Application of Vectorial Wave Method in Free Vibration Analysis of Cylindrical Shells
The vectorial form of the Wave Propagation Method (VWM), regarding the
dispersion of harmonic plain (elasto-dynamic) waves within certain wave-guides, is
developed for the vibration analysis of circular cylindrical shells. To obtain this goal,
all plain waves are divided into positive-negative going wave vectors along with the
shell axis. Based on the Fl ¨ugge thin shell theory, the shell continuity as well as boundary
conditions are well satisfied by introducing the propagation and reflection matrices.
Furthermore, all elements of the reflection matrix are derived for certain classical
supports. As an example, for demonstrating the feasibility of VWM in the shell vibration
analysis, a circular cylindrical shell with two ended flexible support is adopted.
The natural frequencies of the system as well as mode shapes are obtained using VWM.
The aquired results are compared with those of the previous works and found in excellent
agreement. It is also found that VWM could mathematically provide a reduced
dimensional matrix (dominant matrix) to calculate the natural frequencies of the system.
Accordingly, the proposed method can provide high computational efficiency
and remarkable accuracy, simultaneously.
