Vibration of spring-supported massless beams with discrete masses

Versatile examples are essential in any engineering vibration course. However, most examples in current textbooks, especially those of multi-degree-of-freedom systems, are based on mass-spring systems. The system of spring-supported beams is explored in this report with the purpose of developing examples. Firstly, a method using the stiffness infl uence coeffi cient is illustrated in order to establish a vibration equation for a beam with three discrete masses. This is followed by a method using the fl exibility infl uence coeffi cient. Then we analyze a general case, with an arbitrary number of springs and masses, using the energy method. Finally, a reduced case with repeated natural frequencies is explored.