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

Abstract Since it is nondestructive and can produce global properties, the method combining vibration testing and numerical analysis is a potential approach to determine elastic constants of materials. In order to simplify the modeling process and reduce the complexity of the numerical analysis, both the direct determination method and the inverse determination method are presented in this work. In the direct determination method, two special natural frequencies 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. Five natural frequencies obtained from both plate specimens can be used to determine four elastic constants of transversely isotropic materials by substituting them into the existing formulas. In the Inverse determination method, the combination of finite element analysis and optimum design is adopted to inversely calculate the elastic constants. Thin plates of steel and carbon/epoxy composites are selected to demonstrate the procedures and to compare the application of both methods. The results indicate that the elastic constants predicted by both methods are in good agreement with the reference values. Even though the steel plate is treated as a transversely isotropic material, these predicted constants also satisfy the conditions of isotropy. However, it is always difficult and cumbersome to find the X and ring modes in the direct determination method, especially for composite materials. Therefore, the inverse determination method is generally recommended because of its single test and versatility.