Free Vibration Analysis of Curved Laminated Composite Beams with Different Shapes, Lamination Schemes, and Boundary Conditions

Abstract

A general formulation is considered for the free vibration of curved laminated composite beams (CLCBs) with alterable curvatures and diverse boundary restraints. In accordance with higher-order shear deformation theory (HSDT), an improved variational approach is introduced for the numerical modeling. Besides, the multi-segment partitioning strategy is exploited for the derivation of motion equations, where the CLCBs are separated into several segments. Penalty parameters are considered to handle the arbitrary boundary conditions. The admissible functions of each separated beam segment are expanded in terms of Jacobi polynomials. The solutions are achieved through the variational approach. The proposed methodology can deal with arbitrary boundary restraints in a unified way by conveniently changing correlated parameters without interfering with the solution procedure.

Dynamic Stability Analysis of the Laminated Composite Curved Frame Structures

“…Bolotin (1964) indicated that considering 2T= π/λ as period provides significant importance since the widths of the unstable regions are generally larger than those solved with period T = 2π/λ. Hence, performing a periodic solution considering the period as 2T on Equation (19) gives the eigenvalue problem of dynamic stability analysis as…”

“…They considered Hamilton's principle and first-order shear deformation theory to derive the governing equations of motions of the beam which is rested on Vlasov's foundation. Qin et al (2020) examined the vibration characteristics of the composite curved beams. For this purpose, they considered elliptical, parabolic, hyperbolic, and circular curved beams.…”

Location-based effect of decomposition on laminated curved plate structures

“…In this study, elliptical, circular, and parabolic types of curves are considered. The elliptical, circular, and parabolic curves with the relevant geometrical parameters are given in Figure 4 ( Qin et al, 2020). The symbols given in Figure 4 are the drawing parameters of the curved geometries.…”

Third-Order Theory for the Bending Analysis of Laminated Thin and Thick Plates Including the Strain Gradient Effect

“…The displacement field that characterizes the Third-order Shear Deformation Theory (TSDT), for instance, determines a quadratic profile of shear strains and stresses along the thickness [ 7 , 8 ], due to its cubic expansion in the thickness coordinate. Consequently, there is no need for the shear correction factor [ 9 , 10 , 11 , 12 ]. The importance of these cubic terms in the analysis of laminates has been recently highlighted in the paper by Petrolo and Carrera [ 13 ], in which the best theory diagrams for multilayered structures have been widely discussed.…”