Abstract
The dynamic stiffness method is developed to investigate the free vibration behaviour of functionally graded beams. Material properties are assumed to vary continuously in the beam thickness direction according to a power law distribution. Hamilton’s principle is used to derive the governing differential equations of motion and natural boundary conditions in free vibration. For harmonic oscillation the differential equations are solved in closed analytical form. The dynamic stiffness matrix is derived by relating the amplitudes of forces to those of the displacements at the beam ends. The Wittrick–Williams algorithm is used as the solution technique when applying the dynamic stiffness matrix to compute the natural frequencies and mode shapes. A parametric study is carried out to demonstrate the effects of the length to thickness ratio and the variation of the power law index parameter. Numerical results are discussed and compared with the published ones wherever possible. Some conclusions are drawn.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
