One-way mixing of collinear waves in an adhesive layer

Taeho Ju, Jan D. Achenbach, Laurence J. Jacobs, Jianmin Qu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)110-120
Number of pages11
Journaljournal of the Acoustical Society of America
Issue number1
StatePublished - Jan 1 2019

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics


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