The vibrations of axially functionally graded (AFG) beams are examined incorporating shear deformation and an imperfection. A coupled nonlinear model is developed in the Hamiltonian framework for an AFG imperfect beam. Different sources of displacement nonlinearities are involved in this problem, namely, the geometrical nonlinearities due to the large deformations, and the nonlinearities due to the presence of a geometrical imperfection along the length of the beam. Expressions for the virtual work of external excitation and damping as well as formulas for the motion and elastic energies of the system are inserted into Hamilton’s energy/work principle. The equations were evaluated by using differential transform method, a powerful numerical tool in solution of ordinary differential equations, for solving the governing equation of motion. The method is capable of modeling any beam whose cross-sectional area and moment of inertia vary along beam with any two arbitrary functions and any type of cross-section with just one or few elements so that it can be used in most of engineering applications.
Felicitas Uche, I. (2019). APPLICATION OF DIFFERENTIAL TRANSFORM METHOD TO THE VIBRATION ANALYSIS OF SHEAR DEFORMABLE AFG BEAMS. Afribary. Retrieved from https://afribary.com/works/application-of-differential-transform-method-to-the-vibration-analysis-of-shear-deformable-afg-beams
Felicitas Uche, Iwuchukwu "APPLICATION OF DIFFERENTIAL TRANSFORM METHOD TO THE VIBRATION ANALYSIS OF SHEAR DEFORMABLE AFG BEAMS" Afribary. Afribary, 06 Jul. 2019, https://afribary.com/works/application-of-differential-transform-method-to-the-vibration-analysis-of-shear-deformable-afg-beams. Accessed 30 Apr. 2024.
Felicitas Uche, Iwuchukwu . "APPLICATION OF DIFFERENTIAL TRANSFORM METHOD TO THE VIBRATION ANALYSIS OF SHEAR DEFORMABLE AFG BEAMS". Afribary, Afribary, 06 Jul. 2019. Web. 30 Apr. 2024. < https://afribary.com/works/application-of-differential-transform-method-to-the-vibration-analysis-of-shear-deformable-afg-beams >.
Felicitas Uche, Iwuchukwu . "APPLICATION OF DIFFERENTIAL TRANSFORM METHOD TO THE VIBRATION ANALYSIS OF SHEAR DEFORMABLE AFG BEAMS" Afribary (2019). Accessed April 30, 2024. https://afribary.com/works/application-of-differential-transform-method-to-the-vibration-analysis-of-shear-deformable-afg-beams