Multiscale studies on the nonlinear vibration of delaminated composite laminates–global vibration mode with micro buckles on the interfaces

Abstract

This paper presents a multiscale approach to study the nonlinear vibration of fiber reinforced composite laminates containing an embedded, through-width delamination dividing the laminate into four sub-laminates. The equations of motion are established from macroscopic nonlinear mechanics for plates and shells and micro-mechanics of composite material to allow for the influences of large amplitude, membrane stretching in the neutral plane, and the interactions of the sublaminates. Analytical solutions obtained in this paper reveal that the interaction penalty at the interfaces plays a coupling effect between sublaminates, which eventually alters the vibration characters of the four-sublaminate lamina in macroscopic and microscopic mechanism. From a macro perspective, sub-laminates above and below the delamination vibrate in exactly the same mode in spite of their different stiffness and the four-sublaminate lamina has a consistent global vibration mode. In accompanying with the macro vibration, micro buckles occur on the interfaces of the delamination with amplitude about 10−3 times of that of the global mode. It is found that the vibration frequency is an eigenvalue of the delaminated lamina determined only by the geometry of the delamination. Authentication of the multiscale study is fulfilled by comparing the analytical solutions with the FEA results.

Non-linear vibration of delaminated composite beam with two overlapping delaminations

“…Xu et al (2017) presented a multiscale method to investigate the non-linear vibration of delaminated reinforced composite laminates with through-width delamination. According to this study, the interaction penalty between interfaces of delaminated segments has a significant role in the vibration response of delaminated composite structures at both macroscopic and microscopic mechanisms.…”

Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review

“…The classical linear and nonlinear plate equations are the main keys for creating various plate models, including delamination of composite plates (Vasiliev and Morozov [27], Stavroulakis and Panagiotopoulos [28], Storakers and Andersson [29], Xue et al [30], and Haghani et al [31]), contact problems (Ohtake et al [32,33], Borisovich et al [34], and Malekzadeh and Setoodeh [35], Muradova and Stavroulakis [36][37][38][39], Muradova et al [40], Fichera [41]), analysis of buckled plates (Ciarlet and Rabier [3], Caloz and Rappaz [42], Matkowsky; Putnick [43], Chien et al [44], Chien et al [45], Muradova [46][47][48], Dossou and Pierre [49]), etc.…”