Tunable valley filtering in dynamically strained <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>?</mml:mi><mml:mo>?</mml:mo><mml:msub><mml:mi mathvariant="script">T</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> lattices

Mechanical deformations in $\ensuremath{\alpha}\ensuremath{-}{\mathcal{T}}_{3}$ lattices induce local pseudomagnetic fields of opposite directionality for different valleys. When this strain is equipped with a dynamical drive, it generates complementary valley-asymmetric pseudoelectric field, which expected to accelerate electrons. We propose that by combining these effects time-dependent nonuniform strain, tunable valley filtering devices can be engineered extend beyond the static capabilities. demonstrate implementing an oscillating Gaussian bump centered four-terminal Hall bar setup and calculating induced pseudoelectromagnetic analytically. Within recursive Floquet Green-function scheme, we determine time-averaged transmission polarization, as well spatial distributions density states current density. As result periodic detect novel energy regimes highly valley-polarized transmission, depending on $\ensuremath{\alpha}$. Analyzing profiles relate setup. By means driving frequency, manipulate states, might advantageous future device applications.