Determination of ultrasonic vibration modes of a graded solid cylinder using a modified wave‐expansion technique.

Abstract

Research on wave propagation in cylinders—hollow, solid, or graded—has been driven by its potential use in the inspection of long‐span engineering structures. Its practical application largely depends on the understanding of modal vibration inside the structure. Typically, the plane wave approach is used to model phase velocity, group velocity and dispersion curves in periodic systems. This proves cumbersome when used to model finite periodic structures, semifinite plates, or concentric cylinders. Here, a simpler approach to determine the vibration modes and dispersion curves of a solid concentric cylinder using a modified wave‐expansion approach, used mostly in phononic crystals research, is proposed. The advantage of this technique is the possible application on a wide variety of cylindrical geometries and graded structures with various transverse sections. The results of the proposed technique are compared with those obtained by the resonance scattering theory for the simple case of a solid cylinder with a single core having different mechanical properties. [Work partially sponsored by SEP‐CONACYT through project # 58951.