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.

### Coupled bending and torsional free vibrations of beams with in-span supports and attached masses

#### Abstract

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.
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2017
Coupled bending-torsional vibration; Free vibration; Generalized functions; Elastic supports; Attached masses
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/20.500.12318/1505`