Low-frequency behavior in a frictionally excited beam

A cantilevered beam excited by a periodically reciprocating friction contact surface exhibited extremely low-frequency responses (with frequencies as low as 100 times lower than the driver). Example responses near 1:1 and 1:2 resonances, between the excitation and the degree of freedom normal to the direction of sliding, show two-frequency quasiperiodicity, and in one case three-frequency quasiperiodicity. Underlying circle maps were extracted, and winding numbers were matched to response frequencies quantified in the fast Fourier transforms of the responses. A torus doubling bifurcation was documented.