Analog methods in computation and simulation dating, analog methods in computation and simulation.
Two types of excitations are examined: The first method is applicable to systems having cubic nonlinearities. Stationary solutions of the moment equations are determined and their stability is ascertained by examining the eigenvalues of the Jacobian matrix.
Floquet theory is used to analyze the stability of periodic responses. For a single degree of freedom system, the response of a simply supported buckled beam to parametric excitations is investigated. The results are compared with those obtained from numerical integrations of the moment equations and the exact stationary solution of the Fokker-Planck-Komologorov equation.
The perturbation results are verified by integrating the governing equation using both digital and analog computers.
Deterministic and stochastic responses of nonlinear systems The responses of nonlinear systems to both deterministic and stochastic excitations are discussed. The large amplitude responses are investigated by using simulations on a digital computer and are compared with results obtained using an analog computer.
For the nonlinear response to a harmonic axial load, the method of multiple scales is used to determine to second order the amplitude and phase modulation equations. The second method is applicable to systems having quadratic and cubic nonlinearities. The results are compared with those obtained from real-time analysis analog-computer simulation.
Bulletin of the American Mathematical Society
The results are compared with those obtained by numerically integrating the moment equations for the cases of Gaussian and non-Gaussian closure schemes. For two degree of freedom systems, two methods are used to study the response under the action of broad-band random excitations. A comparison between the responses to deterministic and random excitation is presented.
The methods used drastically reduce the computer effort and time.
For small excitation amplitudes, the analytical results are in good agreement with the numerical solutions. It involves an averaging approach to reduce the number of moment equations for the non-Gaussian closure scheme from 69 to 14 equations.
The normality assumption is examined. For the stochastic response to a wide-band random excitation, the Gaussian and non-Gaussian closure schemes are used to determine the response statistics.
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