<p>This paper investigates the two-dimensional steady-state frictional contact characteristics of a functionally graded piezoelectric finite layer with material parameters varying exponentially along its thickness direction under the action of a rigid, insulating flat punch. To analyze the mechanical behavior of functionally graded piezoelectric materials under dynamic contact conditions, an electro-elastic coupled contact model is established. This model incorporates the effects of inertia, with the Galilean transformation introduced to facilitate analysis. To solve the model, the Fourier transform technique is first employed to convert the complex electro-elastic coupled problem into a singular integral equation of the second kind with a Cauchy kernel. A discretization method is then applied to derive the unknown contact stress distribution. Numerical results demonstrate the variation patterns of surface contact stress, in-plane stress, and in-plane electric displacement with respect to relative sliding velocity, friction coefficient, layer thickness, and gradient parameters, while also verifying the singular characteristics of stress and electric displacement at the contact edges of the flat punch. The findings of this study offer analytical insights that may inform the structural design and performance evaluation of functionally graded piezoelectric materials under high-speed frictional contact scenarios.</p>