Analytical model for damping behaviour of an orthotropic cantilever hollow member with polygonal perforations

This work presents a mathematical framework for analysing damping behavior of an orthotropic cantilever hollow member containing polygonal perforations while subjected to base excitation. Amplitude and strain rate depending damping models are considered in the framework. A generalized formulation of stress functions for different shapes of the polygonal perforations is derived using the complex variable approach. For this study, five different shapes of the perforations i.e., circular, triangular, diamond, pentagonal and hexagonal are considered. The final expression of the damping ratio is evaluated in terms of the excitation amplitude, perforation-based stress functions, number of perforations and material dependent damping coefficients. The damping ratio obtained through the proposed approach is validated by comparing with experimental results available in previous study for circular perforations. From results, the amplitude dependent damping behaviour is observed. Later, the damping ratio is obtained for different shapes of perforations. The damping ratio is significantly enhanced when the tube is perforated with triangular perforations along its length, which is increased for more number of perforations in the tube.