A mathematical model for the large deflection dynamics of a compliant beam device is presented. The device simulates the motion of a slider-crank device. The system contains a highly flexible beam that provides the compliant motion from a sliding mass at one end to a rotating hinge point at the other end. Basic models for friction and beam dissipation effects are included. A nonlinear integro-partial differential equation is derived for the complete beam/mass system in the curved space of the deformed beam. The resulting equation is cast into a generalized nondimensional form suitable for studying system behavior for a broad range of system sizes. The dynamic equation is solved in curved space by applying a spatial solution that closely represents the large static deflection measured for the beam. The nonlinear system dynamics are simulated for an initial large deflection of the system and compared to experimental results for an actual physical system.

Issue Section:
Technical Briefs
Keywords:
dynamics, integro-differential equations, nonlinear differential equations, partial differential equations, friction, damping, distributed parameter systems, flexible structures, nonlinear dynamical systems
Topics:
Deflection, Dynamics (Mechanics), Friction, Partial differential equations, Damping, Differential equations, Hinges
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