COMPARISON OF DIFFERENT THIN SHELL THEORIES FOR FREE VIBRATION ANALYSIS OF CYLINDRICAL SHELL

Abstract

In this thesis a study on the thin cylindrical shells have been done. Various thin shell theories have been studied. And further by using these theories free vibration frequency of a thin cylindrical shell which is made of isotropic aluminium material is observed. The material properties and dimensions of the cylindrical shell are given in the thesis. The cylindrical shell has been taken simply supported. Further to study the free vibration of simply supported circular cylindrical shells, a semi-analytical procedure is discussed in detail. In this technique, beam function is used as an approximation for simply supported boundary conditions. A literature review reveals that beam functions are used extensively in predicting natural frequencies of shells. Since this method does not involve with boundary condition equations, there is no need to deal with intense calculations. So this method was applied to ten different shell theories 1) Donnell-Mushtari, 2) Love-Timoshenko, 3) Arnold-Warburton, 4) Houghton-Johns, 5) Flugge-Byrne-Lur’ye, 6) Reissner-Naghdi-Berry, 7) Sanders, 8) Vlasov, 9) Kennard-Simplified and 10) Soedel . Natural frequency of the thin cylindrical shell has been found from these 10 theories and is compared in a table. The approximate procedure was compared favourably with experimental results.