Novel reduced models of partial differential equations (PDE) for piezoelectric (smart material) single and multi-layer beam equations are developed by Finite Differences and Finite Elements. These reduced models accurately predict feedback-controlled vibrations traveling on the beam during the motion. The paired controller and sensor are collocated at the tip of the beam. First, it is shown that the feedback sensor placed at the tip of the beam can be designed by eliminating the short wavelength and high-frequency components of the solutions through the direct Fourier filtering technique. This way, the sensor becomes more able to distinguish one vibrational frequency from another. The filtered sensor data is then fed back to the controller, resulting in all of the vibrations on the beam being successfully suppressed exponentially fast, replicating the dynamics of the PDE case. Another approach, based on order reduction, accurately simulates the suppressed dynamics without the need for direct filtering. Finally, all Mathematica simulations are converted to the computational framework Wolfram`s Computable Document Format (CDF), and they are published at the open-source-code website, Wolfram Demonstrations Project (WDP).