Uniform String Dynamics
To more easily understand a mathematical description of the mechanics associated with the structural dynamics of continuous elastic systems, the classical “vibrating – string problem” is first considered. Although the free-vibration of a string can be described by the linear second-order partial differential equation in one dimension derived in Chapter 2 (see Eq. 2.26), it is typically descriptive of the more complex linearly elastic systems of aerospace vehicles. After the fundamental concepts are reviewed for the string, other components that are more representative of these vehicles are discussed. Although the free vibration of a string can be analyzed using equations of motion of the same form as those governing uniform beam extensional and torsional vibrations, the string is chosen as our first example primarily because—in contrast to the behavior of the other structures—string behavior can be visualized easily. Moreover, typically by this time in their undergraduate studies, most students have had some exposure to the solution of string-vibration problems.