When the piezoelectric is connected to a element such as mirror to use in interferometer, the resonant frequency decreases, we want to use the piezoelectric and mirror on which we can use it, how can this connection be made and that the resonant frequency does not change?
The simple answer is that it can't be done: the piezoelectric element is effectively a spring with a small mass. Attach a mirror, and the spring must drive a larger mass; and this reduces the resonant frequency.
To minimize the change in resonant frequency, you must minimize the mass of the mirror. You might consider, for example, casting a thin photopolymer resin layer on one face of the piezo stack and then depositing a reflective layer on the photopolymer.
@S.McGrew's answer is correct. In fact, the shift in resonant frequency of a piezo can be an incredibly sensitive way to measure mass.
A thin-film thickness monitor can measure the addition of even a few monolayers of atoms on a surface. This principle can even be used to pick up molecules from the air to measure their concentration.
There's nothing wrong with using a piezo resonator to move a mirror in principle, but you have to design the system from scratch, include the mass of the mirror in your calculations, and live with the small resulting amplitude.
You can also decrease the shift in resonance frequency by using a very low-mass mirror and a very large piezo resonator, but both of those may become expensive.