Natural frequency informed finite element modal analysis method for estimating elastic properties of solid materials

Abstract

This study proposes a simple yet effective dynamic method that can nondestructively evaluate the elastic properties of homogeneous isotropic solid materials. Like some dynamic methods, such as resonance ultrasound spectrometry and impulse excitation technique, the proposed method consists of two steps: experimentally acquiring the specimen's natural frequencies and numerically calculating the elastic properties. Compared with the existing methods, the proposed method has much lower requirements on all four aspects of experimental operations: specimen preparation, specimen positioning, vibration excitation, and vibration detection. An inverse method based on finite element modal analysis is proposed to calculate the specimen's elastic properties, and it can deliver optimal estimations with high precision and accuracy. The performance of the proposed method was assessed using the well-established sound speed-based dynamic method, i.e., ultrasound pulse-echo testing. Taking a square aluminum specimen as an example, the differences in the measurements of Young's modulus and Poisson's ratio between these two methods are 2.25% and −2.07%, respectively; the differences in the measurements of shear modulus and bulk modulus are 0.01% and −1.46%, respectively. In summary, the proposed method provides a cheaper and experimentally simpler approach to determining the elastic properties of solid materials while maintaining accuracy and reliability similar to the established methods, which typically require sophisticated, costly equipment.