Dynamic dispersion curves for non-homogeneous, anisotropic beams with cross sections of arbitrary geometry

Abstract

Abstract To accurately predict the dynamic behaviour of spanwise uniform, non-homogeneous, anisotrophic beams with arbitrary cross-sectional geometry is an important part of engineering analysis. Classical one-dimensional beam theory fails in this endeavour, and development of more sophisticated one-dimensional theories is an important task. A basis for development of improved one-dimensional theory is the dispersion curve analysis. A means to find the dispersion curves is discussed in this paper. The code is developed to calculate the dispersion curves, as well as corresponding mode shapes. The code is based on finite element discretization over the cross-sectional domain. Use of this code provides benchmark results for the testing of any existing one-dimensional theory, as well as facilitating the construction of new one-dimensional theories. Dispersion information can also be useful in non-destructive evaluation. As an example of a case where non-classical effects are particularly important, results obtained from this code for an I-beam are presented. Qualitative comparisons with the well-known case of isotropic rectangular beam is provided. Features that are common for all beams are emphasized along with pointing out qualitative differences that exist for beams other than rectangular or circular.