Four-variable refined plate theory for forced-vibration analysis of sigmoid functionally graded plates on elastic foundation

• An S-FGM composed of two power-law functions to define volume fraction is proposed.
• The Pasternak’s parameter has more effect on variation of structural responses.
• The effect of a larger time step is to reduce the amplitude and increase the period.

A refined higher-order shear deformation theory is developed for the analysis of free and forced vibration of sigmoid functionally graded materials (S-FGM) plates. The theory, proposed in this paper, considers the parabolic distribution of the transverse shear stress, and satisfies the condition that requires the transverse shear stress to be zero on the upper and lower surfaces of the plate, without the shear correction factor. Unlike the conventional higher-order shear deformation theory, the refined higher-order shear deformation theory, even though it uses only four unknown variables, shares strong similarities with classical plate theory (CPT) in many aspects such as boundary conditions, equation of motion, and stress-resultant expressions. The material properties of the plate are assumed to vary according to the two power law distributions of the volume fractions of the constituents. The equations of motion are derived from Hamilton׳s principle. The solutions for a simply supported plate are derived, and a comparative analysis is carried out by comparing the results obtained with first-order shear deformation theory and another, higher-order shear deformation theory. The results of the comparative analysis with the proposed theory provide accurate and relevant results for free-vibration problems of Functionally Graded Materials (FGM) plates. Analytical solutions for the forced-vibration problems are presented so as to reveal the effects of the power law index, length, aspect ratio, loading time interval, elastic medium parameters and side-to-thickness ratio of the plate on the dynamic response.