“…Yin T. and Lam H.F [10,11] used a new solution method for investigation of the vibration characteristics of finite-length circular cylindrical shells with a circumferential part-through crack with four representative sets of boundary conditions being considered: simply supported, clamped-clamped, clamped-simply supported, and clamped-free. Li D. H., Yang X., Qian R. L., and Xu D. [12,13] used the extended layer method (XLWM) to analyze the static reaction, free vibration, and transient response of cracked FGM plates.…”