Eigenvalue analysis and impact response analysis for T-shaped structures with new acoustic black hole including residual thickness supported by nonlinear concentrated springs

Abstract

This paper describes numerical analysis using FEM with Model Strain Energy Method for structures having a T-shaped cross section supported by nonlinear concentrated springs under impact load. An edge of the rib plate in the T-shaped structure has an Acoustic Black Hole with residual thickness. A viscoelastic damping layer is covered on the black hole. Finite element for the nonlinear springs with hysteresis are expressed and are connected to the T-shaped structures modeled by linear solid finite elements in consideration of complex modulus of elasticity. We calculated modal loss factors and transient responses using eigenmodes including coupled motions between the nonlinear springs and the T-shaped structures. From the dominant modes and the impact responses, we clarified effects of the black hole with residual thickness on the nonlinear damped responses. By adding the black hole to the structures, modal loss factors increase. Higher modal loss factors are obtained due to set the residual thickness. As the amplitude of the impact force, the responses become complicated due to the nonlinearity, and include more super harmonic and subharmonic components. These nonlinear components are reduced by adding the black hole. The less nonlinear components are given due to set the residual thickness.