In this work a numerical and experimental study of nonlinear motion confinement phenomena in a nonlinear flexible assembly with vibro‐impacts is carried out. The assembly consists of two coupled cantilever beams whose motion is constrained by rigid barriers. In the theoretical model the impact nonlinearities are simulated by clearance nonlinearities with steep stiffness characteristics; special care is taken to model energy dissipation due to inelastic impacts. The theoretical results confirm that the vibro‐impact system possess motion confinement properties. Both transient and steady state motions are studied, and it is shown that under certain conditions the vibrational energy of the system is passively confined to only one of the two beams. These essentially nonlinear responses exist inspite of direct coupling between the two beams, and have no analogs in linear theory. The experimental results confirm the theoretical predictions both in the transient and steady state regimes. The passive nonlinear motion confinement phenomena reported in this and previous works can be utilized to enhance the controllability of flexible structures with symmetries, and to improve current shock and vibration isolation designs of such systems.
The interaction dynamics of a cantilever linear beam coupled to a nonlinear pendulum, a prototype for linear/nonlinear coupled structures of infinite degrees-of-freedom, has been studied analytically and experimentally. The spatio-temporal characteristics of the dynamics is analyzed by using tools from geometric singular perturbation theory and proper orthogonal decompositions. Over a wide range of coupling between the linear beam and the nonlinear pendulum, the coupled dynamics is dominated by three proper orthogonal (PO) modes. The first two dominant PO modes stem from those characterizing the reduced slow free dynamics of the stiff/soft (weakly coupled) system. The third mode appears in all interactions and stems from the reduced fast free dynamics. The interaction creates periodic and quasi-periodic motions that reduce dramatically the forced resonant dynamics in the linear substructure. These regular motions are characterized by four PO modes. The irregular interaction dynamics consists of low-dimensional and high-dimensional chaotic motions characterized by three PO modes and six to seven PO modes, respectively. Experimental tests are also carried out and there is satisfactory agreement with theoretical predictions.
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