Vibration Analysis of Three-Phase Composite Quadrilateral Plates with Different Angles under Artificial Boundary Conditions

This paper examines the free vibrations of three-phase composite quadrilateral plates at various angles under artificial boundary conditions. It derives the Lagrange energy equation based on the first-order shear deformation theory and analyzes the free vibration characteristics of the plates by combining the pb-2 Ritz method with artificial spring technology. This approach allows for the calculation of free vibrations of related plates under different boundary conditions without the need to rewrite the code. After validating the accuracy of the method, the study explores different factors on the effects of the natural frequencies of the plates. The results indicate that the natural frequency is highest with the FG-X distribution. Additionally, natural frequencies increase with higher mass fractions of carbon fibers (CFs) and graphene platelets (GPLs), with GPLs having a more significant effect than CFs. As the laying angle of CFs increases, natural frequencies decrease, and symmetrical three-phase composite quadrilateral plates exhibit slightly lower natural frequencies than asymmetric plates. When the length-to-thickness ratio of the GPLs is maintained at less than 10 5 and the length-to-width ratio is set to one, the plates demonstrate maximum natural frequencies. Our findings provide valuable insights into the potential application of these three-phase composite structures in engineering.