Part 2: Proper Orthogonal Modal Modeling of a Frictionally Excited Beam

Proper orthogonal modes (POMs) are used for order reduction ina beam with frictional excitation. The distributed model is based on anEuler–Bernoulli beam with frictional excitation. The friction ismodeled with Coulomb's law and contact compliance, and the contactsurface undergoes an imposed oscillation. The POMs are selected from achaotic response to build the reduced system model. These POMs areextrapolated into proper orthogonal modal functions (POMFs) by using thelinear normal modes as basis functions. The POMFs are used as the basisfor projection the partial differential equation of motion to alow-order set of ordinary differential equations. Simulated responsesbased on the POMFs and linear normal modes are compared to that of a'truth set' simulation, which is based on ten linear normal modes.