Free and Forced Vibrations of an Undamped Double-Beam System Carrying a Tip Mass with Rotary Inertia

Many civil and mechanical engineering structures can be simplified as double-beam systems, i.e., a primary beam and a secondary beam connected to the primary beam. Many studies have investigated the vibration characteristics of double-beam systems. Those studies investigated the influences of boundary and connecting conditions of two beams on vibration frequency, mode shape, and dynamic responses of the system. None of the previous studies considered a tip mass on the double-beam system. Because some structures that support weight on their tip, such as a wind farm tower with a core that supports a nacelle at the top can for analysis be simplified as a double-beam system, it is therefore necessary to investigate the vibration characteristics of double-beam systems with a tip mass. In the present study, free and forced vibrations of an undamped double-beam system carrying a mass with rotary inertia at the tip of the primary beam are analytically investigated, based on the Euler-Bernoulli beam theory. Comprehensive parametric studies are carried out to investigate the influences of the key parameters of the double-beam system, including tip mass, rotary inertia, elastic layer stiffness connecting the two beams, and mass and rigidity ratio of the secondary beam to primary beam, on the vibration frequencies and dynamic responses of the system. Analytical results show that different parameters have different sensitivities on the system's vibration characteristics, and the tuned mass damper (TMD) theory can be used to explain the structural responses.