, Volume 54, Issue 9, pp 1307–1326 | Cite as

A novel statistical linearization solution for randomly excited coupled bending-torsional beams resting on non-linear supports

  • Andrea BurlonEmail author
  • Giuseppe Failla
  • Felice Arena
Stochastics and Probability in Engineering Mechanics


A novel statistical linearization technique is developed for computing stationary response statistics of randomly excited coupled bending-torsional beams resting on non-linear elastic supports. The key point of the proposed technique consists in representing the non-linear coupled response in terms of constrained linear modes. The resulting set of non-linear equations governing the modal amplitudes is then replaced by an equivalent linear one via a classical statistical error minimization procedure, which provides algebraic non-linear equations for the second-order statistics of the beam response, readily solved by a simple iterative scheme. Data from Monte Carlo simulations, generated by a pertinent boundary integral method in conjunction with a Newmark numerical integration scheme, are used as benchmark solutions to check accuracy and reliability of the proposed statistical linearization technique.


Statistical linearization Coupled bending-torsional vibrations Non-linear supports Random loads Monte Carlo simulations 


Compliance with ethical standards

Conflicts 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, Environmental, Energy and Materials Engineering (DICEAM)University “Mediterranea” of Reggio CalabriaReggio CalabriaItaly

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