So I am designing a MEMS structure consisting of cantilever arrays. For my problem, I want the cantilevers to vibrate only at their 1st mode of resonance and reject all the other modes of resonance passively. Is there anyway I can achieve this mechanically, that is by modulating the cantilever structure?
It is physically impossible to make a real-world structure with only one mode of vibration, though it may be possible to design something with only one mode in the frequency range that you are interested in.
But if you are designing a MEMS system, this is probably irrelevant, because you can easily filter out the response from the unwanted modes. Any MEMS system is likely to have enough computing power to do some real-time digital filtering of the signal from the MEMS transducer.