This work provides a comparative analysis of the effect of nanovoids distribution associated with trigonometric functions on forced mechanical characteristics of functionally graded curved nanobeams. A geometrically exact model is developed for the simply-supported beam utilizing a higher-order beam theory including thickness stretching effect. In order to capture the small-scale effects, the governing motion equations are integrated with the general strain gradient theory. The virtual work statement of Hamilton principle is adopted to gain the governing equation as well as boundary conditions. Then, Navier solving procedure-based Fourier series is exerted for stating the reference surface displacements of the nanobeam. The numerical examples are expanded to know the behave of transverse deflection, axial, normal, and shear stresses which are highlighted by time under the influence of material composition, porosity coefficient and its distribution patterns, small-scale coefficients as well as geometrical parameters. It is manifested that in a periodic domain, the oscillation amplitudes grow smaller extremely by raising the excitation frequency, while the repetition of them increases.