Chapter4 Experimental Nonlinear Dynamics of Laminated Quasi-Isotropic Thin Composite Plates H.G. Kim and R. Wiebe Abstract Composite panels and plates are increasingly used and continuously developed in diverse industrial domains such as aerospace, automobile, civil and naval structures. However, nonlinear dynamic behavior and failure mechanisms of these structures are still obscure in many respects. A representative example of this issue is nonlinear dynamic behavior of damaged curved composite plates, which is not well represented in the literature although the phenomena could have a detrimental effect on the safety of the aforementioned structures. In this work, free vibrations of (a) an isotropic flat plate (ASTM A36 steel) under fully clamped (CCCC) and cantilever (CFFF) boundary conditions, (b) a symmetrically laminated quasi-isotropic flat composite plate (unidirectional carbon/epoxy) under the same boundary conditions (CCCC and CFFF), and (c) a post-buckled symmetrically laminated quasi-isotropic flat composite plate (carbon fibers woven fabrics) under a clamped and free (CCFF) boundary condition are investigated. A single-point laser is used to capture the dynamic responses of the plates. The von Kármán strain-displacement relations and Rayleigh-Ritz method are employed based on the classical laminated plate theory (CLPT) to establish a theoretical model. This research will ultimately be extended to the nonlinear modeling of vibrations and damage of curved laminated composite plates subjected to large deformations. Keywords Nonlinear dynamics • Free vibration • Experimental mechanics • Quasi-isotropic composite plate • Post-buckled plate 4.1 Introduction The industrial application of composite materials has been significantly growing during the last half century due to its wellknown properties, high strength and low density [1]. The Boeing 787 which is the first commercial airliner with a composite fuselage and wings is a compelling example of the structural application of composite materials. Fifty percent of its primary structures, including the fuselage and wings, is made up of carbon fiber/epoxy composite materials, or carbon fiber-reinforced plastics (CFRP) [2]. This design has led to 20 % of weight savings and 30 % lower airframe maintenance cost [3]. Despite the increasing demand and application of the composite structures, its failure mechanism is still obscure. Considerable efforts to develop accurate failure theories of composites and to prove their validity have been made as shown in the so-called World Wide Failure Exercise (WWFE-I: 1996–2004, WWFE-II: 2007–2013, and WWFE-III: 2013–Present); however, no composite material failure criteria are making precise predictions on damage and failure of composite materials and a global consensus about the validity of the leading theories has yet to be reached [2, 4]. Quasi-isotropic laminates have been very popular due to their isotropic behavior under in-plane extension (but not locally), and this fact has motivated engineers to substitute metals with quasi-isotropic laminates simply using the previous designs for the metals [5]. Similarly, black quasi-isotropic carbon/epoxy laminates are called as black aluminumbecause their in-plane effective elastic properties can be remarkably close to those of aluminum alloys [5]. However, this approach overlooks the crucial properties of quasi-isotropic laminates such as anisotropic out-of-plane behavior, delamination, and inter-laminar failure [5]. Moreover, although quasi-isotropic laminates exhibit isotropic behavior under in-plane extension at the laminate level, each ply experiences different magnitude of stresses depending on its material properties and geometry, which determines the failure of the plies. In this paper, to address these challenges, linear and nonlinear out-of-plane dynamic responses of both flat and post-buckled laminated quasi-isotropic composite plates are presented. A robust review and analysis of theories on linear dynamic behaviors of isotropic plates was presented by Leissa in [6] and [7]. Chia exhaustively discussed nonlinear static and dynamic behaviors of isotropic and anisotropic plates in [8]. Many H.G. Kim( ) • R.Wiebe Civil and Environmental Engineering, University of Washington, Seattle, WA 98195, USA e-mail: hgyukim@uw.edu © The Society for Experimental Mechanics, Inc. 2016 G. Kerschen (ed.), Nonlinear Dynamics, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-29739-2_4 29
RkJQdWJsaXNoZXIy MTMzNzEzMQ==