General theory of vibrations of cylindrical tubes. PART-III. Uncoupled flexural vibrations of closed tubes

Abstract

Flexural vibration characteristics of unstiffened doubly symmetric cylindrical tubes are studied using the theory proposed by the authors in part I. An exact solution of a simply supported tube with the cross-section given by x= s²/4π² sin 2πS/S is presented. Natural frequencies of a 'simply supported tube of rectangular cross-section are obtained by using first and second order approximation equations. Numerical results indicate that it is essential to consider, at least, second order approximation equations to study the flexural vibration characteristics of doubly symmetric tubes.