Structural Vibrations

This chapter first presents the basic vibration theories for beams, plates, and shells, and then provides details on how fast different waves travel through solids and how they can reinforce each other in finite structures to form modes. It shows how those modes define a structure's mobility. In impedance functions, resonances appear as sharp dips, indicating frequencies where the structural impedance is weak. Conversely, high impedances correspond to anti-resonances, which occur when a drive is adjacent to a node of a mode. The chapter also shows an example of measured glass plate mobilities, along with the drive point mobility of an infinite glass plate, computed using the well-known formula for bending waves in infinite flat plates. Finally, it examines the coupled oscillator problem analytically, as well as numerically, and extends the analysis to coupling the modal energies of groups of coupled oscillators.