, Volume 54, Issue 9, pp 1365–1383 | Cite as

Random vibration mitigation of beams via tuned mass dampers with spring inertia effects

  • Giuseppe FaillaEmail author
  • Mario Di Paola
  • Antonina Pirrotta
  • Andrea Burlon
  • Iain Dunn
Stochastics and Probability in Engineering Mechanics


The dynamics of beams equipped with tuned mass dampers is of considerable interest in engineering applications. Here, the purpose is to introduce a comprehensive framework to address the stochastic response of the system under stationary and non-stationary loads, considering inertia effects along the spring of every tuned mass damper applied to the beam. For this, the key step is to show that a tuned mass damper with spring inertia effects can be reverted to an equivalent external support, whose reaction force on the beam depends only on the deflection of the attachment point. On this basis, a generalized function approach provides closed analytical expressions for frequency and impulse response functions of the system. The expressions can be used for a straightforward calculation of the stochastic response, for any number of tuned mass dampers. Numerical results show that spring inertia effects may play an important role in applications, affecting considerably the system response.


Beam Tuned mass damper Spring inertia effects Generalized function Stochastic response 



The authors gratefully acknowledge the financial support of PRIN 2015: “Advanced Mechanical Modeling of New Materials and Structures for the Solution of 2020 Horizon Challenges”. PI: prof. Mario Di Paola, University of Palermo, Italy.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Civil, Energy, Environmental and Materials Engineering (DICEAM)University of Reggio CalabriaReggio CalabriaItaly
  2. 2.Department of Civil, Environmental, Aerospace and Materials Engineering (DICAM)University of PalermoPalermoItaly

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