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Jacobs, Laurence J.

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Author: Kim, Jin-Yeon ×

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Characteristics of second harmonic generation of Lamb waves in nonlinear elastic plates

2010-04 , Mueller, Martin Fritz , Kim, Jin-Yeon , Qu, Jianmin , Jacobs, Laurence J.

This paper investigates the characteristics of the second harmonic generation of Lamb waves in a plate with quadratic nonlinearity. Analytical asymptotic solutions to Lamb waves are first obtained through the use of a perturbation method. Then, based on a careful analysis of these asymptotic solutions, it is shown that the cross-modal generation of a symmetric second harmonic mode by an antisymmetric primary mode is possible. These solutions also demonstrate that modes showing internal resonance-nonzero power flux to the second harmonic mode, plus phase velocity matching-are most useful for measurements. In addition, when using finite wave packets, which is the case in most experimental measurements, group velocity matching is required for a cumulative increase in the second harmonic amplitude with propagation distance. Finally, five mode types (which are independent of material properties) that satisfy all three requirements for this cumulative increase in second harmonic amplitude-nonzero power flux, plus phase and group velocity matching-are identified. These results are important for the development of an experimental procedure to measure material nonlinearity with Lamb waves.

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On the excitability of second harmonic lamb waves in isotropic plates

2010-02-22 , Mueller, Martin Fritz , Kim, Jin-Yeon , Qu, Jianmin , Jacobs, Laurence J.

Recent research uses second harmonic waves caused by material nonlinearity to characterize fatigue damage in its early stages. This research investigates this second harmonic Lamb wave generation analytically, using a solution derived by De Lima, in order to provide information on the efficient generation and detection of a second harmonic amplitude for improved signal-to-noise ratio in measurements. Symmetry properties of the second harmonic wave are also clarified, since the published literature is contradictory.

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