Dynamic stability of functionally graded materials skew plates subjected to uniformly distributed tangential follower forces

Abstract

The dynamic stability of functionally graded material (FGM) skew thin plate subjected to uniformly distributed tangential follower force is investigated. The material properties are assumed to vary continuously through their thickness according to a power-law distribution of the volume fractions of the plate constituents based on the Voigt model. In skew coordinate system, the differential equations of motion of the FGM skew plate subjected to uniformly distributed tangential follower force are derived by the Kirchhoff thin plate theory, and the different boundary conditions are obtained of the plate for arbitrary curve edges. By eliminating the in-plane displacement components on the neutral plane, the differential equations of motion can be expressed in terms of deflection only. Then the equations are discretized by the differential quadrature method, and the curves of real parts and imaginary parts of the first second-order dimensionless complex frequencies vs. uniformly distributed tangential follower force are obtained. The effects of the gradient index, skew angle and aspect ratio on the instability type and the corresponding critical load of the non-conservation FGM skew plate are analyzed.

Nonconservative stability of viscoelastic plates subject to triangularly distributed follower loads

“…Dynamic stability of functionally graded plates under uniformly distributed axial loads was studied by Ruan et al (2012) and shells by Torki et al (2014a,b). These studies neglected the effect of viscoelasticity on the stability of the columns and plates.…”

Mode shapes and frequencies of thin rectangular plates with arbitrarily varying non-homogeneity along two concurrent edges

“…(2014) as generalized differential quadrature finite element method (GDQFEM) etc. have emerged the powerful technique for producing highly accurate results with minimum computational efforts for both initial and boundary value problems (Wu and Liu, 2004; Tomasiello, 1998; Shu, 1996; Viola and Tornabene, 2006; Honga and Jane, 2013; Ruan et al., 2011; Asadi and Qatu, 2012; Lal and Rani, 2014) arising in the mechanics.…”

“…In the recent years, differential quadrature (DQ) method introduced by Bellman and Casti (1971) and Bert et al (1988) and its improved versions proposed by Shu and Richards (1992) as generalized differential quadrature (GDQ) method, Striz et al (1995) as harmonic differential quadrature (HDQ) method, Shu and Chew (1997) as Fourier expansionbased differential quadrature (FDQ) method, Liu and Wu (2001) as generalized differential quadrature rule (GDQR), Karami and Malekzadeh (2013) as new differential quadrature (NDQ) method, Krowiak (2006aKrowiak ( , 2006b as spline-based differential quadrature method (SDQM), Fantuzzi et al (2014) as generalized differential quadrature finite element method (GDQFEM) etc. have emerged the powerful technique for producing highly accurate results with minimum computational efforts for both initial and boundary value problems (Wu and Liu, 2004;Tomasiello, 1998;Shu, 1996;Viola and Tornabene, 2006;Honga and Jane, 2013;Ruan et al, 2011;Asadi and Qatu, 2012;Lal and Rani, 2014) arising in the mechanics.…”

Nonlinear vibration and dynamic response of imperfect eccentrically stiffened shear deformable sandwich plate with functionally graded material in thermal environment

“…The dynamic stability of FGM skew thin plate subjected to a uniformly distributed tangential follower force has been investigated by Miao Ruan et al. [7]. Duc et al.…”