A Dynamic Matrix for the Study of Free Vibrations of Thin Circular Cylindrical Shells under Different Boundary Conditions

Abstract

Although free vibrations of thin-walled cylinders have been extensively addressed in the relevant literature, finding a good balance between accuracy and simplicity of the procedures used for natural frequency assessment is still an open issue. This paper proposes a novel approach with a high potential for practical application for rapid esteem of natural frequencies of thin-walled cylinders under different boundary conditions. Starting from Donnell–Mushtari’s shell theory, the differential problem is simplified by using the principle of virtual work and introducing the flexural waveforms of a beam as constrained as the cylinder. Hence, the formulation is reduced to the eigenvalue problem of an equivalent 3 × 3 dynamic matrix, which depends on the cylinder geometry, material, and boundary conditions. Several comparisons with experimental, numerical, and analytical approaches are presented to prove model reliability and practical interest. An excellent balance between fast usability and accuracy is achieved. The user-friendliness of the model makes it suitable to be implemented during the design stage without requiring any deep knowledge of the topic.

Keywords

• thin-walled cylinder
• free vibrations
• natural frequencies
• eigenvalue problem
• closed-form solution