Abstract
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.
Highlights
The nanostructures have at least one nanometer in scope because they are small, as they are made of nanosized structural elements
In this article, bending, buckling, and vibration behaviors of viscoelastic functionally graded (FG) curved nanobeam embedded in an elastic medium are investigated based on nonlocal strain gradient theory
Bending, buckling, and vibration behaviors of nonlocal strain gradient for viscoelastic FG curved nanobeam embedded in an elastic medium under various boundary conditions are studied
Summary
The nanostructures have at least one nanometer in scope because they are small, as they are made of nanosized structural elements. Methods of analysis of plates and beams on elastic foundation have been developed for a long time, up-to-date, practical application of these methods is a difficult problem Analytical methods such as method of initial parameters and method of superposition based on Winkler’s soil model are complex and cannot be used by practicing engineers. In this article, bending, buckling, and vibration behaviors of viscoelastic FG curved nanobeam embedded in an elastic medium are investigated based on nonlocal strain gradient theory. The nonlocal equations of motion of strain gradient viscoelastic FG curved nanobeam are derived based on Hamilton’s principle. Effects of all parameters involving the nonlocal parameter, the structural damping of the FG curved nanobeam, coefficients of elastic foundation, and strain gradient length scale parameter on bending, buckling, and vibration behaviors of viscoelastic FG curved nanobeam are investigated separately.
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