Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena.–Leonard Euler
As discussed in Chapter 1, both structural dynamics and aeroelasticity are built on the foundations of dynamics and structural mechanics. Therefore, in this chapter, we review the fundamentals of mechanics for particles, rigid bodies, and simple structures such as strings and beams. The review encompasses laws of motion, expressions for energy and work, and background assumptions. The chapter concludes with a brief discussion of the behavior of single-degree-of-freedom systems and the notion of stability.
The field of structural dynamics addresses the dynamic deformation behavior of continuous structural configurations. In general, load-deflection relationships are nonlinear, and the deflections are not necessarily small. In this chapter, to facilitate tractable, analytical solutions, we restrict our attention to linearly elastic systems undergoing small deflections—conditions that typify most flight-vehicle operations.
However, some level of geometrically nonlinear theory is necessary to arrive at a set of linear equations for strings, membranes, helicopter blades, turbine blades, and flexible rods in rotating spacecraft. Among these problems, only strings are discussed herein. Indeed, linear equations of motion for free vibration of strings cannot be obtained without initial consideration and subsequent careful elimination of nonlinearities.