Modeling of the bio-inspired vibration isolation platform supported by X-structures via D'Alembert’s principle of virtual power

Most bio-inspired vibration isolators have wide frequency isolation band and high loading capacity simultaneously, thanks to their high-static-low-dynamic-stiffness. However, accurate modeling and multi-directional isolation analysis are always needed for real applications because of their structural complexity. In this work, an innovative accurate model is established for the 2D bio-inspired X-structure isolators and the corresponding 3D isolation platforms respectively based on D'Alembert’s Principle of virtual power, which is very beneficial for the system with many degrees-of-freedom. After that, the perturbation method is utilized to investigate the difference between the simplified and accurate models. Regarding the elastic limit of the springs, boundaries of the initial velocity and the applied force are calculated via the dichotomy method. Results reveal that our model has similar dynamic response but higher loading capacity, compared with the simplified one. Moreover, the Stewart platform shows better multidirectional vibration suppression performance.