In this work, a fifth-order shear deformation theory is computed using the layer-wise model to determine non-dimensional fundamental frequencies. The theoretical, experimental, and finite element analysis (FEA) results are compared for a standard isotropic material. Hand layup technique is used to prepare glass fiber reinforced polymer composites (GFRPC) with selective layers filled with graphene and flyash. This technique helps to reduce the fabrication cost as the whole structure is not to be strengthened by the fillers. Six classes of the laminated-composite-plate (LCP) such as outer layer graphenated LCP (O-LCP), core layer graphenated LCP(C-LCP), functionally graded LCP (FG-LCP), LCPs only rich in graphene (G-LCP), LCPs only rich in flyash (F-LCP) along with a neat epoxy-glass LCP (N-LCP) are fabricated. A low-cost frequency measurement module is set-up to measure the fundamental frequency (FF) of the fabricated LCPs. FFs, amplitudes, non-dimensional stress parameters, and central deflection of the LCPs under harmonic load, the buckling strength, and displacements of the LCPs are calculated. It is found that harmonically excited C-LCP and O-LCP have better stability accompanied by lower deflections, followed by G-LCP as compared to other kinds of LCPs. Also, the addition of graphene increases the buckling strength of LCPs, which portrays that the local layer filling is a useful technique to enhance the strength of the LCPs.