Application of Vectorial Wave Method in Free Vibration Analysis of Cylindrical Shells (Advances in Applied Mathematics and Mechanics, 2018)
The vectorial form of the Wave Propagation Method (VWM), regarding thedispersion of harmonic plain (elasto-dynamic) waves within certain wave-guides, isdeveloped 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 theshell axis. Based on the Flügge thin shell theory, the shell continuity as well as boundaryconditions are well satisfied by introducing the propagation and reflection matrices.Furthermore, all elements of the reflection matrix are derived for certain classicalsupports. As an example, for demonstrating the feasibility of VWM in the shell vibrationanalysis, 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 excellentagreement. It is also found that VWM could mathematically provide a reduceddimensional matrix (dominant matrix) to calculate the natural frequencies of the system.Accordingly, the proposed method can provide high computational efficiencyand remarkable accuracy, simultaneously.