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A method is presented of determining the mean square transversal deflection of an isotropic and homogeneous linear viscoelastic beam having a certain number of lengthwise distributed lumped masses. It is assumed that the beam is acted upon by a stationary random process uniformly distributed along the beam. The method is useful in vibration level control by means of additional lumped masses.
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.
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.
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.
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.
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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.
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.
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.-
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.
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.