Nonlinear models for double-wall systems for vibrations and noise control

A theoretical model is developed for active control of vibrations and noise transmission of nonlinear double-wall systems to random wideband inputs. A velocity feedback control mechanism is integrated into governing nonlinear equations of motion using piezoelectric materials as sensors and actuators. The nonlinear von Karman thin plate theory is used to model vibrations of the face plates. A soft elastic core of the double wall is used. The nonlinear panel response is obtained by utilizing modal analyses and Monte Carlo simulation techniques. Transmitted noise inside a rectangular enclosure is obtained by solving the linearized acoustic wave equation subject to time-dependent boundary conditions of the vibrating interior panel. Numerical results include vibration response time histories, spectral densities, rms responses, and noise reduction. The feasibility of using piezoelectric velocity feedback actuators for active control of nonlinear vibrations and noise transmission to random inputs is demonstrated.