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

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

A Test Program to Measure Fluid Mechanical Whirl-Excitation Forces in Centrifugal Pumps

Much speculation has surrounded the possible unsteady hydrodynamic forces which could be responsible for the excitation of whirl instabilities in turbomachines. However there exist very few measurements of these forces which would permit one to evaluate the merits of the existing fluid mechanical analyses. In keeping with the informal nature of this workshop we will present details of a proposed test program for the measurement of the unsteady forces on centrifugal impellers caused by either (i) azimuthal asymmetry in the volute geometry or (ii) an externally imposed whirl motion of the impeller. In the second case the forces resulting from the imposed whirl motions with frequencies ranging from zero to synchronous will be measured by means of a force balance upon which the impeller is mounted. This work is presently being carried out under contract with the NASA George Marshall Space Flight Center, Huntsville, Alabama (Contract NAS 8-33108)

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