Wave propagation and group velocity

Finite element analysis of the vibrations of waveguides and periodic structures

The present work addresses the question of guided wave properties in structures. Guided multi-modal dispersion curves and diffusion of waves at singularities are the main concern. A propagative approach, based on a finite element model, is formulated. It provides an effective way to calculate the dispersion curves of complex guided structures. Some properties of guided waves are deduced from the formulation. The question of wave diffusion at substructures coupling locations is also considered. A closed formulation of the problem using Lagrange multipliers is presented. Its numerical implementation is detailed. Ultimately, a numerical test is offered. The case study concerns a thin walled structure.

Multi-mode propagation and diffusion in structures through finite elements

This paper introduces the point of view that elastic deformations in large spacecraft structures may be aptly viewed in terms of propagating disturbances. Since the main topic of this paper is the control concepts, which result from such a viewpoint, the required structural dynamic description in terms of travelling disturbances is described only briefly, with reference to previously published works. The active control of these structures is approached from the point of view of actively modifying the natural disturbance propagation paths. Elastic energy is shunted into unimportant portions of the structure or is absorbed by an active "wave absorber." Several computational examples demonstrate the remarkable theoretical performance achievable by propagation-based controllers. Some discussion of practical difficulties in the implementation of such controllers is included.

Traveling wave control for large spacecraft structures

A survey of vibration localization phenomena in the context of structural dynamics and vibrations is presented The review covers the more common and relevant cases where mode localization and vibration confinement are likely to occur in engineering structures Examples considered include periodic or nearly periodic multi-span beams and multi-bay trusses, large space structures, space antennas, and almost periodic (ap) structures with circular symmetry, eg, bladed disks in turbomachines Both analytical and numerical methods for analyzing and predicting localization in finite and infinite systems are discussed In this paper, we show how the problem of mode localization and vibration confinement can be formulated as a problem in the theory of stability of differential equations with ap coefficients Using stability theory, new definitions of mode localization can be established for both linear and nonlinear structures The possibility of stabilizing certain nonconservative fluid-structure systems using structural disorder is demonstrated, and stability theorems are given for aeroelastic systems governed by normal operators We also illustrate how the results from localization theory and the associated stability theory can be applied to the vibration control problem, by triggering vibration confinement by active or passive means

Localization phenomena in structural dynamics

A structural network is taken to be an assemblage of slender structural members (beams, cables, rods) connected to each other at structural junctions. The junctions may include flexible bodies which, in this work, are restricted to those whose dynamics are described by a finite set of ordinary differential equations. Elastic disturbances in such a network are calculated in terms of propagation concepts. Members are described in the frequency domain by the propagation coefficients of their intrinsic wave-modes, junctions by frequency-dependent wave-mode reflection and transmission coefficients, grouped in the junction scattering matrix. Component impulse responses are calculated by a combination of analysis and application of the fast Fourier transform algorithm. Network time responses are synthesized by convolution of component impulse responses. A consistent analytical framework is constructed within which descriptions of various member types and junctions can be accommodated. The analysis is set up for computer implementation. Computational examples are used to demonstrate the techniques.

A.H. von Flotow

Papers

Disturbance propagation in structural networks