Traditional Modal Analysis Research Articles

General approach for representing and propagating partially coherent terahertz fields with application to Gabor basis sets.

We discuss a general theoretical framework for representing and propagating fully coherent, fully incoherent, and the intermediate regime of partially coherent submillimeter-wave fields by means of general sampled basis functions, which may have any degree of completeness. Partially coherent fields arise when finite-throughput systems induce coherence on incoherent fields. This powerful extension to traditional modal analysis methods by using undercomplete Gaussian-Hermite modes can be employed to analyze and optimize such Gaussian quasi-optical techniques. We focus on one particular basis set, the Gabor basis, which consists of overlapping translated and modulated Gaussian beams. We present high-accuracy numerical results from field reconstructions and propagations. In particular, we perform one-dimensional analyses illustrating the Van Cittert-Zernike theorem and then extend our simulations to two dimensions, including simple models of horn and bolometer arrays. Our methods and results are of practical importance as a method for analyzing terahertz fields, which are often partially coherent and diffraction limited so that ray tracing is inaccurate and physical optics computationally prohibitive.

Identification of modal parameters including unmeasured forces and transient effects

In this paper, a frequency-domain method to estimate modal parameters from short data records with known input (measured) forces and unknown input forces is presented. The method can be used for an experimental modal analysis, an operational modal analysis (output-only data) and the combination of both. A traditional experimental and operational modal analysis in the frequency domain starts respectively, from frequency response functions and spectral density functions. To estimate these functions accurately sufficient data have to be available. The technique developed in this paper estimates the modal parameters directly from the Fourier spectra of the outputs and the known input. Instead of using Hanning windows on these short data records the transient effects are estimated simultaneously with the modal parameters. The method is illustrated, tested and validated by Monte Carlo simulations and experiments. The presented method to process short data sequences leads to unbiased estimates with a small variance in comparison to the more traditional approaches.

Experimental evaluation of force frequency shifting for low-frequency vibration excitation

A novel approach known as force frequency shifting (FFS) has been previously proposed for low-frequency (less that 1 Hz) vibration excitation. The technique requires a time-varying forcing function to be applied in a spatially varying fashion. The non-linear dynamic response produces excitation forces and moments at sum and difference frequencies of the force (i.e. f z ) and translational motion (i.e. f x ) frequencies. It is the difference frequency component (i.e. f z − f x ) that produces the desired low-frequency excitation. The purpose of this paper is to examine the fundamental behaviour of the FFS concept in depth and explore the feasibility of the method for structural excitation of large-scale systems with low natural frequencies. First, a set of tests was performed on a laboratory prototype to quantify the character of the excitation output. The prototype system was instrumented at component interfaces allowing reaction forces to be measured and compared to analytical model results. The tests show that the model frequency predictions were very accurate. Force and moment amplitude predictions were nominally within 5% of the experimental values. However, some amplitude comparisons showed larger errors and can be attributed to a number of identified modelling and experimental issues. Next, a full-scale FFS prototype was used to perform vibration tests on a large test structure (inertial vibration isolation platform). The results from two tests were compared: (1) a traditional modal analysis using an impact excitation and (2) an operating deflection shapes analysis using the FSS as the excitation. The comparison was excellent demonstrating the potential for the FFS technology to be used for modal testing of large structures.

Reduced models for the medium-frequency dynamics of stochastic systems.

In this paper, a frequency domain vibration analysis procedure of a randomly parametered structural system is described for the medium-frequency range. In this frequency range, both traditional modal analysis and statistical energy analysis (SEA) procedures well-suited for low- and high-frequency vibration analysis respectively, lead to computational and conceptual difficulties. The uncertainty in the structural system can be attributed to various reasons such as the coupling of the primary structure with a variety of secondary systems for which conventional modeling is not practical. The methodology presented in the paper consists of coupling probabilistic reduction methods with dynamical reduction methods. In particular, the Karhunen-Loeve and Polynomial Chaos decompositions of stochastic processes are coupled with an operator decomposition scheme based on the spectrum of an energy operator adapted to the frequency band of interest.

Simplified analysis of asymmetric structures with supplemental damping

AbstractThis study investigated the effects of neglecting off‐diagonal terms of the transformed damping matrix on the seismic response of non‐proportionally damped asymmetric‐plan systems with the specific aim of identifying the range of system parameters for which this simplification can be used without introducing significant errors in the response. For this purpose, a procedure is presented in which modal damping ratios computed by neglecting off‐diagonal terms of the transformed damping matrix are used in the traditional modal analysis. The effects of the simplification are evaluated first by comparing the aforementioned modal damping ratios with the apparent damping ratios obtained from the complex‐valued eigenanalysis. The variation of a parameter that was defined by Warburton and Soni as an indicator of the errors introduced by the simplification is examined next. Finally, edge deformations obtained from the simplified procedure are compared with those obtained from the direct integration of the equations of motion. It is found that the simplified procedure may be used without introducing significant errors in response for most practical values of the system parameters. Furthermore, estimates of the edge deformations, in general, tend to be on the conservative side. Copyright © 2001 John Wiley & Sons, Ltd.

Rapid, Wide-Field Measurements of Complex Transient Shell Vibrations

The mapping and evaluation of complex vibrational fields is often highly desirable in the pressure vessel and piping industry. It is also tedious and expensive using conventional technology such as strain gage and accelerometer arrays. This paper describes field and laboratory measurements made with a portable pulsed laser system that instantaneously captures displacement data over areas up to 2 m2, with submicron sensitivity. The results indicate that pulsed holographic or electronic speckle interferometry facilitates the evaluation of nonstationary vibrational fields with significant advantages over conventional techniques. Pulsed interferometry is an effective tool for rapidly determining locations of worst-case dynamic displacements and strains. Initial field measurements at a natural gas pumping station provided an exciting glimpse at both the measurement capability of the pulsed interferometry system and never before seen dynamic responses of turbo-compressor discharge piping. The piping immediate to the compressor discharge nozzle as well as a recycle pipe was investigated at a range of operating conditions. Several characteristic patterns were observed in the instantaneous operating deflection shapes. Most notable were spiral waves progressing both clockwise and counterclockwise relative to the axial flow direction. A “shock,” sudden drop in deformation, presumably caused by instantaneous back pressure, was also captured during an extensive statistical survey. Subsequently, laboratory measurements were made on a pressure vessel built to ASME Code requirements, with various internal fluid and pressure conditions. During shaker excitation, dynamic strains logged from gage rosettes were compared to captured displacements and mode shapes. Interestingly, the ratio of circumferential to axial dynamic strains was found to depend on the operating deflection shape of the vessel. Long, thin antinodes resulted in strain ratios expected for static loading, but short antinodes typical of higher frequency responses were accompanied by significantly increased axial strains. The authors intend to continue investigating the usefulness of pulsed interferometry measurements for the oil and gas industry. It is considered important to further correlate the interferometry measurements with traditional modal analysis and strain measurement techniques. Follow-up efforts will also attempt to quantify the relationship between wide-area vibrations and noise emanation from piping systems. An additional goal is to increase the efficiency of noise abatement solutions using insight obtained from wide-field vibration measurements.

Modal Parameter Estimation for Piezostructures

This paper is motivated by the need for consistency between piezostructure measurements and existing modal analysis approaches. Fundamental relationships are developed which reveal that the existing framework of traditional modal analysis approaches can be used to estimate modal parameters which describe the piezostructure dynamics. The modal analysis technique is a frequency domain method where the relationship between pole-residue models for conventional structures and piezostructures is developed. Since typical arrangements of piezoelectric sensors and actuators for modal testing lead to ambiguous mode shape estimates, the use of sensoriactuator transducers provides critical drive-point response information. Also, the existence of a transformation between the structure’s modal matrix and the piezostructure’s electromechanical coupling matrix is shown. It is shown that combining the results of a traditional modal test and a piezostructure modal test enables a modal filtering operation which produces experimental measurements of the electromechanical coupling matrix. This method of modal analysis of a piezostructure is demonstrated numerically for a cantilevered beam.