Nonlinear continuum thermo-mechanics of the composite thick panel used in concrete ceilings via general expression of the polynomial series theory

Proper concrete vibration is vital to the final quality and durability of concrete structures. There is a lack of objective methods to assess conformance to the requirements of vibration behavior of concrete systems used in various engineering structures. So, in the current work for the first time, nonlinear vibrations of a composite thick panel made of concrete materials are presented. In the current work, the GPLs are used to reinforce the thick concrete panel in the length direction. In the current work, according to the higher-order shear deformation shell theory the effects of the von Kármán strain-displacement kinematic nonlinearity are presented in the constitutive laws of the shell. The nonlinear governing equations for various nonlinear boundary edges are solved via discretization of equations on the space domain, derivation of Duffing-type equations, and Hadamard and Kronecker Products. The results are validated by comparing the current results with deep neural networks (DNN) and open-source results in the literature. For DNN, it is introduced a supervised neural network based on physical information to predict the vibrational behavior of the current system. In this context, data-driven solutions and data-driven discovery are presented to solve the problem of determining nonlinear frequency. Consequently, new results are investigated to show the effects of the Pasternak modulus, Winkler modulus, and the GPLs’ weight fraction on the nonlinear vibrations of concrete panels.