Abstract
The present paper investigates the transverse vibration of a non-uniform axially functionally graded Timoshenko beam with cross-sectional and material properties varying in the beam length direction. The Chebyshev collocation method is used to spatially discretize the governing partial differential equations of motion of the beam into time-dependent ordinary differential equations in terms of Chebyshev differentiation matrices. An algebraic eigenvalue equation in matrix form is then formed to study the free vibration behavior of non-uniform axially functionally graded Timoshenko beams. Several results of natural frequencies of the beams are evaluated and compared with those in the published literature to assure the accuracy of the proposed model. The effects of taper ratio, material graded index, slenderness ratio, material compositions and restraint types on the natural frequencies of tapered axially functionally graded Timoshenko beams are examined.
Highlights
Graded materials (FGMs) have been used increasingly in various engineering and scientific fields recently because of their promising material properties over the traditional composites
The dynamic problems of engineering structures constructed from Functionally graded materials (FGMs) have received considerable attention, especially for the beam members commonly used in bridges, buildings and machine components
Four types of axially FGM beams (AFGM) beam constructed from Alumina and Stainless steel (A/S), Zirconia and Stainless steel (Z/S), Alumina and Aluminum (A/A), and Zirconia and Aluminum (Z/A), respectively, are considered
Summary
Graded materials (FGMs) have been used increasingly in various engineering and scientific fields recently because of their promising material properties over the traditional composites. The free vibration of non-uniform axially FGM Euler-Bernoulli beams with various end supports was presented by Huang and Li (2010) based on the integral equation method. Based on the lowest-order differential quadrature element and differential transform element methods, the vibration and stability problems of axially FGM Euler–Bernoulli beams with tapered cross-section were investigated by Shahba and Rajasekaran (2012). The free vibration of axially FGM Timoshenko beams with non-uniform cross-section was studied by Huang et al (2013) based on a unified approach. The bending vibration of non-uniform axially FGM Euler-Bernoulli beams was investigated by Chen (2020) based on the Chebyshev collocation method. An attempt has been made to apply the Chebyshev collocation method to analyze the transverse vibration of FGM Timoshenko beams with axially varying material and cross-sectional properties. Relevant parameter analyses are performed to demonstrate the effects of various material and geometric parameters on the free vibration characteristics of the AFGM Timoshenko beams
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