Abstract
In this work, nonlocal strain gradient integral model is applied to study the elastic buckling and free vibration response of functionally graded (FG) Timoshenko beam which is made of two constituents varying along thickness direction. The differential governing equations and corresponding boundary conditions are derived via the Hamilton's principle, and the relations between nonlocal stresses and strains are expressed as integral equations. The Laplace transform technique is applied to solve directly the integro-differential equations, and the explicit expression for bending deflections and moments, as well as cross-sectional rotation and shear force is expressed with eight unknown constants. The nonlinear characteristic equations to determine the characteristic buckling load and vibration frequency are derived explicitly in consideration of corresponding boundary conditions and constitutive constraints. The buckling load and vibration frequency from present model are validated against to the existed results in literature. Consistent softening and toughening responses with respect to length-scale parameters can be obtained.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.