Free Vibration Analysis of AFGPM Non-uniform Beam: A Mathematical Modeling

Purpose This work is an extension of the previously published work. In this study vibration behavior of an axially functionally graded piezoelectric material (AFGPM) non-uniform beam is investigated. The material properties are assumed to vary continuously along the length according to a power law. The polynomial function is used to define the width of the beam at the specific cross section. Two types of boundary conditions are taken into consideration, i.e. clamped-clamped (C-C) and clamped-free (C-F). Methods Hamilton's theory is adopted to model the equations of motion. The results are obtained using the generalized differential quadrature (GDQ) method. Results The effects of the degree of a polynomial function, boundary conditions, taper ratio, geometric parameter and volume fraction index on natural frequencies are reported. Conclusions The natural frequency increases with the increase in the degree of polynomial under the C-C boundary condition. However, the rate of increment is somewhat slow with the increment of the divergence of the beam. It may be revealed that the natural frequency decreases with the increase in degree of polynomial. Moreover, the decrement rate is faster with the increment of the convergence of the beam. The same variation is observed for higher values n. The natural frequency decreases with the increase in the degree of polynomial under the C-F boundary condition. However, the decrement rate is promptly with the increment of the divergence of the beam. It may be revealed that the natural frequency increases with the increase in the degree of polynomial. Although, the rate of decrement is somewhat prompt with the increment of the convergence of the beam. The same variation is observed for higher values of n. It can be seen that with the increase in slenderness ratio, the natural frequency decreases under both types of boundary conditions. It can be revealed that the natural frequency becomes almost same after 35 (l/h > 35) for all degrees of polynomial. It is found that with the increase in the volume fraction index, natural frequency decrease for both the convergent and divergent beams.