A Study on Nonlinear Vibrations in the Impact-Echo Method for Void Flaw Detection in Solids

This paper presents a study on the nonlinear vibrations in the impact-echo (IE) method for void flaw detection of solid structures. Linear theory has historically served as the foundational framework for non-destructive methods, including the IE method, particularly for estimating flaws in solids. This paper gives a comprehensive analysis of the nonlinear theory behind the IE method for detection of voids in solids such as concrete structures. The general equation of motion is presented for the flexural vibration of a void-defected solid with general nonlinear constitutive material properties, and then the simplified solutions for polynomial nonlinearity and hysteresis nonlinearity are derived comprehensively. The solutions of principal frequency and sub- and super-harmonics as well as the frequency of combined modes are elaborated, and the theoretical formula of resonant frequency shift with amplitude is derived. As conventional nonlinear IE methods have been conducted by only using a phenomenological model of linear shift in resonant frequency with amplitude, the proposed new frame of nonlinear vibration theory can be used to implement the IE method more comprehensively and accurately for void detection in solids.