Strain modes based dynamic displacement estimation of beam structures with strain sensors

This paper presents a new technique to estimate the dynamic displacement based on strain mode shapes of beam structures with strain sensors. Strain mode shapes are first estimated from the cross-correlation function of the measured dynamic strain data. Then, the displacement mode shapes can be estimated from the strain mode shapes based on the displacement-strain relation. For an oscillating beam structure under service conditions, the dynamic response can be expressed as the superposition of their corresponding mode shapes weighed by the corresponding modal coordinates. Thus, by knowing the strain mode shapes and strain data, the corresponding modal coordinates can be estimated. The dynamic displacement can then be estimated by the obtained displacement mode shapes and modal coordinates. This method is verified by numerical simulations of a simply supported beam subjected to impulsive excitation and earthquake excitation. Experimental tests of a simply supported beam under various hammering excitations are also conducted to verify the effectiveness of the proposed method. Both the numerical and test results show that the proposed method can estimate the dynamic displacement of beam structures with high accuracy.