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This article investigates bending, buckling, and vibration analysis in viscoelastic functionally graded curved nanobeam embedded in an elastic medium under different boundary conditions. The stresses can be calculated based on not only the nonlocal stress field but also the strain gradient stress field according to the nonlocal strain gradient elasticity theory. The present higher order refined curved nanobeam theory which captures shear deformation influence does not need any shear correction factors. Two power-law models are used to describe the continuous variation of material properties of viscoelastic functionally graded curved nanobeam. Governing equations of nonlocal strain gradient viscoelastic functionally graded curved nanobeam are obtained using Hamilton’s principle. To establish the present model, the results are compared with those of functionally graded curved nanobeams. The effects of nonlocal parameter, length scale parameter, viscoelastic damping coefficient, spring stiffness, boundary conditions, and power-law exponent on the bending, buckling, and vibration responses of viscoelastic functionally graded curved nanobeam are discussed.

Nonlocal strain gradient theory for bending, buckling, and vibration of viscoelastic functionally graded curved nanobeam embedded in an elastic medium