TABLE OF CONTENTS The essential tools needed for analyzing the structural dynamics of rotorcraft must address a variety of issues. The principal problem areas are characterized by 1) small motions, usually sinusoidal in nature; 2) several degrees of freedom of motion; and 3) a variety of loadings arising from rotational effects. Much attention is therefore paid to identifying and reviewing pertinent methods for analyzing linear dynamic systems, starting from the simplest configuration (single degree of freedom) and progressing to general configurations involving several degrees of freedom. Basic techniques dealing with "frequency-domain" problems are also identified and reviewed.
The archetypical dynamic system to be understood and used repeatedly as an analog for understanding more complicated systems is the single-degree-of-freedom (spring-mass-damper) system shown in Fig. 2.1, where the force elements can be assigned engineering units [ U( ), based on lbf, ft, and s], given as
| (2.1a) |  |
| (2.1b) |  |
| (2.1c) |  |
| (2.1d) |  |
The appropriate dynamic equation is obtained by taking the mass as a free body and examining and equilibrating the forces acting on it. One indispensable tool for analyzing dynamic systems is D' Alembert's principle, which allows the conversion of dynamic problems to static ones. Typical usage of this principle consists of representing the statement of Newton's second law (that F = ma) by an inertial load equal to ma, but directed opposite to the acceleration a. With this approach the forces acting on the mass can be equilibrated, as shown in Fig. 2.2, where the individual...
