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The nonlinear free and forced vibration responses of the lattice sandwich plates are calculated. The nonlinear equations of motion of the structures are derived by Hamilton’s principle with the assumed mode method. In the structural modeling, the von Kármán large deflection theory is applied to establish the strain–displacement relations. Three types of the sandwich plates with pyramidal, tetrahedral and Kagome cores are considered. This paper is devoted to investigate the nonlinear vibration characteristics and active control of composite lattice sandwich plates using piezoelectric actuator and sensor. The research results of this paper provide a theoretical reference for the selection of membrane materials, the subsequent calculation of wind-induced stability of steel skeleton membrane structure and the design of wind-driven rain resistance. The results were compared with the numerical results obtained by Runge-Kutta method to verify the accuracy of the method. The calculation and analysis of different membrane prestress, different length width ratio, different rise span ratio and different material parameters (elastic modulus ratio, viscous damping and material density) were carried out.
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The calculation examples of membrane material parameters were given. In order to verify the effectiveness and effective range of the method, the fourth order Runge-Kutta method was used for numerical calculation. By using Galerkin and KBM perturbation method, the analytical expressions of frequency function, displacement function and mode shape of nonlinear free vibration were obtained. In this paper, based on von Karman's large deflection theory and D’Alembert's principle, the governing equations of nonlinear viscous damped prestressed free vibration of frame supported anisotropic membrane structures were established. In order to study the influence of geometric nonlinearity and material parameters on the free vibration behavior of the cylindrical skeleton supported prestressed fabric composite membrane.
![Membrane structures calculation](https://kumkoniak.com/100.jpg)