In-plane vibration of laminated curved beams with variable curvature by dynamic stiffness analysis

Spectral finite element for wave propagation analysis of laminated composite curved beams using classical and first order shear deformation theories

“…A circular cross-ply composite (90 =0 ) beam with subtended angle a ¼ 1 rad Þ, obtained using the present FSDT and CLT based SFEs, are presented in Table 1 for thickness ratio h=R ¼ 0:1; 0:2 and 0.25. These results are compared with those presented by Tseng et al [4] based on the FSDT and by Lu and Lu [39] based on the exact 2D elasticity solution. The FSDT formulation in [4] does not consider 1=ð1 þ z=RÞ term in the shear strain expression [Eq.…”

“…These results are compared with those presented by Tseng et al [4] based on the FSDT and by Lu and Lu [39] based on the exact 2D elasticity solution. The FSDT formulation in [4] does not consider 1=ð1 þ z=RÞ term in the shear strain expression [Eq. (2)] and retains terms up to z 2 =R 2 in the stiffness coefficients.…”

“…For laminated composite beams, the shear deformation and rotary inertia play a key role in the response. The first order shear deformation theory (FSDT) or the Timoshenko beam theory, accounting for the effects of shear deformation and rotary inertia, is a simple and efficient 1D model for analysing moderately thick structures [3,4]. Several higher order shear deformation theories (HSDT) [5,6] and layerwise approaches [7] have also been employed for the vibration response of curved composite beams.…”

Differential Equations of Motion for Naturally Curved and Twisted Composite Space Beams

“…Yildirim [6] studied the free vibration of symmetrically orthogonal laminated curved beams, in which rotary inertia and axial and shear deformation effects are considered. Tseng et al [7] studied the free vibration of laminated curved beams with variable curvature based on Timoshenko theory. However, a transverse shear strain is constant along the thickness direction, and the shear shape factor was used in this research to adjust the lateral shear stiffness.…”

“…The abovementioned studies [1][2][3][4][5][6][7][8][9][10][11] included one or several items of the anisotropy of the rod material, the curvature and torsion of the rod axis, the effects of rotary inertia, and the shear and axial deformations. The effect of the warping deformation of the cross section on natural frequencies is disregarded.…”