Hybrid holographic-numerical method for modal analysis of complex structures

摘要

This paper presents a hybrid holographic-numerical method for modal analysis of complex structures. Acontinuous structure is first lumped into a number of discrete elements to form an elastically connectedlumped linear system. The matrix of influence coefficients of the lumped linear system are thendetermined by exerting a static load to the element centers and measuring the corresponding whole-field displacement using digital holographic interferometry. The eigenvalues and eigenvectors of theinfluence coefficients, which in a physical sense represent the natural frequencies and mode shapes ofthe structure, are then calculated using the numerical method. A major advantage of the proposedhybrid method is that it is not necessary to know the Young's modulus, the Poisson's ratio of thematerial and the boundary conditions, as the displacement field measured by the optical method hasautomatically reflected the real boundary conditions and the material properties, which makes thismethod particularly useful for studying objects made from anisotropic materials such as composites.Another advantage of the proposed method is that structures of any complex and irregular shape willnot increase the complexity of the characterization process. The proposed is also suitable forexperimentally validating the modal analysis results from finite element method models.