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Moving boundary value problems in the dynamics of structures

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WHTW01 - Factorisation of matrix functions: New techniques and applications

The dynamics of structures partially inserted into a frictionless sliding sleeve defines a moving boundary value problem revealing the presence of an outward configurational force at the constraint, parallel to the sliding direction. The configurational force, differing from that obtained the quasi-static case only for a negligible proportionality coefficient, strongly affects the motion and introduces intriguing structural dynamic response. This will be shown through the two following problems:
The sudden release of a rod with a concentrated weight attached at one end [1]. The solution of a differential-algebraic equation (DAE) system provides the evolution, where the elastic rod may slip alternatively in and out from the sliding sleeve. The nonlinear dynamics eventually ends with the rod completely injected into or completely ejected from the constraint;
  The vibrations of a periodic and infinite structural system [2]. Through Bloch-Floquet analysis it is shown that the band gap structure for purely longitudinal vibration is broken so that axial propagation may occur at frequencies that are forbidden in the absence of a transverse oscillation.
Moreover, conditions for which flexural oscillation may induce axial resonance are disclosed.  
The results represent innovative concepts ready to be used in advanced applications, ranging from soft-robotics to earthquake protection.  

Acknowledgments: Financial support from the Marie Sklodowska-Curie project 'INSPIRE – Innovative ground interface concepts for structure  protection' PITN -GA-2019-813424-INSPIRE.  

[1]  Armanini, Dal Corso, Misseroni, Bigoni (2019). Configurational forces and nonlinear structural dynamics. J. Mech. Phys. Solids, doi: 10.1016/j.jmps.2019.05.009
[2] Dal Corso, Tallarico, Movchan, Movchan, Bigoni, (2019). Nested Bloch waves in elastic structures with configurational forces. Phil. Trans. R. Soc. A, doi: 10.1098/rsta.2019.0101

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