Nonlinear random vibration of laminated FRP plates using high-order shear theory.

摘要

The nonlinear response of laminated fiber reinforced plastic (FRP) plates modeled with finite elements and excited by stochastic loading is studied. The use of FRPs has been extended rapidly for structural applications in recent years due to their outstanding mechanical properties. Most FRP materials have strong anisotropic properties and exhibit significant nonlinearity in the shear stress-strain law. A high-order shear theory is used to account for the variation of strains through the thickness, since Kirchhoff and Mindlin plate theories are usually inadequate for modeling laminated FRP plates of reasonable thickness. Approximate nonlinear random vibration analysis is performed using the method of equivalent linearization to account for material nonlinearity. The solutions are obtained using an iterative approach, where linear random vibration analysis is performed in each iteration. A computer program is developed and implemented for the nonlinear random vibration analysis. Cantilevered FRP plates consisting of single-ply and three-ply plates with rectangular geometry and Boron/Epoxy Narmco 5505 FRP material are considered in numerical examples. Various types of fiber orientations and stacking sequences are considered. The results show that the effect of nonlinearity on the responses becomes more pronounced as the excitation level is raised, and hence the number of iterations required for convergence also increases. The material nonlinearity significantly affects some displacement, strain, and stress responses, depending on the fiber orientations, stacking sequences, material properties and plate geometry. Use of the high-order shear deformation theory also significantly affects the responses in comparison to simpler theories such as the classical and first-order shear deformation theories. A formulation for deterministic dynamic analysis is also developed and some deterministic simulations are performed to verify the accuracy of the approximate nonlinear random vibration method. The random vibration analysis is found to be sufficiently accurate and considerably more cost effective than the use of deterministic simulations.