Abstract
Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonant frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.
Highlights
Linear ultrasonic methods, widely used in non-destructive evaluation (NDE), are only sensitive to macro-damages in the order of the wavelength of the ultrasound but they are not capable for micro-damages such as micro-cracks or material degradation,[1] which usually occur at very early stage of the operation
The numerical models were first demonstrated in an aluminum plate which can be compared with analytical solutions, and they were applied on a rectangular steel bar which can only be analyzed by numerical methods
Two examples were studied using the simulation tool discussed above: an aluminum plate which can be compared with analytical solutions, and a steel bar with rectangular cross section which can only be investigated by finite element models
Summary
Widely used in non-destructive evaluation (NDE), are only sensitive to macro-damages in the order of the wavelength of the ultrasound but they are not capable for micro-damages such as micro-cracks or material degradation,[1] which usually occur at very early stage of the operation. Such challenge may be overcome by using nonlinear ultrasonic methods, as they are much more sensitive to incipient damages.[2,3,4,5] In recent years, nonlinear ultrasonic guided waves, combining advantages of nonlinear ultrasound and guided waves, have emerged as a useful tool for the characterization of incipient damages in large structures, as guided waves can travel a long distance with little loss in energy and provide capability for the remote inspection of areas with difficult access.[5]. The numerical models were first demonstrated in an aluminum plate which can be compared with analytical solutions, and they were applied on a rectangular steel bar which can only be analyzed by numerical methods
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