## Abstract

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 language | English (US) |
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Pages (from-to) | 110-120 |

Number of pages | 11 |

Journal | journal of the Acoustical Society of America |

Volume | 145 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2019 |

### Funding

This work was supported in part by the National Science Foundation (NSF) through Grant No. CMMI-1613640.

## ASJC Scopus subject areas

- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics