Previous ultrasonic additive manufacturing (UAM) models ignore higher-order modes or do not simulate the entire weld cycle when studying the dynamics near critical height-to-width ratios. A multi-modal model was developed to study the dynamics near critical build heights. The cause for the critical height-to-width ratio is dynamic interaction between the substrate and sonotrode. As the build height approaches the critical height-width-ratio, the current model predicts a local maxima in the transverse velocity response directly under the moving load (simulated sonotrode excitation). This is validated by experimental observations from previous studies. However, the current model predicts that as the height is further increased, a maximum in the transverse velocity response occurs at a height-to-width ratio of 1.2 due to resonance of higher-order modes. This result indicates that a single mode-approximation is insufficient to describe the dynamics near critical build heights. In studying the time response for an entire weld cycle (1.5 s), the amplitude of the velocity response in the transverse direction varies greatly. This indicates that assuming a quasi-static or analyzing a short time period in a model excludes potential dynamics during an entire weld cycle (on the order of 1 s).

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