Geodesic
Periodic wave propagation in nonlocal beams resting on a bilinear foundation
Theoretical and applied mechanics, Tome 50 (2023) no. 2.

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The free wave propagation of periodic flexural waves on an infinite elastic Euler--Bernoulli nonlocal beam embedded in bilinear Winkler-type foundation is investigated. A general formulation of the elastic potential energy leads to a nonlinear nonlocal model with spatial derivatives up to the sixth order. The effect of the nonlocal parameters and of the different soil stiffnesses on the dynamical characteristics of the system is critically discussed. An enrichment of the system response with respect to the local beam is unveiled, and the crucial role played by the sixth-order nonlocal term is highlighted.
Keywords: wave propagation, bilinear foundation, nonlocal theory, Euler-Bernoulli beam, single wave 
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     author = {Valeria Settimi and Stefano Lenci},
     title = {Periodic wave propagation in nonlocal beams resting on a bilinear foundation},
     journal = {Theoretical and applied mechanics},
     pages = {117 - 131},
     publisher = {mathdoc},
     volume = {50},
     number = {2},
     year = {2023},
     url = {http://geodesic.mathdoc.fr/item/TAM_2023_50_2_a2/}
}
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Valeria Settimi; Stefano Lenci. Periodic wave propagation in nonlocal beams resting on a bilinear foundation. Theoretical and applied mechanics, Tome 50 (2023) no. 2. http://geodesic.mathdoc.fr/item/TAM_2023_50_2_a2/