Showing papers on "Random vibration published in 1971"

Nonlinear Theory of Random Vibrations

Abstract: Publisher Summary Random vibration analysis of mechanical systems has become an important subject in recent years, principally because of advances in high speed flight. To design structures and equipment that will survive the randomly fluctuating loads caused by the flow of turbulent air or the efflux of jet or rocket engines, it has become necessary to develop a theory capable of analyzing the effect of such fluctuating loads on structures and equipment. Many of the techniques developed for the analysis of random excitation of nonlinear control systems are applicable to the analysis of nonlinear random vibrations, and conversely many of the techniques developed in the theory of nonlinear random vibrations are equally applicable to problems in communication theory and electronics. The chapter presents modeling in nonlinear random vibrations by Markov processes. The chief reason for adopting the idealized model of a system of differential equations excited by white noise is that the computations are much simpler in this case. One of the difficulties involved in modeling nonlinear random vibrations by Markov processes is that—one is restricted to quasi-linear systems. In the subsequent development of the theory, no distinction has been made between the physical nonlinearity and the mathematical model of that nonlinearity. Further, the chapter also discusses the basic theory of stochastic processes and its applications and solution techniques.

An introduction to mechanical vibrations

Abstract: Dynamics. Periodic Motion. Energy Methods. Forced Periodic Motion. Initial Conditions and Transient Vibration. Damping. Damped Forced Vibrations. Nonlinear Vibration. Two Degrees of Freedom. Torsional Vibration. Discrete Systems: Matrix Methods. Discrete Systems: Finite Elements. Distributed Systems. Random Vibration. References. Index.

Ambient Vibration of Two Suspension Bridges

Abstract: The dynamic characteristics (i.e., normal mode natural frequencies, damping, and shapes) of two suspension bridges are estimated from experimentally measured ambient motion time histories. These characteristics were estimated using random vibration theory and the power spectral densities of ambient time histories. Twenty normal modes of vibration were observed in the 0 cycle per min-60 cycle per min frequency range for the Newport Bridge in Rhode Island. These modes include nine vertical, six lateral, and two torsional deck modes, plus three longitudinal tower modes. For each mode, estimates are obtained of natural frequency of vibration, damping, and shape. For the other suspension bridge, the William Preston Lane Memorial Bridge, 13 normal modes of vibration were observed. These modes are six vertical, six lateral, and one torsional deck mode. No tower modes were observed in the 0 cycle per min-60 cycle per min frequency range.

Failure detection of a space shuttle wing flutter model by random decrement

Abstract: On-line monitoring of characteristic structural response of space shuttle wing flutter model for failure detection and repair

Random Vibration of Thin Elastic Plates and Shallow Shells

Abstract: : The large amplitude vibrations of thin elastic plates and shallow shells having boundary conditions and subjected to random excitation are investigated by using various approximate techniques. The random vibrations of rectangular plates and circular plates subjected to white random excitation are simulated numerically by two different methods. The first method is that the governing equations are reduced to a single-degree-of-freedom dynamical system and the reduced equation is then integrated numerically by the Runge-Kutta method employing the simulated approximate white noise as an input. The second method consists in integrating the equation of motion and the compatibility equation numerically by a finite-difference method employing the simulated approximate white noise as an input.

Random Behavior of Columns

Abstract: Using an analog computer for simulations, an empirical relationship is developed for the stability condition of a pin-ended column, which is excited by a physical white noise. The effect of initial curvature to the random behavior of columns is also considered. This relationship is then applied in two practical examples. In the first example, the column stability of a typical building subjected to earthquake loads is considered. The results of this example suggest that dynamic instability caused by earthquake excitation is not likely to be a problem in structures designed according to the current AISC specifications. In the second example, a hypothetic column for a spacecraft structure is subjected to the Saturn V random vibration design environment. In this example, it is found that under certain conditions, dynamic instability may be a problem.

Dynamic responses of railroad car models to vertical and lateral rail inputs

Abstract: Simplified dynamic models were applied in a study of vibration in a high-speed railroad car. The mathematical models used were a four-degree-of-freedom model for vertical responses to vertical rail inputs and a ten-degree-of-freedom model for lateral response to lateral or rolling (cross-level) inputs from the rails. Elastic properties of the passenger car body were represented by bending and torsion of a uniform beam. Rail-to-car (truck) suspensions were modeled as spring-mass-dashpot oscillators. Lateral spring nonlinearities approximating certain complicated truck mechanisms were introduced. The models were excited by displacement and, in some cases, velocity inputs from the rails by both deterministic (including sinusoidal) and random input functions. Results were obtained both in the frequency and time domains. Solutions in the time domain for the lateral model were obtained for a wide variety of transient and random inputs generated on-line by an analog computer. Variations in one of the damping properties of the lateral car suspension gave large fluctuations in response over a range of car speeds for a given input. This damping coefficient was significant in reducing lateral car responses that were higher for nonlinear springs for three different inputs.

Statistical Approach to Complex Random Vibration

Abstract: A statistical approach to response prediction is a method for estimating the gross features of the response of complex structures to random excitation. A method of this type is presented and illustrated by means of two simple examples. In the first example, the mean‐square velocity at a specific point of a single homogeneous beam excited by a stochastic point force is considered; in the second, the mean power flow between two homogeneous beams weakly coupled by a spring is considered when one of the two beams is excited by a stochastic point force.

Reflection of signals from a randomly oscillating conducting plane

Abstract: The problem of signal reflection from a conducting plane in random oscillation is considered. The mean reflected signal is found to depend, in general, on the characteristic function of the stochastic process that describes the random oscillation of the conducting plane. Asymptotic expressions for the mean reflected signal are derived. For a monochromatic signal it is shown that the amplitude of the reflected signal depends on the ratio between the wavelength and the rms displacement of the conducting plane from its mean position. Also, from the mean reflected signal, information about the statistical properties of the random oscillation may be obtained under certain conditions.

On the Stationary Impact Vibration of a Mechanical System with Two Degrees of Freedom

Abstract: In this paper, it is studied theoretically that a harmonic exciting displacements generate the stationary impact vibrations in such a mechanical system with two degrees of freedom as consists of two masses with a clearance. The conditions for maintaining stable periodic vibration are analyzed and ranges of parameters are determined where asymptotic stability is assured. It is found from the results of theoretical analysis and numerical calculation, that stable fundamental impact vibration occurs in a wide range of the exciting frequencies when the clearance between two masses is close to the exciting displacement and a sub-impact vibration occurs when the frequency is high, while a two-impacts vibration occurs as the frequency becomes low.

Applications III.: Failure Due to Random Vibration 2

Abstract: The preceding chapter on failure has shown how an expected life under random loading can be calculated when there is either a threshold stress at which failure occurs with probability one, or where the Miner criterion of cumulative damage is valid. The present chapter will consider the applicability of the Miner criterion in the light of certain probabilistic models of the fatigue process in polycrystalline materials. Experimental studies and proposed modifications of the Miner criterion will also be discussed.

Applications IV: Simulation

Abstract: Many of the engineering systems which suffer from random vibration are of considerable complexity, so that fully instrumented testing in service is just not practicable. Also sub-components of such complex systems are often separately supplied, so that there is a need to demonstrate their capacity for survival by tests which take place outside the parent equipment. Such considerations have led to an interest in simulating in the laboratory vibration conditions which occur in service. It is therefore important to consider how vibration conditions can be simulated, and to consider in particular how this can be done economically, using relatively simple testing equipment.

Applications I: Vehicle Response

Abstract: When a vehicle travels along a road the undulations of the road-surface impose continuously varying displacements at the points of contact of tyres and road, and so give rise to responses in the form of stresses or acceleration in the various components of the vehicle.