This paper proposes an exact approach to coupled bending and torsional free vibration analysis of beams with monosymmetric cross section, featuring an arbitrary number of in-span elastic supports and attached masses. The proposed method relies on the elementary coupled bending-torsion theory and makes use of the theory of generalized functions to handle the discontinuities of the response variables. Based on a simple procedure, exact natural frequencies and closed-form eigenfunctions are calculated from a characteristic equation built as determinant of a 6×6 matrix, for any number of supports/masses. Likewise, the exact dynamic stiffness matrix of the beam is obtained in a closed form, with size 6×6 regardless of the number of supports/masses, to be assembled for frame analysis. In addition, the orthogonality condition among the eigenfunctions is derived. Two numerical examples show the advantages of the proposed exact method.
|Titolo:||Coupled bending and torsional free vibrations of beams with in-span supports and attached masses|
BURLON, Andrea (Corresponding)
|Data di pubblicazione:||2017|
|Appare nelle tipologie:||1.1 Articolo in rivista|