Active damping of sound transmission through an electrorheological fluid-actuated sandwich cylindrical shell

Abstract

An exact model is proposed for sound transmission through a sandwich cylindrical shell of infinite extent that includes a tunable electrorheological fluid core, and is obliquely insonified by a plane progressive acoustic wave. The basic formulation utilizes Hamilton’s variational principle, the classical and first order shear deformation shell theories, the Kelvin–Voigt viscoelastic damping model (for the electrorheological fluid-core layer), and the wave equations for internal/external acoustic domains coupled by the proper fluid/structure compatibility relations. The Fourier–Bessel series expansions are used to arrange the governing (coupled) system equations in state-space form. The classical Sliding Mode Control law is then applied to semi-actively reduce sound transmission through the composite cylinder by smart variation of stiffness and damping characteristics of the electrorheological fluid-core actuator layer according to the control command. Numerical results present both the uncontrolled and controlled sound transmission loss spectra of the sandwich cylindrical shell at three angles of incidence for three distinct sets of material input parameters that represent the electric-field dependency of the complex shear modulus of the electrorheological fluid-core layer. The superior soundproof performance of electrorheological fluid-based sliding mode control system in avoiding the highly detrimental sound transmission loss dips occurring throughout the critical resonance and coincidence regions is demonstrated. Likewise, remarkable enhancements in the sound insulation characteristics of the electrorheological fluid-actuated structure utilizing the first or second electrorheological fluid material model are achieved within the stiffness-controlled region, especially at lower frequencies in near-grazing incidence situation. A number of limiting cases are introduced and validity of the formulation is confirmed by comparison with the available data.