Semnan University Press Mechanics of Advanced Composite Structures 2423-4826 5 1 2018 04 01 Theoretical, numerical, and experimental analyses of free vibrations of glass fiber reinforced polymer plates with central cutouts and free boundaries 67 74 2956 10.22075/macs.2018.12167.1116 EN Sina Soleimanian Department of Materials and Manufacturing Processes, Malek Ashtar University of Technology, Lavizan, Tehran, Iran Ali Davar Malek Ashtar University of Technology Reza Azarafza Department of Materials and Manufacturing Processes, Malek Ashtar University of Technology, Lavizan, Tehran, Iran Jafar Eskandari Jam Department of Materials and Manufacturing Processes, Malek Ashtar University of Technology, Lavizan, Tehran, Iran Mohammad Reza Zamani Department of Mechanical Engineering, MalekAshtar University of Technology, Tehran, Iran Journal Article 2017 08 06 This study explored the free vibration problem in relation to glass fiber reinforced polymer (GFRP) plates with central cutouts and free boundaries using theoretical, experimental, and numerical methods. The theoretical formulations were derived from the classical lamination plate theory. The rectangular cutout was mathematically modeled into the stiffness matrix of the plate by multiplying Heaviside distribution functions. The theoretical values for the fundamental frequency were obtained by solving the standard eigenvalue problem, and the theoretical solution was validated by comparison to the literature. Modal testing was performed in the laboratory. For additional validation, the accuracy of theoretical and experimental results was checked using the finite element method and ABAQUS. The results of all three methods agreed; thus, the applicability of the Heaviside functions to stiffness modeling of structures with cutouts was proven. It was also observed that the fundamental frequency decreased when cutout size increased. https://macs.semnan.ac.ir/article_2956_0c1b2c36164876ea2d5e6c73246316d3.pdf