A novel statistical linearization solution for randomly excited coupled bending-torsional beams resting on non-linear supports. (English) Zbl 1532.74071
Summary: 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.
MSC:
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |
| 74S60 | Stochastic and other probabilistic methods applied to problems in solid mechanics |
Keywords:
statistical linearization; coupled bending-torsional vibrations; nonlinear supports; random loads; Monte Carlo simulationsReferences:
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