Modeling large amplitude vibration of matrix cracked hybrid laminated plates containing CNTR-FG layers

Abstract

• A numerical framework for large amplitude vibration analysis of matrix cracked hybrid laminated plates. • Matrix crack is considered based on self-consistent model. • We show that the crack density of matrix cracks plays an important role in vibration of hybrid laminated plates. • Parametric studies are conducted to investigate effects of various parameters on nonlinear vibration responses. This paper presents the mathematical modeling of the nonlinear vibration behavior of a hybrid laminated plate composed of carbon nanotube reinforced functionally graded (CNTR-FG) layers and conventional fiber reinforced composite (FRC) layers. Three type symmetric distributions of single walled carbon nanotubes (SWCNTs) through the thickness of layers are considered. The cracks are modeled as aligned slit cracks across the ply thickness and transverse to the laminate plane. The distribution of cracks is assumed to be statistically homogeneous corresponding to an average crack density. The obtained partial differential equations are solved by the element-free kp-Ritz method, and the iteration process is dealt with using the linearized updated mode method. Detailed parametric studies are conducted investigate the effects of matrix crack density, CNTs distributions, CNT volume fraction, plate aspect ratio and plate length-to-thickness ratio, boundary conditions and number of layers on the frequency-amplitude responses of hybrid laminated plates containing CNTR-FG layers.