An approximate analytic method of obtaining the vertical mechanical impedance of the bellow air spring is proposed and developed in this paper. Firstly, the sound pressure distribution in the interior space of bellow air spring divided into several regular zones can be calculated based on the linear air wave theory and Boltzmann superposition principle. Secondly, a 1-order ordinary differential matrix equation for the state vector of revolutionary shells under internal pressure is derived based on the non-moment theory of elastic thin shell. Referring to the transfer matrix method, a kind of expanded homogeneous capacity high precision integration method is introduced to solve the non-homogeneous matrix differential equation. Combined the solved stress field of shell with the calculated sound pressure field in the bellow air spring under the displacement harmonic excitation, the approximate analytical expression of the input and transfer mechanical impedance for the bellow air spring can be achieved, and its mechanical impedance characteristics are analyzed systematically, which are verified by the numerical simulation with the Comsol Multiphysics software.
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