Three-Dimensional Dynamics of Laminated Curved Composite Structures: A Spectral-Tchebychev Solution

Abstract

Composite structures have been widely used in many diverse industries due to their high stiffness, high strength, and lightweight. Furthermore, since they exhibit directional material properties, it enables superior advantages in the design process such as achieving tailor-made characteristics. Since these structures are subjected to dynamic excitations during operation, it is highly crucial to accurately and efficiently capture the dynamics of composite structures. This study presents a new spectral-Tchebychev (ST) solution to investigate the dynamic behavior of (curved) laminated composite structures. To derive the integral boundary value problem for each lamina, extended Hamilton principle is used. The strain energy is expressed using three-dimensional elasticity equations. To discretize the domain of the problem, Gauss–Lobatto sampling scheme is followed and the deflections (generalized coordinates) are expressed using the triple expansion of Tchebychev polynomials. Then, the system matrices for each lamina is calculated using the derivative and the integral operations defined in the Tchebychev domain. To connect the individual laminae, compatibility equations are written. To incorporate the compatibility equations and to incorporate any type of boundary condition, projection matrices approach (that is based on singular value decomposition) is used. To validate the accuracy of the presented approach, two case studies (straight and curved laminated composite) are investigated. In each case, the natural frequencies and the mode shapes are compared to those obtained from a commercial finite element (FE) software. The comparison indicates that presented three-dimensional spectral-Tchebychev solution technique enables the accurate and efficient prediction of the vibrational behavior of curved laminated composite structures.KeywordsCompositeCurved plateSpectral-TchebychevLayer-wise