responses of linear and nonlinear systems. This formulation is based on a spatial perspective of the nonlinearity as an internal feedback force. The present article gives a general interpretation of both the feedback perspective and the previously derived modulation frequency response relationships. A new method of characterizing nonlinear structural dynamic systems that is based on the frequency response relationships is then introduced.

Discrete Frequency Models: A New Approach to Temporal Analysis

Forced vibration responses of nonlinear systems contain harmonics of the excitation frequency. These harmonics are either directly forced or are subharmonic, superharmonic, or combination resonances. Nonlinear responses of this type have been modeled historically using continuous time, discrete time, and continuous frequency models. A new approach to dynamic systems analysis is introduced here that uses difference equations in the discrete frequency domain to describe the evolution of forced, single degree of freedom, steady state vibration responses in frequency instead of time. A variety of possible applications in nonlinear experimental structural vibrations are also discussed.

Suppression of undesired inputs of linear systems by eigenspace assignment

In this paper, a method using output feedback is proposed to suppress the response of linear systems to undesired inputs and, in particular, to reduce the vibration response of flexible structures to these inputs. This method does not need to measure undesired inputs (or external forces). The analysis assumes that the location of the undesired inputs are known, although the general time dependency is unknown. The feedback gain matrix is calculated to assign the eigenvalues and left-hand eigenvectors of the closed-loop system to specified values. The effect of the undesired inputs on a closed-loop system can be altered or significantly reduced by properly choosing the left-hand eigenvectors of the system. The stability of the control system is guaranteed by properly choosing the output matrix, which can decouple the controlled modes from the uncontrolled modes. An example of forced vibration of a simple flexible structure is presented to demonstrate the proposed method.

Autonomous Modal Parameter Estimation: Methodology

Traditionally, the estimation of modal parameters from a set of measured data has required significant experience. However, as the technology has matured, increasingly, analysis is being performed by less experienced engineers or technicians. To address this development, frequently software solutions are focusing upon either wizard-based or autonomous/semiautonomous approaches. A number of autonomic approaches to estimating modal parameters from experimental data have been proposed in the past. In this paper, this history is revewed and a technique suitable for either approach is presented. By combining traditional modal parameter estimation algorithms with a-priori decision information, the process of identifying the modal parameters (frequency, damping, mode shape, and modal scaling) can be relatively simple and automated. Examples of the efficacy of this technique are shown for both laboratory and real-world applications in a related paper.

Initial evaluation of an active/passive structural neural system for health monitoring of composite materials

Structural health monitoring is an underlying technology that can help to ensure safe operation and provide cost effective maintenance of advanced composite structures. While several general methods of health monitoring have evolved in recent years, there is still the goal of reducing the overall cost of applying health monitoring to large structures. Data acquisition hardware typically consumes most of the investment in a structural monitoring system. On a conventional system based on acoustic emission monitoring, a separate high sampling rate data acquisition channel is needed for each sensor to convert analog signals to digital signals to locate damage. Other methods of damage detection are likewise complicated, and require many sensors and actuators, auxiliary signal processing, and data storage instrumentation. This paper proposes a structural neural system that uses firing of sensor neurons to reduce the number of data acquisition channels needed for damage detection. The neural system can perform passive acoustic emission sensing or active wave propagation monitoring. A prototype structural neural system with four sensor inputs was built and tested, and experimental results are presented in the paper. One signal output from the structural neural system is used to predict the location of damage. A second signal provides the time domain response of the sensors. Therefore, passive and active health monitoring can be performed using two channels of data acquisition. The structural neural system significantly reduces the data acquisition hardware required for health monitoring, and combines some of the advantages that exist individually for passive and active health monitoring.

Residual frequency autocorrelation as an indicator of non-linearity

Abstract A new temporal analysis approach using discrete frequency models has recently been introduced by the authors. These models relate the steady-state output of non-linear vibrating systems at each frequency to the excitation at that frequency and the output at other frequencies. The discrete frequency modeling approach is used here to derive an experimental frequency domain indicator function for non-linear vibrations. These indicator functions are autocorrelation functions of residuals from multiple input, multiple output frequency response function estimates. Unlike ordinary spectral coherence functions, which only indicate input–output linearity locally at a single frequency, the autocorrelation functions relate the error at each frequency to the errors at frequencies across the frequency band of interest. This feature enables residual autocorrelation functions to distinguish between system non-linearities and bias errors localized in frequency. Non-linearities in a simulated single-degree-of-freedom system, an analog computer system, and a complicated multiple-degree-of-freedom system are detected using the new indicator function.