Eigenfrequencies and eigenmodes of anisotropic thick cylindrical shell

Abstract

Thick cylindrical shells are used in various applications, and there are many studies on strength and vibration analysis. In vibration analysis of isotropic and orthotropic thick cylindrical shells, it is commonly assumed that displacements are affected by rotational inertia and shear deformation and the shell thickness does not change during deformation. On the other hand, vibration analysis of orthotropic cylinders has been studied based on three-dimensional analysis theory without these assumptions. However, vibration analysis of thick cylindrical shells based on three-dimensional analysis theory has not been conducted. Previously, we studied an orthotropic parallelepiped as a single continuum and reported the relationships between dimensions and natural angular frequencies and vibration modes. In this report, a thick cylindrical shell with deformation in thickness direction and orthotropy is investigated. The natural angular frequencies and modal functions of the axisymmetric vibration are derived using three-dimensional analytical theory. In the calculation example, the relationship between dimensionless axial wavenumber and natural angular frequencies and modal functions of the model with varying thickness ratios are illustrated. The frequency veering of natural angular frequencies occurs, and the wavenumber where the frequency veering occurs depends on the thickness ratio. The number of radial nodes varies independently of the frequency veering, and the sign of the slope of radial node vs. dimensionless wavenumber changes around the wavenumber where veering occurs. The number of axial nodes and their positions vary only around the value of the wavenumber where veering occurs.