Earl H. Dowell - Böcker

The great bulk of the literature on aeroelasticity is devoted to linear models. The­ oretical work relies heavily on linear mathematical concepts, and experimental results are commonly interpreted by assuming that the physical model behaves in a linear manner. Nevertheless, significant work has been done in nonlinear aero­ elasticity, and one may expect this trend to accelerate for several reasons: our ability to compute has increased at an astonishing rate; as linear concepts have been assimilated widely, there is a natural increase in interest in the foundations of nonlinear modeling; and, finally, some phenomena long recognized to be of interest, but beyond the effective range of linear models, are now known to be essentially nonlinear in nature. In this volume, an exhaustive review of the literature is not attempted. Rather the emphasis is on fundamental ideas and a representative selection of problems. Despite obvious successes in research on problems of aeroelasticity and the existence of a broad literature, including a number of excellent monographs, up to now little attention has been devoted to a general nonlinear theory of interac­ tion. For the most part nonlinearity has been considered either solely in the description of the behavior of a shell or in the description of the motion of a gas.

While the field began in response to the rapid development of aviation, it has now expanded into many branches of engineering and scientific disciplines and treats physical phenomena from aerospace engineering, bioengineering, civil engineering, and mechanical engineering in addition to drawing the attention of mathematicians and physicists.

While the field began in response to the rapid development of aviation, it has now expanded into many branches of engineering and scientific disciplines and treats physical phenomena from aerospace engineering, bioengineering, civil engineering, and mechanical engineering in addition to drawing the attention of mathematicians and physicists.

This book describes the Asymptotic Modal Analysis (AMA) method to predict the high-frequency vibroacoustic response of structural and acoustical systems. Then the development of AMA is presented for an individual structural system and an individual acoustic cavity system, as well as a combined structural-acoustic system.

Many books on dynamics start with a discussion of systems with one or two degrees of freedom and then turn to the generalization to the case of many degrees of freedom. For linear systems, the concept of eigenfunctions provides a compact and elegant method for decomposing the dynamics of a high dimensional system into a series of independent single-degree-of-freedom dynamical systems. Yet, when the system has a very high dimension, the determination of the eigenfunctions may be a distinct challenge, and when the dynamical system is nonconservative and/or nonlinear, the whole notion of uncoupled eigenmodes requires nontrivial extensions of classical methods. These issues constitute the subject of this book.

Many books on dynamics start with a discussion of systems with one or two degrees of freedom and then turn to the generalization to the case of many degrees of freedom. For linear systems, the concept of eigenfunctions provides a compact and elegant method for decomposing the dynamics of a high dimensional system into a series of independent single-degree-of-freedom dynamical systems. Yet, when the system has a very high dimension, the determination of the eigenfunctions may be a distinct challenge, and when the dynamical system is nonconservative and/or nonlinear, the whole notion of uncoupled eigenmodes requires nontrivial extensions of classical methods. These issues constitute the subject of this book.