Band gaps in phononic crystal beam-foundation systems

Phononic crystal (PC) beam-foundation systems are introduced to study the flexural vibration band gaps (BGs). Two general beam types, Euler beam and Timoshenko beam, are both considered. The finite periodic structures are constructed to describe the PCs in practice. The finite element analysis of the finite periodic structures shows that the stiffness of foundation influences the distribution of BGs. Moreover, the PC Timoshenko beam-foundation system has wider applicability in the engineering than the system with Euler beam. The periodic numbers of the finite structures affect the attenuation in BGs; the more periodic numbers give more distinct BGs.