Dynamic response of structures constructed from smart materials

The dynamic analysis of structures constructed of homogeneous smart materials is greatly simplified by the observation that the eigenfunctions of such structures are identical to those of the same structures constructed entirely of purely elastic materials. The dynamic analysis of such structures is thus reduced to the analysis of the temporal behaviour of the eigenmodes of the structure. The theory is illustrated for both continuous and discrete structures using the generalization of 'positive position feedback' to distributed control

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

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

Response of a nonlinear string to random loading

This paper considers the response of a nonlinear string to random excitation. It is shown that, owing to the additional stress induced by the stretching of the string, the mean squared deflection at every point is smaller than that for the equivalent linear string

Whirling of a heavy chain

Approximate solutions are obtained for the non-linear problem of the forced whirling of a heavy chain. It is shown that for a given mode of whirling, triple valued solutions are obtained for speeds of rotation above the linear critical speed for that mode. It is also shown that two of these solutions are stable while the third is unstable

Comments on "On the Stability of Random Systems"

Dr. Samuels [1] is to be congratulated on a most interesting paper. It is unfortunate that a number of errors appear in Sec. III which invalidate both that section and Sect. IV

The Steady-State Response of a Class of Dynamical Systems to Stochastic Excitation

In this paper a class of coupled nonlinear dynamical systems subjected to stochastic excitation is considered. It is shown how the exact steady-state probability density function for this class of systems can be constructed. The result is then applied to some classical oscillator problems

Effect of Damping on the Natural Frequencies of Linear Dynamic Systems

An analysis is presented of the effect of weak damping on the natural frequencies of linear dynamic systems. It is shown that the highest natural frequency is always decreased by damping, but the lower natural frequencies may either increase or decrease, depending on the form of the damping matrix

Attitude stability of spinning satellites

Since the attitude instability experience by Explorer 1, many papers have been written on the effects if internal dissipation on the attitude stability of spinning satellites. In the engineering literature, stability analysis is restricted to the variational or linearized perturbational equations, despite the fact that spinning satellites are almost always critical cases in the Liapunov-Poincaré stability theory. This is certainly true in the case of dual spin satellites, which have the further complication that the linearized perturbational equations have periodic coefficients. The purpose of this note is to treat some problems of attitude stability of spinning satellites in a rigorous manner and to show that, with certain restrictions, the linearized stability analysis correctly predicts the attitude stability of spinning satellites

Structural dynamics analyses testing and correlation

This report examines some aspects of the lack of close correlation between the predictions of analytical modeling of dynamic structures and the results of vibration tests on such structures, and suggests ways in which the correlation may be improved