Feed-Forward Control of a Cracked Simply Supported Beam

This paper demonstrates the use of two feed-forward control algorithms in order to mitigate crack propagation in a simply supported beam with a pre-existing crack. The main objective of the control algorithms is to minimize or reduce transverse deflection at the crack location so as to contain the damage resulting from the pre-existing crack and, thereby, reduce the rate of crack propagation. A point-load sinusoidal excitation, from a known disturbance, is used as the input load acting on the beam. Two control algorithms are used — the first control algorithm computes a control force to eliminate transverse displacement at the crack location resulting from the excitation force, and the second control algorithm minimizes the mean square transverse displacement over a section of the beam that contains the crack. Both the control algorithms are a-causal and assume that the excitation input is completely known a-priori. Simulation results for a simply supported beam are presented and discussed in detail. It is observed that the rate of crack propagation can be significantly reduced by implementing the proposed feed-forward control algorithms, increasing the useful life of the damaged beam. Also, it is found that the transverse displacement over a significant length of the beam can be substantially reduced when the beam response is dominated by a specific mode.