TRANSVERSE VIBRATION OF MULTI MASS LOADED VARIABLE SECTION BEAMS UNDER RANDOM EXCITATION

Dynamic analysis of non-uniform section beams with general end conditions having arbitrary mass and stiffness distributions and proportional viscous damping distribution with several arbitrarily located point mass loadings has been presented for non-stationary random input excitation. Modal analysis has been employed to obtain expressions for second order response statistics after decoupling the system equations. The natural frequencies and mode shape functions for such beams are obtained in closed form as an intermediate step in the outlined approach. Theoretical results for natural frequencies have been compared with experimental evaluations and with data available in the literature. The complete approach is illustrated with an example of a cantilever beam subjected to support excitation.