In this research, a novel method is developed to manipulate smart structures' natural frequencies to eliminate or alleviate the detrimental effects caused by vibrating close to the natural frequencies. To this end, this work considers a sandwich plate structure with Terfenol-D, which is a magnetostrictive material, comprising its middle layer. The stiffness of this smart material changes based on the magnetic field that it is exposed to. Thus, natural frequencies and resonances of the whole structure can be manipulated. Furthermore, in this research, the Terfenol-D in the middle layer is divided into five parallel sections so that each of them can be controlled separately. Therefore, it is possible to selectively activate portions of the magnetostrictive layers that run parallel along one of the plate's directions to create periodic changes in the structure's stiffness. Thus, the structure can be kept safe when excitations or disturbances approach one of its natural frequencies by activating sections to produce configurations that modify the natural frequencies. To this end, the structure's natural frequencies are obtained analytically for a thin plate with Kirchhoff equations. Then, the results are verified by the numerical results obtained using the finite element method. Moreover, activating certain portions of the Terfenol-D layer provides a periodic structure with a band gap that can filter out oscillatory motions with frequencies that fall within the band gap. This structure's band gap has been examined in two one-dimensional (1D) periodic, two two-dimensional (2D) periodic, and two non-periodic conditions using the finite element method.