Although the study of vibration isolation has a very long history, when an isolated structure is so flexible that it cannot be properly approximated with a rigid body or a single-degree-of-freedom model, its vibration isolation brings about some new questions and problems. By transforming the dynamic equation of motion of the coupled structure formed by the isolator and the isolated structure into the modal space and following the tradition of studying features of the vibration transmissibility across the isolator, questions and problems associated with the flexible structure vibration isolation are studied. It is found from the study that a lower isolation frequency and a higher damping level can both increase the isolation effectiveness, the isolated structure is a vibration absorber to the isolator, and a combination of the vibration isolation and the vibration attenuation can be more effective in mitigating the vibration. A numerical example of the whole spacecraft vibration isolation has proved the above conclusions.

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