Determination of elastic constants of transversely isotropic materials by combining vibration testing and numerical method

Since it is nondestructive and can produce global properties, the method co mbining vibration testing and numerical analysis is a potential approach to determine elastic constants of materials. In order to simplify the modelin g process and reduce the complexity of the numerical analysis, both the dir ect determination method and the inverse determination method are presented in this work. In the direct determination method, two special natural freq uencies of an X mode and a ring mode are obtained by the vibration testing of a plate with special dimensions decided from another arbitrary plate. Fi ve natural frequencies obtained from both plate specimens can be used to de termine four elastic constants of transversely isotropic materials by subst ituting them into the existing formulas. In the inverse determination metho d, the combination of finite element analysis and optimum design is adopted to inversely calculate the elastic constants. Thin plates of steel and car bon/epoxy composites are selected to demonstrate the procedures and to comp are the application of both methods. The results indicate that the elastic constants predicted by both methods are in good agreement with the referenc e values. Even though the steel plate is treated as a transversely isotropi c material, these predicted constants also satisfy the conditions of isotro py. However, it is always difficult and cumbersome to find the X and ring m odes in the direct determination method, especially for composite materials . Therefore, the inverse determination method is generally recommended beca use of its single test and versatility.