The work deals with the development of the R-functions theory for investigation of geometrically nonlinear free vibrations of functionally graded shallow shells with a complex plan-form. The considered shells are made of a mixture of metal and ceramics. Volume fraction distribution of materials through the thickness is governed by the power law. The mathematical statement of a problem is stated in a framework of the refined first-order shallow shells theory. The test problem and numerical results are presented to validate the developed approach and demonstrate its efficiency. New results are presented for the nonlinear free vibrations of clamped spherical and cylindrical shell panels of a complex shape.
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