A novel numerical approach based on the weak form quadrature element method is developed to study the effect of initial stress on the attenuation zones and attenuation coefficients of periodic Timoshenko beams resting on a two-parameter elastic foundation. For some special cases, comparisons with other related investigations are conducted to validate the proposed method, and good agreement is found. The results show that the compressive initial stress enhances the maximum attenuation in the second attenuation zone while it weakens the maximum attenuation in the first attenuation zone. In addition, based on the detailed modal analysis, simplified models are proposed to determine the bound frequencies of the lowest attenuation zone. Furthermore, frequency domain analysis and transient response analysis for a beam with finite unit cells are performed to verify the theoretical analysis of the infinite-unit cell beam. The present investigation is very helpful for the design and application of periodic strip foundations and pipelines for vibration isolation in buildings and infrastructures.
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