Accurate determination of the elastic moduli of optimized cantilever beams by efficient time-averaged ESPI system

Abstract

Elastic moduli, including Young’s modulus, shear modulus, bulk modulus, etc, are key parameters that are used to characterize the ability of a solid material to resist various types of deformation. The moduli can be extracted from the natural frequencies of a cantilever beam. In this paper, the relationships between moduli and natural frequencies, for the first time, are quantified by the finite element method. The optimized three-dimensional proportion of the cantilever beam is selected to be implemented simple error compensation. Experimentally, to precisely obtain the natural frequencies of the cantilever beam, an efficient time-averaged electronic speckle pattern interferometry(ESPI) system has been developed. The efficiency and precision are reflected in the following aspects: firstly, according to the slender character of the cantilever beam, a large shear optical path arrangement is designed to facilitate isolation from environmental interference; secondly, a resonance search method, based on the moiré effect is employed to recognize the natural frequencies accurately and efficiently; thirdly, a novel dynamic phase-shifting method is proposed based on the arrangement of the large shear optical path for clearer visualization of the mode shape of the cantilever beam. The proposed methods are verified by three kinds of common materials. The results suggest that Young’s modulus and shear modulus derived from natural frequencies are higher than the known value, and the error compensation can significantly reduce the calculation error. Furthermore, the experiments carried out on the woven carbon fiber reinforced plastic laminates illustrate the potential of the proposed methods in the evaluation of elastic moduli of composites. Given that the exciter attached to the specimen surfaces can be replaced with some special counterparts, the proposed ESPI system has considerable potential to test the objects loaded in some extreme environments, e.g. at high temperatures or underwater, where contact detection methods are difficult to be implemented.