Dynamic response to harmonic transverse excitation of cantilever Euler-Bernoulli beam carrying a point mass

Abstract

In this paper, the calculation of the dynamic response to harmonic transverse excitation of cantilever Euler-Bernoulli beam carrying a point mass with the mode superposition method is presented. This method uses mode shapes and modal coordinate functions which are calculated by separation of variables and Laplace transformations. The accuracy of defined expressions is confirmed on examples with and without Rayleigh damping. All calculations are in good agreement with the results of commercial software based on finite element methods.

Keywords

• dynamic response
• euler-bernoulli beam
• point mass
• mode superposition method
• rayleigh damping