When a structure is disturbed from its static equilibrium position, a motion ensues. When the motion involves a cyclic exchange of kinetic and strain energy, the motion is called a vibration. When this occurs under zero loads, it is called a free or natural vibration; whereas if the only loads are dissipative, then it is called a damped vibration. An example of a damped vibration is shown plotted in Figure 3.1; observe that the amplitudes eventually decreases to zero, but oscillates as it does so.
The explorations in this chapter consider the linear vibrations of structures. The first exploration uses a simple pretensioned cable to introduce the two basic concepts in vibration analyses; namely, that of natural frequency and mode shape. The second exploration looks at the meaning of mode shape in complex thin-walled structures. The stiffness properties are affected not only by the elastic material properties but also by the level of stress; the third exploration looks at the effect of prestress on the vibration characteristics. A significant insight into linear dynamics can be gained by analyzing it in the frequency domain. The fourth exploration introduces DiSPtool as the tool to switch between the time and frequency domains. Generally, increasing the mass of a structure decreases the vibration frequencies; however, in the presence of gravity, the mass can increase or decrease the stiffness and thereby affect the vibrations differently.