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RESEARCH PAPERS: Modal Analysis

J. Vib., Acoust., Stress, and Reliab. 1986;108(1):1-8. doi:10.1115/1.3269298.

The paper describes a method that uses a multivariate model in the form of a nonhomogeneous finite difference equation to identify modal parameters of a mechanical structure. The modal parameters of this equation are estimable using a model that involves multiple input, multiple output vibration data. Thus, improved global estimates of modal parameters can be obtained, including the identification of highly coupled and pseudo-repeated modes of vibration. When the data are in the form of impulse or free decay responses, then the parameters of the homogeneous part of the equation can be estimated separately, and the method is then related to the Least Squares Complex Exponential method, the Polyreference Time Domain method and the Ibrahim Time Domain method.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1986;108(1):9-16. doi:10.1115/1.3269310.

A procedure is presented to calculate the mass, damping, and stiffness matrices of mechanical systems from measured input/output data. It works on the basis of the Instrumental Variable Method which is well suited for the estimation of models from data with superimposed measurement noise. Noise is present in many practical cases. The theory of the method is described with regard to vibrating systems. The first application is the estimation of the matrices of a simulated system where the noise level is varied. The results show the expected properties: less sensitivity to noise compared to the Least Squares Method. Furthermore, the procedure is applied to a real system.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1986;108(1):17-25. doi:10.1115/1.3269297.

The identification of linear systems based on their dynamic responses has been the object of a great number of studies. In this work, we propose three new identification procedures which can be programmed on a microcomputer. The first of these methods uses an analytical extension of the transfer function, the second method uses a special integral transformation based on the Cauchy-Weierstrass theorem and the last method uses orthogonalization of the experimental displacement shapes by the Ritz-Galerkin procedure. These methods allow rapid detection of the modal parameters. Presented separately, they are applied to identical structure models defined in the first part of this study.

Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Mechanical Signature Analysis

J. Vib., Acoust., Stress, and Reliab. 1986;108(1):26-31. doi:10.1115/1.3269299.

This paper is concerned with the preventive maintenance of roller and journal bearings installed in induction motors. Almost all kinds of failure modes happening on both roller and journal bearings have been reproduced and classified using time and frequency domain data analysis. Diagnostic procedure also has been derived using these analyzed results and statistical method. Finally, an actual diagnostic system for the early stage detection of defected roller bearings has been developed for practical field use.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1986;108(1):32-38. doi:10.1115/1.3269300.

Described is a method of extracting modal deflection patterns by means of acceleration measurements only. This enables the testing of systems/machines under normal operating conditions with many potential advantages. A single inertance measurement can be used in conjunction with these results to estimate true modal parameters. The method is demonstrated for a drill under machining conditions. Error associated with the proposed method are discussed, and estimated for the given example.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1986;108(1):39-43. doi:10.1115/1.3269301.

In the study of the response of systems to an excitation there are circumstances when it is desirable to obtain some overall or average characterization of the system and its response rather than a detailed description. In this paper two methods are used to describe the overall features of the system: one appropriate for the frequency domain and one for the time domain. For modally dense systems the main features of the frequency response function are described in terms of low-order parametric models. While these models may be adequate for the frequency domain representation, they may not produce a good approximation to the response of the system in the time domain. The second approach relates the envelope of the input signal to the envelope of the response signal, in order to describe the overall time domain response characteristics.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1986;108(1):44-49. doi:10.1115/1.3269302.

The accuracy of the frequency response measurement obtained using impact excitation and a Fast Fourier Transform based spectrum analyzer has been investigated. It has been shown that with impact excitation, provided the impacts are reproducible and the extraneous noise level is low, the coherence estimates obtained from the analyzer are unity, irrespective of the frequency resolution employed. Hence the H1 (Sxy /Sxx ) and H2 (Syy /Sxy *) frequency response function estimates are identical. However, these frequency response function estimates are affected by a bias error caused by inadequate frequency resolution so unity coherence does not necessarily imply accurate results. The results with impact excitation are compared with those obtained using random excitation where both the coherence and frequency response function estimates are affected by bias error. The bias error in the frequency response function estimates with impact excitation is intermediate between that in the H1 and H2 estimates when random excitation is used. The theoretical predictions have been verified by tests on an analogue computer and on a built-up structure.

Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Damping

J. Vib., Acoust., Stress, and Reliab. 1986;108(1):50-55. doi:10.1115/1.3269303.

This paper presents a general approach for modeling shrouded blade vibration that takes into consideration the nonlinear friction constraint at the shroud interface. In this approach, linear structures are characterized by receptances and shroud constraints by nonlinear impedances. The proposed methodology is presented in detail for simplified models of the bladed disk and shroud interface. The corresponding governing equations for the dynamic response are derived for both tuned and mistuned stages. As an example the method is applied to an idealized tuned stage. Two cases are considered, a lubricated shroud for which the coefficient of friction is equal to zero, and a frictionally constrained shroud. The effect of varying the shroud-to-shroud preload is studied. In the lubricated case nonlinear behavior is seen when vibrations are strong enough to result in separation of the shroud interfaces. In the case of finite friction there is a profound change in resonant frequencies when the preload is increased sufficiently to prevent gross slip at the shrouds.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1986;108(1):56-64. doi:10.1115/1.3269304.

The equations of motion governing the vibration of a beam consisting of two metal layers bonded together with a soft viscoelastic damping adhesive are derived and solved. The adhesive is assumed to undergo both shear and thickness deformations during the vibration of the beam. In previous investigations the thickness deformation has been assumed to have negligible effect on the total damping. However, if the adhesive is very soft, and if at least one of the metal layers is stiff in bending, the thickness deformation in the adhesive can become the dominant damping mechanism. The analysis presented here comprises an extension of the well-known sixth order theory of DiTaranto, Mead, and Markus to include thickness deformation. The equations of motion are derived using Hamilton’s Principle and solutions are obtained by the Ritz method. It is shown that the use of a lightweight constraining layer which is stiff in bending will result in a design which is considerably more damped than a conventional configuration in which the adhesive is undergoing predominant shear deformation.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1986;108(1):65-68. doi:10.1115/1.3269305.

This paper investigates the control effects of sandwich beam to random excitation. The statistical properties of the transverse displacement and stress are analyzed. The control effects of the damping layer (including the viscoelastic layer and the constraining layer) on random transverse displacement and random stress are investigated. The results for a sandwich beam are compared with those for the original beam. Finally, examples are given to illustrate the method.

Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Noise Control and Acoustics

J. Vib., Acoust., Stress, and Reliab. 1986;108(1):69-81. doi:10.1115/1.3269306.

The interaction of ultrasonic waves with solid, liquid, gaseous, or multiphase media offers many opportunities for accurate process control, but users risk disappointment because of the influence of “unwanted” variables. The present paper illustrates the use of ultrasonic transit time or amplitude measurements as a basis for calculating flow, temperature, and liquid level. The interrogating wave types include longitudinal, extensional, Rayleigh, transverse shear and torsional modes, at frequencies on the order of 0.1 to 1 MHz. Buffer techniques, special paths, or other means are illustrated for minimizing, avoiding, or compensating for the influence of undesired variables.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1986;108(1):82-90. doi:10.1115/1.3269307.

Analytical solutions for the three-dimensional inhomogeneous wave equation with flow in a hardwall rectangular wind tunnel and in the free field are presented for a stationary monopole noise source. Dipole noise sources are calculated by combining two monopoles 180 deg out of phase. Numerical calculations for the modal content, spectral response and directivity for both monopole and dipole sources are presented. In addition, the effect of tunnel alterations, such as the addition of a mounting plate, on the tunnels reverberant response are considered. In the frequency range of practical importance for the turboprop response, important features of the free field directivity can be approximated in a hardwall wind tunnel with flow if the major lobe of the noise source is not directed upstream. However, for an omnidirectional source, such as a monopole, the hardwall wind tunnel and free field response will not be comparable.

Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Other Vibration and Sound Papers

J. Vib., Acoust., Stress, and Reliab. 1986;108(1):91-94. doi:10.1115/1.3269308.

The stiffness of taperd-bore ring seals was measured with air as the sealed fluid. Static stiffness agreed fairly well with results of a previous analysis. Cross-coupled stiffness due to shaft rotation was much less than predicted. Part of the disparity may be due to simplifying assumptions in the analysis; however, these do not appear to account for the entire difference observed.

Topics: Stiffness , Rotation , Fluids
Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1986;108(1):95-100. doi:10.1115/1.3269309.

Simple and accurate prediction methods of gear unit noise have been desired. This paper offers a new prediction equation for spur and helical gears under speed reduction service. A semi-empirical equation was developed by means of the addition of a dynamics term to Kato’s equation which represented the overall noise level by using gear’s specification data. As the proposed method takes into account the gear error characteristics in the vibration analysis of gear pairs, it can calculate the noise levels considering the influence of the tooth flank finishing method. It is shown that the predicted values agree with the measured values in an experiment within a range of approximately 5dB, under almost all the operating conditions and for all test gears having different finishing methods such as hobbing, Niles-type grinding and Maag-type grinding. Moreover, good agreement with data of some actual gear units indicates that the developed method may be used for general application.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1986;108(1):101-106. doi:10.1115/1.3269292.

A constraint function approach is presented for finding design changes that remove natural frequencies from undesirable frequency bands for lightly damped structures. The technique requires the minimization of a function which becomes smaller when (1) natural frequencies clear out of undesirable bands, and (2) design changes become small. Useful forms of these functions are defined, and the number of possible minima is explored. Graphical intepretations of the constraint functions are given, and an example is included which shows the effects of the parameters which weight these two functions.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Vib., Acoust., Stress, and Reliab. 1986;108(1):107-108. doi:10.1115/1.3269293.
Abstract
Topics: Stress
Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. Vib., Acoust., Stress, and Reliab. 1986;108(1):109-110. doi:10.1115/1.3269294.
FREE TO VIEW
Abstract
Topics: Testing
Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1986;108(1):110-112. doi:10.1115/1.3269295.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1986;108(1):112. doi:10.1115/1.3269296.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster

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