Analytical analysis of forced vibration of the hard-coating cylindrical shell with material nonlinearity and elastic constraint

In this paper, the nonlinear vibration characteristics of the hard-coating cylindrical shell with the base excitation and un-classical elastic constraint are investigated based on the Rayleigh-Ritz method. A continual variable stiffness elastic constraint is presented to introduce the actual uneven distribution of connection stiffness into the analytical vibration analysis. The nonlinear governing equations of motion are formulated by the Love's first approximation theory and von Karman-type nonlinear strain-displacement relationship. The admissible displacement functions are constructed by the Gram-Schmidt orthogonal polynomials. To effectively consider the effects of the strain dependences of storage modulus and loss factor of hard coating on the vibration characteristics of the shell, a modified domain decomposition method is employed to determine the equivalent strain of hard coating under the action of base excitation. By extending the Newton-Raphson iterative scheme, a unified iterative solution method is developed for solving the nonlinear resonant frequencies and responses of the hard-coating cylindrical shell. The numerical and experimental examples of the cylindrical shell coated with NiCoCrAlY + YSZ are performed to validate the accuracy and reliability of the developed analytical model. The mechanism of soft nonlinearity displayed in the amplitude-frequency curves of the hard-coating cylindrical shell is discussed as well.