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

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

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

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

Aerodynamics of Engine-Airframe Interaction

The report describes progress in research directed towards the efficient solution of the inviscid Euler and Reynolds-averaged Navier-Stokes equations for transonic flows through engine inlets, and past complete aircraft configurations, with emphasis on the flowfields in the vicinity of engine inlets. The research focusses upon the development of solution-adaptive grid procedures for these problems, and the development of multi-grid algorithms in conjunction with both, implicit and explicit time-stepping schemes for the solution of three-dimensional problems. The work includes further development of mesh systems suitable for inlet and wing-fuselage-inlet geometries using a variational approach. Work during this reporting period concentrated upon two-dimensional problems, and has been in two general areas: (1) the development of solution-adaptive procedures to cluster the grid cells in regions of high (truncation) error;and (2) the development of a multigrid scheme for solution of the two-dimensional Euler equations using a diagonalized alternating direction implicit (ADI) smoothing algorithm

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