Fundamental frequency optimization of variable stiffness composite skew plates
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O R I G I NA L PA P E R
Touraj Farsadi
· Davood Asadi · Hasan Kurtaran
Fundamental frequency optimization of variable stiffness composite skew plates
Received: 28 May 2020 / Revised: 14 September 2020 / Accepted: 23 October 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract In this study, natural frequencies and vibrational mode shapes of variable stiffness composite skewed plates are optimized applying a genetic algorithm. The variable stiffness behavior is obtained by altering the fiber angles continuously according to two selected curvilinear fıber path functions in the composite laminates. Fundamental frequency and related mode shapes of the plates are optimized for two different fiber path functions using the structural model obtained based on the virtual work principle. A three-layer composite skewed plate with four types of boundary conditions and different plate geometries is considered as case study in this research. Diverse sweptback angles as well as different aspect ratios are considered as various plate geometries. The present study aims to calculate the best fiber path with maximized fundamental frequency or in-plane strengths for a composite skewed plate. The generalized differential quadrature method of solution is employed to solve the governing equations of motion. Moreover, the linear kinematic strain assumptions are used, and the first-order shear deformation theory is employed to generalize the formulation for the case of moderately thick plates including transverse shear effects. Numerical results demonstrate the effect of the fiber angles, boundary conditions, and diverse geometries on the natural frequencies of the composite plate. The optimal fiber angles of each layer are presented for the above cases in free vibration analysis. It is verified that the application of optimized curvilinear fibers instead of the traditional straight fibers introduces a higher degree of flexibility, which can be used to adjust frequencies and mode shapes.
1 Introduction Fiber-reinforced composite plates are widely used in the aerospace industry and aerial vehicles especially as lifting surfaces, canards, fins, and jet vanes due to their excellent properties of high stiffness and the strength-to-weight ratio [1–3]. A very interesting characteristic of the fiber-reinforced lamination and especially variable stiffness laminates is the possibility of tailoring the desired mechanical and aeroelastic properties with minimal weight and cost penalties [4]. In aerospace applications, it may be quite interesting to use variable stiffness composite laminates (VSCL) to increase or decrease the natural frequencies and avoid vibrational resonance of plates. In fact, without suffering weight penalties, the vibrational characteristics can be enhanced by tailoring the fiber angles of different layers. Initially, Gürdal et al. applied the curved fibers to vary the stiffness of rectangular composite plates [5]. Later, Gürdal et al. considered the effects of fiber path definitions on in-plane and ou
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