<p>The Bloch–Floquet theorem is not directly applicable in polar coordinates. Prior research has demonstrated that radial periodicity in circular plates can induce wave band gaps at sufficiently large radii. In this study, two new efficient numerical methods for computing dispersion relations and forced responses of Kirchhoff–Love circular plates with radial periodicity are presented. The presented methods can be used to model plates in polar coordinates with mechanical and geometric properties varying arbitrarily along the radius. The first one consists of reformulating the elastodynamic equation of the circular plate in the frequency domain into a state-space formulation, and then applying the Bloch–Floquet solution due to the periodicity of the system’s geometrical and mechanical parameters. Computationally, the matrix exponential is performed in a discretized state-space matrix with constant coefficients. The second one is the plane wave expansion method, which consists of expanding the periodic elastodynamic equation coefficients and the solution in a Fourier series based on the Bloch–Floquet theorem. After some algebraic manipulations and approximations, the problem can be rewritten as an eigenproblem, imposing wavenumber values on the irreducible Brillouin zone and yielding the angular frequencies. The results computed using these methods were validated against approximate dispersion diagrams and forced responses computed using the finite element method, as well as against the analytical solution expressed in terms of Bessel and modified Bessel functions. Finally, the methods are applied to a complex external loading case that simulates a potential vibration attenuation application.</p>