Abstract: Solutions to the linear unforced Mathieu equation, and their stabilities, are investigated. Floquet theory shows that the solution can be written as a product between an exponential part and a periodic part at the same ...

Abstract: The Floquet theory has been classically used to study the stability characteristics of linear dynamic systems with periodic coefficients and is commonly applied to Mathieu’s equation, which has parametric stiffness. The ...

Abstract: Abstract. This study presents a reduced-order modeling framework for nonlinear metastructures with the aim of enabling programmable dynamic behavior. For a metastructure composed of a beam and an array of resonators with ...

Abstract: Abstract. Resonances of the externally forced Mathieu equation under quasiperiodic excitation are studied. The external forcing frequency is assumed to be independent of the parametric-stiffness frequency and the system’s ...

Abstract: Coupled blade-hub dynamics of a coupled three-blade-rotor system with parametric stiffness, which is similar to a horizontal-axis wind turbine, is studied. Blade equations have parametric and direct excitation terms due ...