Impact of a Customized Shape Function on the Prediction of Vibrations in Composite Laminates Using Shear Deformation Theory

Abstract

This paper investigates the free vibrations of composite laminates using shear deformation theory, with a particular focus on the application of an adapted shape function that accounts for transverse shear deformation. The developed mathematical model allows for accurate analysis of the dynamic behavior of laminate structures, improving precision compared to classical theories that neglect these effects. Using the Matlab software package, a numerical algorithm has been implemented to solve the differential equations describing the free vibrations of laminates, enabling a detailed analysis of their dynamic characteristics. The study considers various geometric and material parameters of the laminates to assess their impact on natural frequencies and vibration dynamics. The results obtained from the numerical processing indicate a significant influence of the shape function on the accuracy of vibration predictions. This approach provides valuable insights for improving the vibration models of composite laminates, as well as for optimizing material and structural design in engineering applications.