Abstract
This paper develops a method of forced vibration analysis for a stepped cantilever beam with an elastically coupled rigid body at its intermediate point, according to the standard modal analysis. Starting from governing equations (one PDE, one ODE and boundary conditions,) the deflection function of PDE is then lifted into piecewise continuous functions at mechanical discontinuities. Using corresponding mode functions for the beam vibration and the rigid body motion, which are obtained in free vibration analysis, the problem is cast into solving a set of DAEs under boundary conditions. By establishing orthogonality and normalization conditions of the mode functions, a method of forced vibration analysis is finally derived. These conditions are considered as extended results of existing ones and main contributions of this work. Steady-state and transient responses can be computed analytically. The proposed method is primarily expected to serve as an alternative to FEM based vibration analysis, but it can also be utilized in designing vibration systems.
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