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Variational finite element-tensor formulation for the large deflection random vibration of composite plates

A numerical integration routine is derived from a set of unified single step integration algorithms using a weighted satisfaction of the equilibrium equation governing the large deflection random response of laminated composite plates. The equilibrium equation is derived using a constant matrix large deflection finite-element formulation. In-plane inertia terms are considered in the formulation, however, rotary inertia terms are assumed negligible. Probability density, spectral density and autocorrelation functions of the maximum displacement and strain responses are presented for three acoustic excitation levels. Classical thin plate boundary conditions and pseudo white noise excitation are used in this investigation.

Robinson, Jay H.

On the first-excursion probability in stationary narrow-band random vibration. II.

The first-excursion probability of a stationary narrow-band Gaussian process with mean zero has been studied. Within the framework of point process approach, series approximations derived from the theory of random points and approximations based on the maximum entropy principle have been developed. With the aid of numerical examples, merits of the approximations proposed previously as well as of those developed in this paper have been compared. The results indicate that the maximum entropy principle has not produced satisfactory approximations but the approximation based on nonapproaching random points is found to be the best among all the approximations proposed herein. A conclusion drawn from the present and the previous studies is that the point process approach produces a number of useful approximations for the first-excursion probability, particularly those based on the concepts of the Markov process, the clump-size, and the nonapproaching random points.

Yang, J.-N.

First-excursion probability in non-stationary random vibration.

The first-excursion probability of a non-stationary Gaussian process with zero mean has been studied. Within the framework of the point process approach, a variety of analytical approximations applicable to stationary random processes is extended herein to non-stationary random processes. The extension is possible owing to a recent definition of non-stationary envelope processes proposed by the author. With the aid of numerical examples, merits of each approximation are examined by comparing with the results of simulation. It is found that under non-stationary excitations with short duration, the Markov approximation is the best among all the approximations discussed in this paper.

Yang, J.-N.

The development and verification of shuttle orbiter random vibration test requirements

The unique space shuttle vehicle size, weight, and configuration gave rise to problems in determining vibration requirements and in verifying structural integrity for anticipated mission environments. The applications of large-scale vibration testing played a prominent part in qualifying the shuttle for its intended missions. Severe vibration excitation from rocket engines, aerodynamic noise, and onboard equipment are expected on each shuttle flight. Scale-model wind tunnel and rocket firing tests, as well as full-size rocket engine tests were relied on to define the random forcing functions. The determination of structural response to these environments is described as well as evaluations of measured flight data and comparison with predicted design and test criteria.

Coody, M. C.

On-line analysis of random vibrations

Measuring device, Randomdec, provides continuous on-line signatures representative of system free vibration curve. Selected points on curve are used in control and failure detection systems. Apparatus applied to both linear and nonlinear systems under nonstationary vibratory states.

Cole, H. A., Jr.

Random vibrations of quadratic damping systems

An oscillating system with quadratic damping subjected to white noise excitation is replaced by a nonlinear, statistically equivalent system for which the associated Fokker-Planck equation can be exactly solved. The mean square responses are calculated and the optimum damping coefficient is determined with respect to the minimum mean square acceleration criteria. An application of these results to the optimization of automobile suspension damping is given.

Sireteanu, T.

A comparison of acoustic and random vibration testing of spacecraft

Before selecting the most suitable testing technique in a particular case, it has to be considered which of the two methods duplicates better the distribution of vibration responses to be expected during the actual launch phase. An investigation is conducted of the case of a large, low density spacecraft launched by a vehicle which produces significant acoustic noise and transmits relatively little vibration through the mechanical path provided by the vehicle structure in the area of the spacecraft interface. Criteria for vibration-acoustic equivalence are discussed along with tests conducted with the Synchronous Meteorological Satellite, the Radio Astronomy Explorer, and the Orbiting Geophysical Spacecraft. The investigation indicates that the vibration test is generally a poor substitute for an acoustic study.-

Bangs, W. F.

Non-Gaussian approach for parametric random vibration of non-linear structures

The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.

Ibrahim, R. A.

Remarks on a dynamical higher-order theory of laminated plates and its application in random vibration response

This paper presents an analysis of the equations governing the dynamics of shear-deformable composite plates, without recourse to a variational procedure. It is noted that the operator associated with the governing equations is nonsymmetric; using a first-order perturbation technique, it is shown to be positive-definite. In addition, using the biorthogonality condition, the dynamic response of the plate is formulated.

Cederbaum, G.

Optimum seismic structural design based on random vibration and fuzzy graded damages

This paper presents the fuzzy dynamical reliability and failure probability as well as the basic principles and the analytical method of loss assessment for nonlinear seismic steel structures. Also presented is the optimization formulation and a numerical example for double objectives, initial construction cost and expected failure loss, and dynamical reliability constraints. The earthquake ground motion is based on a stationary filtered non-white noise and the fuzzy damage grade is described by damage index.

Cheng, Franklin Y.

Random Vibration and Torque Tests of Fasteners Secured With Locking Cable, Room Temperature Vulcanized (RTV) Rubber, and Closed Cell Foam to Support the Launch of STS-82

During a walkdown of the Space Transportation System (STS) orbiter for the 82nd Space Shuttle flight (STS-82), technicians found several safety cables for bolts with missing or loose ferrules. Typically, two or three bolts are secured with a cable which passes through one of the holes in the head of each bolt and a ferrule is crimped on each end of the cable to prevent it from coming out of the holes. The purpose of the cable is to prevent bolts from rotating should they become untightened. Other bolts are secured with either a locking cable or wire which is covered with RTV and foam. The RTV and foam would have to be removed to inspect for missing or loose ferrules. To determine whether this was necessary, vibration and torque test fixtures and tests were made to determine whether or not bolts with missing or loose ferrules would unloosen. These tests showed they would not, and the RTV and foam was not removed.

Yost, V. H.

Using the Saturn V and Titan III Vibroacoustic Databanks for Random Vibration Criteria Development

This is an update to TN D-7159, "Development and Application of Vibroacoustic Structural Data Banks in Predicting Vibration Design and Test Criteria for Rocket Vehicle Structures", which was originally published in 1973. Errors in the original document have been corrected and additional data from the Titan III program have been included. Methods for using the vibroacoustic databanks for vibration test criteria development are shown, as well as all of the data with drawings and pictures of the measurement locations. An Excel spreadsheet with the data included is available from the author.

Ferbee, R C.