T. K. Caughey

Equivalent Linearization Techniques

The method of equivalent linearization of Kryloff and Bogoliubov is generalized to the case of nonlinear dynamic systems with random excitation. The method is applied to a variety of problems, and the results are compared with exact solutions of the Fokker‐Planck equation for those cases where the Fokker‐Planck technique may be applied. Alternate approaches to the problem are discussed, including the characteristic function method of Rice.

Random excitation of a system with bilinear hysteresis

An analysis is made of the response of a system with bilinear hysteresis to random excitation. It is shown that for moderately large inputs, the additional damping created by the bilinear hysteresis decreases the mean squared deflection compared with that for a linear system with the same viscous damping. However, for large inputs, the decrease in the stiffness of the system due to the bilinear hysteresis causes the mean squared deflection to increase over that for the equivalent linear system.

Identification of Nonlinear Dynamic Systems Using Neural Networks

This paper explores the potential of using parallel distributed processing methodologies (artificial neural networks) to identify the internal forces of structure unknown non linear dynamic systems

Derivation and Application of the Fokker-Planck Equation to Discrete Nonlinear Dynamic Systems Subjected to White Random Excitation

The Fokker-Planck equation is derived and applied to discrete nonlinear dynamic systems subjected to white random excitation. For the class of problems in which the nonlinearities involve only the displacements of the system, it is shown that exact solutions can be constructed for the stationary Fokker-Planck equation. It is further shown that if stationary solutions exist they are unique.

Development of adaptive modeling techniques for non-linear hysteretic systems

Abstract Adaptive estimation procedures have gained significant attention by the research community to perform real-time identification of non-linear hysteretic structural systems under arbitrary dynamic excitations. Such techniques promise to provide real-time, robust tracking of system response as well as the ability to track time variation within the system being modeled. An overview of some of the authors’ previous work in this area is presented, along with a discussion of some of the emerging issues being tackled with regard to this class of problems. The trade-offs between parametric-based modeling and non-parametric modeling of non-linear hysteretic dynamic system behavior are discussed. Particular attention is given to (1) the effects of over- and under-parameterization on parameter convergence and system output tracking performance, (2) identifiability in multi-degree-of-freedom structural systems, (3) trade-offs in setting user-defined parameters for adaptive laws, and (4) the effects of noise on measurement integration. Both simulation and experimental results indicating the performance of the parametric and non-parametric methods are presented and their implications are discussed in the context of adaptive structures and structural health monitoring.

Identification of Nonlinear Vibrating Structures: Part I—Formulation

A self-starting multistage, time-domain procedure is presented for the identification of nonlinear, multi-degree-of-freedom systems undergoing free oscillations or subjected to arbitrary direct force excitations and/or nonuniform support motions. Recursive least-squares parameter estimation methods combined with nonparametric identification techniques are used to represent, with sufficient accuracy, the identified system in a form that allows the convenient prediction of its transient response under excitations that differ from the test signals. The utility of this procedure is demonstrated in a companion paper.

The exact steady-state solution of a class of non-linear stochastic systems

Abstract In this paper exact steady state solutions are constructed for a class of non-linear systems subjected to stochastic excitation. The results are then applied to both classical and non-classical oscillator problems.

Analysis of a Nonlinear First‐Order System with a White Noise Input

A general technique for computing the power spectrum of nonlinear systems is presented, and the method is applied to the Brownian motion of a particle with idealized Coulomb damping. In this method the transition probability is obtained by solving the appropriate Fokker‐Planck equation. Then the autocorrelation function is calculated by an appropriate integration, and finally the power spectrum is found by means of the Wiener‐Khintchine relation. Comparison is made with the method of equivalent linearization, which is applicable to a wide class of nonlinear problems.

Rotor-Stator Interaction in a Diffuser Pump

The interaction between impeller blades and diffuser vanes in a diffuser pump was investigated. Steady and unsteady pressure measurements were taken on the diffuser vanes, and the shroud wall of a vaned and a vane less diffuser. Steady, unsteady, and ensemble averaged unsteady data, as well as frequency spectra are presented. The measurements were made for different flow coefficients, shaft speeds, and radial gaps between impeller blade trailing and diffuser vane leading edge (1.5% and 4.5% based on impeller discharge radius). The resulting lift on the vane, both steady and unsteady, was computed from the pressure measurements at mid vane height. The magnitude of the fluctuating lift was found to be greater than the steady lift. The pressure fluctuations were larger on the suction side than on the pressure side attaining their maximum value, of the same order of magnitude as the total pressure rise across the pump, near the leading edge. Pressure fluctuations were also measured across the span of the vane. and those near the shroud were significantly smaller than those near the hub. The pressure fluctuations on the shroud wall itself were larger for the vaned diffuser than a vaneless diffuser. Lift, vane pressure, and shroud wall pressure fluctuations decreased strongly with increasing radial gap.

Structure-unknown non-linear dynamic systems: identification through neural networks

Explores the potential of using parallel distributed processing (neural network) approaches to identify the internal forces of structure-unknown non-linear dynamic systems typically encountered in the field of applied mechanics. The relevant characteristics of neural networks, such as the processing elements, network topology, and learning algorithms, are discussed in the context of system identification. The analogy of the neural network procedure to a qualitatively similar non-parametric identification approach, which was previously developed by the authors for handling arbitrary non-linear systems, is discussed. The utility of the neural network approach is demonstrated by application to several illustrative problems.