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• Instabilities, bifurcations and chaos in the response of nonlinear dynamic systems.
• Approximate  analytic and combined analytic-geometric methods for the analysis of nonlinear dynamic systems.
• Rotor dynamics  modeling and vibration analysis.
• Mode localization and frequency veering in continuous systems. 
• Dynamic wrinkling in metal sheets.
• Sound propagation in porous media with application to diesel particulate filters
•   Control  and modeling of dynamic performance of  micro- pumps.
• Dynamics of tensegrity systems