Quasinormal modes of thick branes in $f(R,T)$ gravity

We study tensor perturbations and quasinormal modes (QNMs) of thick branes in $f(R,T)=R+αT$ gravity. Starting from the background thick brane solutions, we derive the Schrödinger-like equation for gravitational perturbations and construct the corresponding effective potential. The effective potential exhibits a double-barrier structure whose properties depend on the model parameters. We analyze transmission spectra and find good agreement between resonance peaks and the real parts of the quasinormal frequencies. The parameters $b$ and $α$ mainly control the width and height of the potential barriers, respectively. QNMs are extracted using both time-domain evolution and direct integration methods, showing consistent results for low-lying modes. Higher overtones become increasingly difficult to extract due to stronger damping and numerical contamination. Our results indicate that $f(R,T)$ corrections significantly affect both the effective potential and the quasinormal spectrum, providing a possible imprint of modified gravity in braneworld perturbations.