Attenuation zones of initially stressed periodic Mindlin plates on an elastic foundation

Abstract

A new numerical approach based on the weak form quadrature element method is proposed to study attenuation zones of initially stressed periodic Mindlin plates on an elastic foundation. The proposed method is validated by the results available in the previous studies of initially stressed homogeneous plates on elastic foundations. A comprehensive parametric study is conducted to highlight the effects of initial stress, geometric parameters and elastic foundation on the attenuation zones. The results show that the compressive initial stress shifts the attenuation zones to lower frequencies and enhances the attenuation of waves in the attenuation zones, while the tensile initial stress shifts the attenuation zones to higher frequencies and weakens the attenuation of waves in the attenuation zones. The elastic foundation shifts the attenuation zones to higher frequencies and narrows the width of the attenuation zones. In addition, wave propagation and attenuation in a periodic Mindlin plate with finite unit cells on an elastic foundation are examined. The results achieved in this paper are very useful for the design and application of periodic plates in vibration reduction in most of engineering fields.