2016 **Abstract:** A new model for the free transverse vibration of axially functionally graded (FG) tapered Euler-Bernoulli beams is developed through the spline finite point method (SFPM) by investigating the effects of the variation of cross-sectional and material properties along the longitudinal directions. In the proposed method, the beam is discretized with a set of uniformly scattered spline nodes along the beam axis instead of meshes, and the displacement field is approximated by the particularly constructed cubic B-spl…

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“…22 Liu et al analysed the free bending vibration of axially FG Euler-Bernoulli beams with tapered cross-section using the spline finite point method. 23 The effects of the material and cross-sectional properties varying along the axial direction on the natural frequencies were discussed. Cao and Gao investigated the free vibration of axially FG beams with non-uniform cross-section by using the asymptotic development method.…”

confidence: 99%

“…22 Liu et al analysed the free bending vibration of axially FG Euler-Bernoulli beams with tapered cross-section using the spline finite point method. 23 The effects of the material and cross-sectional properties varying along the axial direction on the natural frequencies were discussed. Cao and Gao investigated the free vibration of axially FG beams with non-uniform cross-section by using the asymptotic development method.…”

confidence: 99%

“…where 3 ( ) is the cubic B-spline function, which can be seen in [30,31,33]. If the spline interpolation basis function ( ) satisfies the following relation, the boundary problem can be solved easily, and the computation is greatly simplified:…”

confidence: 99%

“…(5) After processing all the elements by step (4), the load increment array under current iteration can be obtained by (29), (31), and (33):…”

confidence: 99%

“…Shahba and Rajasekaran [40] studied the free vibration analysis of AFG-tapered Euler-Bernoulli beams employing the differential transform element method. Liu et al [41] applied the spline finite point method to investigate the same problems. Rajasekaran [42] researched the free bending vibration of rotating AFG-tapered Euler-Bernoulli beams with different boundary conditions using the differential transformation method and differential quadrature element method.…”

confidence: 99%