Free vibration analysis of bio-inspired helicoid laminated composite plates resting on elastic foundation using isogeometric analysis and artificial neural network

The main aim of this study is to further extend isogeometric analysis (IGA) based on higher-order shear deformation theory (HSDT) with Soldatos’s continuous function \(f(z)\) for examining the free vibration characteristics of bio-inspired helicoid laminated composite (BiHLC) plates resting on elastic foundation (EF). The foundation follows Pasternak’s model with springer stiffness (\(k_{1}\)) and shear stiffness (\(k_{2}\)). The governing equation is derived by using Hamilton’s principle. The performance of the proposed formula is confirmed by comparing the obtained results with those of previous publications. In addition, an artificial neural network (ANN) model is set up by using Matlab software to accurately predict the natural frequencies of BiHLC plates without running code. Finally, some examples are conducted to provide novel results in the free vibration of BiHLC plates with different values of geometrical dimensions, material properties, boundary conditions (BCs), and foundation stiffness.