Project Report

In the present work, the nonlinear response behavior of a dynamic pressure sensor diaphragm is studied for excitation frequencies corresponding to the fundamental and the 1-3 internal resonance. It is important to understand the specific behavior of the diaphragm in order to develop accurate pressure-deflection curves for calibration and to determine the operation limits. In this manner, the benefit of the present work is widespread across the many industries and research applications that incorporate these sensors. The dynamic pressure sensor is modeled as a thin plate under initial tension. Results are obtained using AUTO bifurcation and continuation software. Numerical continuation methods such as this allow identification of the complex behavior exhibited by this system, including unstable responses and regions where multiple solutions are possible – common characteristics in highly nonlinear systems. The present work expands upon initial work presented by Long et al. (2008) which incorporates a more refined model than those used by other authors such as Zhou (2001) and Yu et al. (2008). Zhou accounted for initial tension within the diaphragm but assumed only a weak nonlinearity in the equations of motion. Yu et al. extended the model to account for a strong nonlinearity but considered only symmetric oscillations. The present work uses the model developed by Long et al. which accounts for initial tension, strong nonlinearity and asymmetric oscillations. Three main results are achieved in the present research. First, the scope of the results presented in the initial work by Long et al. is extended to include a larger range of material thickness, verifying that the trends observed by Long et al. are also accurate for thinner materials. Second, force-response curves are constructed for each material of differing thickness to identify the relationship between the magnitude of the excitation pressure and the response behavior. It is observed that the standing wave is dominant at low pressures and the traveling wave is dominant at high pressures, with an intermediate range of pressures where both solutions are possible. Thicker materials are shown to maintain standing wave behavior up to larger pressures, a desirable characteristic since a transition to traveling wave behavior would likely distort the sensor measurement. Finally, the case of the 1-3 internal resonance is considered and the corresponding frequency-response and force-response behavior is studied. Thicker diaphragm materials with higher damping are suggested in order to avoid a traveling wave response component for this internal resonance case.

National Science Foundation (NSF)
Office of International and Integrative Activities (IIA)
Application #
Program Officer
Carter Kimsey
Project Start
Project End
Budget Start
Budget End
Support Year
Fiscal Year
Total Cost
Indirect Cost
Eason Richard P
United States
Zip Code