TY - JOUR
T1 - One-way mixing of collinear waves in an adhesive layer
AU - Ju, Taeho
AU - Achenbach, Jan D.
AU - Jacobs, Laurence J.
AU - Qu, Jianmin
N1 - Publisher Copyright:
© 2019 Acoustical Society of America.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - This paper studies the one-way collinear mixing of a pair of longitudinal and shear waves in an adhesive layer. The objective is to establish a theoretical framework for developing ultrasonic methods for nondestructively characterizing adhesive bonds by using only one side of the adhesive joint. The adhesive joint is modeled as a nonlinear elastic layer embedded in a linear elastic matrix of infinite extent. First, a solution is developed for the general case where the elastic impedance of the layer is different from that of the surrounding matrix. Then, a nonlinear spring model is developed that yields a reduced order solution for the one-way collinear wave mixing problem at hand. It is shown that in the limit of vanishing layer thickness, the solution to a layer of finite thickness reduces to that of the spring model, provided that a proper relationship is used between the properties of the nonlinear layer and the nonlinear spring. In other words, a very thin layer can be effectively replaced by a nonlinear spring. Finally, numerical analyses show that such effective replacement is valid when the layer thickness is less than a few percent of the shortest wavelength used in the measurement.
AB - This paper studies the one-way collinear mixing of a pair of longitudinal and shear waves in an adhesive layer. The objective is to establish a theoretical framework for developing ultrasonic methods for nondestructively characterizing adhesive bonds by using only one side of the adhesive joint. The adhesive joint is modeled as a nonlinear elastic layer embedded in a linear elastic matrix of infinite extent. First, a solution is developed for the general case where the elastic impedance of the layer is different from that of the surrounding matrix. Then, a nonlinear spring model is developed that yields a reduced order solution for the one-way collinear wave mixing problem at hand. It is shown that in the limit of vanishing layer thickness, the solution to a layer of finite thickness reduces to that of the spring model, provided that a proper relationship is used between the properties of the nonlinear layer and the nonlinear spring. In other words, a very thin layer can be effectively replaced by a nonlinear spring. Finally, numerical analyses show that such effective replacement is valid when the layer thickness is less than a few percent of the shortest wavelength used in the measurement.
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U2 - 10.1121/1.5084734
DO - 10.1121/1.5084734
M3 - Article
C2 - 30710914
AN - SCOPUS:85059561837
SN - 0001-4966
VL - 145
SP - 110
EP - 120
JO - Journal of the Acoustical Society of America
JF - Journal of the Acoustical Society of America
IS - 1
ER -