Abstract: The present study deals with the response of a damped Mathieu equation with hard constant external loading. A second-order perturbation analysis using the method of multiple scales (MMS) unfolds resonances and stability. ...

Abstract: This work concerns the response of a damped Mathieu equation with hard cyclic excitation at the same frequency as the parametric excitation. A second-order perturbation analysis using the method of multiple scales unfolds ...

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 complex modes of an end-damped cantilevered beam are studied as an experimental example of a nonmodally damped continuous system. An eddy-current damper is applied, for its noncontact and linear properties, to the end ...

Abstract: This work represents an investigation of the complex modes of continuous vibration systems with nonmodal damping. As an example, a cantilevered beam with damping at the free end is studied. Assumed modes are applied to ...

Abstract: Reducedorder mass weighted proper orthogonal decomposition (RMPOD), smooth orthogonal decomposition (SOD), and state variable modal decomposition (SVMD) are used to extract modal parameters from a nonuniform experimental ...

Abstract: Complex orthogonal decomposition (COD) is applied to an experimental beam to extract the dispersive wave properties from response measurements. The beam is made of steel and is rectangular with a constant cross section. ...

Abstract: Gear manufacturing errors are key parameters in planetary gear trains and have effects on load sharing, tooth stress, and so on. Accurate estimation of manufacturing errors can help monitor the conditions of planetary gear ...

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: We study the primary resonance of a parametrically damped Mathieu equation with direct excitation. Potential applications include wind-turbine blade vibration with cyclic stiffening and aeroelastic effects, which may induce ...