Vibration analysis of a partially covered beam with a shear thickening fluid core

The vibration responses of a sandwich beam with partially covered by shear thickening fluid (STF) layer under an impact load are investigated. The nonlinear governing equations of the flexural vibration are derived based on extended Hamilton’s principle and are solved by the finite difference method. The model is then validated and used to develop a complete parametric study of partially covered beams with the STF-filled core to properly design and place the STF patch. It is found that, for the first vibration mode, maximum damping, and the smallest change in the natural frequency are achieved when the coverage length of the partial STF patch exceeds 50% and the center of the patch is positioned at 56.25% from the left edge. For the second vibration mode, the coverage length is 37.5% and the center of the patch is located at 75% from the left edge of the beam. Additionally, it has been observed that maintaining a thickness ratio of 0.75 between the constraining layer and the base beam leads to increased damping, while simultaneously minimizing alterations in the natural frequency of the original beam. The results can be used for the structural design of sandwich beams partially covered by STF.