<p>A numerical scheme grounded on the Boundary Element Method expressed in the Frequency Domain is proposed to perform Nonsmooth Modal Analysis of one-dimensional bar systems. The latter aims at finding continuous families of periodic orbits of mechanical components featuring unilateral contact constraints. The proposed formulation does not assume a semi-discretization in space of the governing Partial Differential Equations, as achieved in the Finite Element Method, and so mitigates a few associated numerical difficulties, such as chattering at the contact interface, or the questionable approximation of internal resonances.&nbsp; The unknowns of this numerical methods are on the boundary, and boundary states are assumed as discrete Fourier series to enforce periodicity. The nonsmooth Signorini condition stemming from the unilateral contact constraints is enforced in a weighted residual sense via the Harmonic Balance Method. Periodic responses are investigated in the form of energy-frequency backbone curve along with the associated displacement fields. The two-bar system including a spring-attched bar contacting with a clamped bar, for which no known results are reported in the literature, exhibits very rich nonsmooth modal dynamics with entangled nonsmooth modal motions combining hardening and softening effects via the intricate interaction of various, possibly subharmonic and internally resonant nonsmooth modes of the two bars.</p>

Nonsmooth Modal Analysis of a Two-Bar System via Boundary Element Method

Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2021/volume/85369

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