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RESEARCH PAPERS: Vibration and Sound

J. Vib., Acoust., Stress, and Reliab. 1988;110(4):429-438. doi:10.1115/1.3269547.

An investigation of the effects of small structural irregularities on the dynamics of nearly periodic structures with cyclic symmetry is presented. The system studied may be regarded as a simple model of a continuously shrouded blade assembly accounting for one structural mode per blade. A key aspect of the approach is the use of perturbation methods that lead to a physical insight into the effects of mistuning. The study shows that the sensitivity to mistuning depends primarily upon the ratio of mistuning strength to coupling strength. For a small mistuning to coupling ratio, the mistuned system behaves like a perturbation of the corresponding tuned system, in which case mistuning has a relatively small effect on both the free and forced responses. On the other hand, for a large mistuning to coupling ratio (i.e., weak coupling), the mistuned system behaves like a perturbation of the corresponding decoupled mistuned system, in which case small mistuning dramatically changes the dynamics of the system. This paper, Part I, investigates the effects of small mistuning on the free response of the system. Specifically, it is shown that strong mode localization and eigenvalue loci veering phenomena occur in the weakly coupled system when mistuning is introduced. The effects of mistuning on the forced response are studied in the companion paper, Part II (Wei and Pierre, 1987).

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):439-449. doi:10.1115/1.3269548.

The effects of disorder on the forced response of nearly periodic structures with cyclic symmetry are investigated. The force model adopted here is relevant to blade assemblies. Perturbation methods for the forced response are developed to gain a physical insight into the effects of mistuning. The study shows that the internal coupling between component systems is the key parameter governing the sensitivity to mistuning and that localized forced vibrations do occur in the disordered assembly for weak internal coupling. However, although both localized free and forced vibrations occur for finite or large values of the mistuning to coupling ratio, the deflection patterns for these two types of localized vibrations are different. Also, for the forced response, the degree of localization does not necessarily increase as this ratio increases—a fundamental difference from localized free modes. An important conclusion is that the common periodicity assumption for cyclic structures may lead to qualitative errors for the forced response of weakly coupled systems when small mistuning is present.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):450-455. doi:10.1115/1.3269549.

This paper examines the application of matrix transformations from the experimentally obtained receptance matrix to the dynamic stiffness matrix to determine changes of blade stiffness and/or mass characteristics which will achieve desired modifications of blade dynamic behavior. Results for a specific turbine blade configuration are used to illustrate the approach.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):456-463. doi:10.1115/1.3269550.

The present paper used the modal frequency method to diagnose the fracture damage experimentally in simple structures, based on the analytical theory of the spring-loaded “fracture-hinge.” It is illustrated that the damage geometry uniquely defines the spring constant of the “fracture hinge,” which is therefore independent of the loading strength, the frequency of vibration, and the damage location. The experiment also measures the change in modal frequencies to locate the damage on the beam. With an accurate analytical model for the experimental samples, the locations of the damages can be predicted to within an accuracy of one percent of the length. The damage intensity is around four percent in accuracy.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):464-467. doi:10.1115/1.3269551.

It has been noted in numerous practical applications that the sensitivities of mass elastic systems to external disturbance are closely bound up with the nonzero values of the normalized boundary and field actions, both forces and displacements. This leads in many cases to rapid analyses without, for example, the need for a separate calculation of “participation factors” in seismic applications. This short paper sets down some relationships in general terms and indicates examples of practical interest.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):468-472. doi:10.1115/1.3269552.

In this paper, the transfer matrix impedance coupling method for calculating the eigensolutions of multi-spool rotor systems with several intershaft bearings is developed. This method can also be used for the eigensolutions of the damped rotor systems. The numerical examples of dual and tri-spool rotor systems with intershaft bearings show that the results are in good agreement with the exact solutions.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):473-477. doi:10.1115/1.3269553.

This paper is concerned with the finite element technique for predicting the dynamic properties of anisotropic fiber-reinforced composite laminated plates. Considering the effect of transverse shear deformation, a higher order shear deformation theory which satisifes the zero shear stress conditions at the upper and bottom surfaces is assumed. The natural frequencies and mode shapes of a rectangular plate with all free edges are obtained by finite element method and the modal damping values by finite damped element technique. An equivalent stiffness method is introduced to reduce computation time. Four different theoretical predictions of natural frequencies and damped values of a laminated plate are compared with experimental results. Discussions on the effect of transverse shear deformation to the dynamic properties of composite plates are given.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):478-484. doi:10.1115/1.3269554.

Over the last two decades in experimental modal analysis many different approaches have been developed for application to a great variety of structural engineering problems. The effectiveness of modal testing depends directly on the capability to construct optimal excitation force vectors in order to identify a complete set of normal modes in a frequency band of interest and to extract the corresponding modal parameters. These tasks can be considerably facilitated by means of so-called mode indicator functions (MIF) the most current of which will be thoroughly investigated in order to reveal their features and capabilities. Furthermore, emphasis will be placed on the problem of finding appropriate force vectors to excite either real or complex normal modes. A new concept to determine optimal force vectors for the excitation of complex normal modes will be presented. In the context with the definition of complex normal modes the problem of transforming complex normal modes into real normal modes will be treated as well.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):485-492. doi:10.1115/1.3269555.

The vibration of a constrained dynamical system, consisting of an Euler-Bernoulli beam with homogeneous boundary conditions, supported in its interior by arbitrarily located pin supports and translational and torsional linear springs, is studied. A generalized differential equation is obtained by the method of separation of variables and is solved in terms of the Green’s function and its derivatives of the unconstrained beam. System natural frequencies and modes are obtained, and the orthogonality relation for the natural modes is derived. A general solution for the forced response is given. Finally, two pertinent problems from the literature are examined, and results obtained are compared with those of a small, dedicated finite element formulation to assess the relative accuracy and efficiency of each.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):493-500. doi:10.1115/1.3269556.

Electromagnetic bearings can support a flexible rotor without any contact and simultaneously influence its dynamics. Such an active suspension and vibration control requires closed-loop control of the rotor motions. In practical applications, the design of the controller is based on a simplified reduced-order model of the mechanical system. As a result, one must deal with the reduced-order control problem. A nonexpansive direct output control scheme for mechanical systems with collocated actuators and sensors (“DCD-control”) is presented. This scheme inherently guarantees stability for the real actively controlled system despite reduced-order control effects like spillover. This concept has been experimentally verified through the active suspension of an elastic rotor by means of two digitally controlled, contactless, electromagnetic bearings. Numerical results of the control design procedure and the full-order system behavior are confirmed by measurements in the experimental setup.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):501-506. doi:10.1115/1.3269557.

The vibration of a helical geared shaft system is studied, considering the coupling between the torsional, flexural, rotational (about the diametral axis), and axial motions of the gear carrying shafts. The effects of the nonlinear backlash function and time varying tooth stiffness are also considered. The excitation to the geared shaft system is in the form of a static transmission error which has deterministic and filtered white noise components. The equations of motion are formulated in state space form and solved using matrix exponential approach. Piecewise linearization is used in the simulation and results for the mean and variance of the dynamic response are presented.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):507-514. doi:10.1115/1.3269558.

Thin spinning annular disks, which have widely varying applications ranging from inertial wheels in spacecraft to computer data storage devices, experience some inherent vibration problems during operation. One of the techniques to control the vibrations of the disk, being analyzed in this paper, is to stiffen it by attaching a reinforcing ring at its outer edge. The present work considers the effect of adding such a ring and discusses the changes in the natural frequencies for a large range of design parameters. The classical plate bending equation based upon small deflection theory which includes the contribution of rotational membrane stresses has been used in the eigenvalue formulation. Numerical results presented in a nondimensional form should be useful in predicting the dynamic response of such a disk stiffened with a circular ring under the spinning conditions.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):515-520. doi:10.1115/1.3269559.

The transient dynamic response of a flexible rotor in nonlinear supports has been investigated using time marching methods. Several marching techniques such as Newmark β, Wilson θ, and Houbolt have been utilized in this study of rotor-bearing dynamic systems, to examine the stability of the system, and the suitability of each technique for predicting the onset of instability. The given rotor system has been modeled both in space and time using the transfer matrix method and the Houbolt method. The transient orbital response data so obtained have been compared with those obtained by a finite element model. Differences in the order of 6 percent were found. A nonlinear representation of a finite bearing has been included in the transient matrix model and the stability characteristics of different rotor systems of varied complexity have been studied. The nonlinear results have been compared with earlier results obtained using linear bearing representations.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):521-527. doi:10.1115/1.3269560.

The authors describe an integrated approach to the modelling and active control of lateral vibrations in turbomachinery. Starting with consideration of the control of multiple rotor bending modes, the generation of a state vector from available measurements using an observer is discussed together with the effect on stability of employing a controller of reduced order. The various points are illustrated in an extended case study which also compares the active schemes with one involving a simple passive damper.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):528-532. doi:10.1115/1.3269561.

The stored energy type of impact printer is a commonly used computer output device. It can be operated at quite high frequencies due to the fact that it has a large initial activation force. However, limitations on printer speed exist; these are thought to be due primarily to uncertainties in the position and velocity of the armature during settle-out between excitation pulses. This results in variations in flight times and in print forces. In this paper we consider an open-loop control strategy which modifies the driving pulse in such a manner that it aids the restoring force of the print hammer and armature during the settle-out phase of the motion. Simulation studies of our simplified piecewise linear model (Tung and Shaw, 1988) and Hendriks’ (1983) model indicate that the operating speed of impact printers can be significantly increased using this method. Printer performance criteria are also established in the paper. These are based on the requirement that acceptable print quality be achieved for arbitrary combinations of driving pulses which have some minimum time lapse between pulses. We use these criteria to demonstrate the limitations on printer speed and to indicate how the control method is able to increase printer speed. Such criteria are quite general and may be used for more complicated models and controllers.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):533-537. doi:10.1115/1.3269562.

The free vibrations of thick circular cylindrical shells and rings are discussed in this paper. The well-known energy method, which is based on the three-dimensional theory of elasticity, is used in the derivation of the frequency equation of the shell. The frequency equation yields resonant frequencies for all the circumferential modes of vibration, including the breathing and beam-type modes. Experimental investigations were carried out on several models in order to assess the validity of the analysis. This paper first describes briefly the method of analysis. In the end, the calculated frequencies are compared with the experimental values. A very close agreement between the theoretical and experimental values of the resonant frequencies for all the models was obtained and this validates the method of analysis.

Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Noise Control and Acoustics

J. Vib., Acoust., Stress, and Reliab. 1988;110(4):538-544. doi:10.1115/1.3269563.

The growth and decay of a wavepacket convecting in a boundary layer over a concave-convex surface is studied numerically using direct computations of the Navier-Stokes equations. The resulting sound radiation is computed using the linearized Euler equations with the pressure from the Navier-Stokes solution as a time-dependent boundary condition. It is shown that on the concave portion the amplitude of the wavepacket increases and its bandwidth broadens while on the convex portion some of the components in the packet are stabilized. The pressure field decays exponentially away from the surface and then algebraically exhibiting a decay characteristic of acoustic waves in two dimensions. The far field acoustic pressure exhibits a peak at a frequency corresponding to the inflow instability frequency.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):545-551. doi:10.1115/1.3269564.

A quasi one-dimensional analysis of sound transmission in a flow duct lined with an array of nonlinear resonators is described. The solution to the equations describing the sound field and the hydrodynamic flow in the neighborhood of the resonator orifices is performed numerically in the time domain, with the object of properly accounting for the nonlinear interaction between the acoustic field and the resonators. Experimental data are compared to numerical computations in the time domain and generally very good agreement is noted. The method described here may readily be extended for use in the design of exhaust mufflers for internal combustion engines.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):552-557. doi:10.1115/1.3269565.

Acoustic agglomeration of power plant fly ash is an intermediate treatment of the flue gases to increase the size of the small micron (1–5) and submicron (0.1–1) particulates to large micron sizes (5–10) so that the conventional particle removal devices such as bag houses, electrostatic precipitators, and scrubbers can operate more efficiently. This paper provides a brief history of the topic, introduces some of the fundamental issues and gives some recent results of analytical models of the processes. The experimental facility is briefly described and some analytical results are shown which compare well with the experimental results. Most important of all, the paper shows that acoustic agglomeration is a technically and potentially economically viable method to improve air pollution control.

Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Reliability, Stress Analysis, and Failure Prevention

J. Vib., Acoust., Stress, and Reliab. 1988;110(4):559-563. doi:10.1115/1.3269568.

Categorization is the procedure of determining set membership based on either necessary or statistically suggestive conditions for membership. This procedure lies at the heart of automated metallurgical failure analysis, controlling the accuracy of the final conclusion. This article examines the tradeoff between the number of questions posed by the computer during data collection and the certainty of the final decision. After a brief overview of failure analysis decision making, a model of categorization is proposed which is derived from Bayes’ theorem that asks questions in order of relevance and stops when an adequate level of certainty is achieved. This eliminates irrelevant questions without significantly compromising the accuracy of the final conclusion. The model has been implemented as part of an artificial intelligence computer program.

Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):564-570. doi:10.1115/1.3269569.

Techniques that use qualitative reasoning for structural configuration synthesis and form design are critically examined. Both algorithmic and heuristic methods are considered. Because of the limitations of these methods a hybrid approach is presented. A shape algebra is developed for structural synthesis which leads to a systematic method for generating structural arrangements. This algebra raises the possibility of transforming structural synthesis into a science instead of the art that it currently is. The method is well-suited to automation exploiting a computer’s capability to manipulate symbols. The method searches for good candidate structures that can be used as the initial form for numerical programs for shape and size optimization.

Topics: Optimization , Shapes , Design
Commentary by Dr. Valentin Fuster

DISCUSSIONS

BOOK REVIEWS

J. Vib., Acoust., Stress, and Reliab. 1988;110(4):571-572. doi:10.1115/1.3269570.
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Commentary by Dr. Valentin Fuster
J. Vib., Acoust., Stress, and Reliab. 1988;110(4):572-573. doi:10.1115/1.3269571.
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J. Vib., Acoust., Stress, and Reliab. 1988;110(4):573-574. doi:10.1115/1.3269572.
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J. Vib., Acoust., Stress, and Reliab. 1988;110(4):574-575. doi:10.1115/1.3269573.
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J. Vib., Acoust., Stress, and Reliab. 1988;110(4):575-576. doi:10.1115/1.3269574.
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J. Vib., Acoust., Stress, and Reliab. 1988;110(4):576-577. doi:10.1115/1.3269575.
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Commentary by Dr. Valentin Fuster

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