Critical Frequencies of Composite Cylindrical Shells

Abstract

The sound radiation characteristics of a structure depend on its critical frequency. The expression for theoretically estimating the critical frequency of a composite cylindrical shell has not yet been reported. Thus, the practice is to use the expression for the composite panel for determining the critical frequency of a composite shell. In this work, critical frequencies of composite shells are investigated. As the critical frequency depends on the speed of the bending wave, an expression for the speed of the bending wave is first derived. It is seen that the curvature causes an increase in the speed of the bending wave and the orthotropic nature of the cylinder reduces the speed. An expression for the critical frequency of a composite cylindrical shell is then derived. The curvature causes a reduction in the critical frequency and the influence is significant in acoustically thick cylinders. Hence, the critical frequencies of such cylinders cannot be determined by using the expression for the panels. Effects of transverse shear deformation on the speed of the bending wave as well as the critical frequency are then investigated. Transverse shear deformation causes both reduction in the speed of the bending wave and an increase in the critical frequency. The orthotropic nature of the cylindrical shell increases the critical frequency further. The critical frequency of a typical composite cylinder is determined through a numerical simulation and the results are in agreement with the results obtained using the expressions derived. The critical frequency of a typical composite cylinder obtained through an experiment is presented. With this work, expressions for theoretically estimating the speeds of the bending waves and critical frequencies are derived for a composite cylindrical shell considering transverse shear deformation.