On the dynamics of viscoelastic discontinuous beams

• Beams with Kelvin–Voigt viscoelastic rotational joints, translational supports, and lumped masses are studied.
• Discontinuous response variables are treated by the theory of generalized functions.
• Exact closed-form eigenfunctions inherently fulfilling the required internal conditions are derived.
• Exact characteristic equation is built as determinant of a 4 × 4 matrix for any number of discontinuity points.
• Forced vibrations are solved by modal superposition based on orthogonality conditions of eigenfunctions.

This paper concerns the dynamics of beams with an arbitrary number of Kelvin–Voigt viscoelastic rotational joints, translational supports, and attached lumped masses. Using the theory of generalized functions to treat the discontinuities of the response variables, the free vibration problem is solved upon deriving exact closed-form eigenfunctions, that inherently fulfill the required conditions at the discontinuity points. The forced vibration response is computed in time and frequency domain by modal superposition, based on appropriate orthogonality conditions of the eigenfunctions.