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Coupled Systems Mechanics Volume 5, Number 2, June 2016 , pages 157-190 DOI: https://doi.org/10.12989/csm.2016.5.2.157 |
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Frequency analysis of beams with multiple dampers via exact generalized functions |
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Giuseppe Failla
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| Abstract | ||
| This paper deals with frequency analysis of Euler-Bernoulli beams carrying an arbitrary number of Kelvin-Voigt viscoelastic dampers, subjected to harmonic loads. Multiple external/internal dampers occurring at the same position along the beam axis, modeling external damping devices and internal damping due to damage or imperfect connections, are considered. The challenge is to handle simultaneous discontinuities of the response, in particular bending-moment/rotation discontinuities at the location of external/internal rotational dampers, shear-force/deflection discontinuities at the location of external/internal translational dampers. Following a generalized function approach, the paper will show that exact closed-form expressions of the frequency response under point/polynomial loads can readily be derived, for any number of dampers. Also, the exact dynamic stiffness matrix and load vector of the beam will be built in a closed analytical form, to be used in a standard assemblage procedure for exact frequency response analysis of frames. | ||
| Key Words | ||
| Euler-Bernoulli beam; dynamic Green | ||
| Address | ||
| Giuseppe Failla: Department of Civil, Environmental, Energy and Materials Engineering, University of Reggio Calabria Via Graziella, 89124 Reggio Calabria, Italy | ||
