A formulation for turbulent-flow-induced vibration of elastic plates with general boundary conditions

•A formulation for turbulent-flow-induced plate with general boundary conditions is developed.•The Monte Carlo integral method is used to solve the quadruple integral.•The increase of the vibration level with the increase of the turbulent flow speed is similar under different boundary conditions.•The effects of the flow direction are different for the FEFE plate and the FFFE plate when the variable stiffness of the boundary spring is above 105 N m−2. A formulation for studying the vibration characteristics of the rectangular plate with general boundary conditions excited by the turbulent boundary layer is developed in this paper. The Rayleigh-Ritz method, modified Fourier spectral approach, and the classical theory of elastic plates are employed to establish the vibration model of the rectangular plate. Besides, the sound pressures are calculated by the Rayleigh integral and the turbulent boundary layer pressure field is described by the cross-spectral density expression of the Corcos model. The power spectral density of vibration characteristics can be obtained according to the stochastic theory. The results indicated that the power spectral density of responses calculated in this paper are consistent with those in the references, which validate the accuracy of the developed formulation. The innovation of this formulation lies in the application of modified Fourier spectral approach to the turbulent-flow-induced vibration for the first time. The velocity power spectral density of the plate with classical and elastic boundary conditions are studied, and the influences of the boundary conditions are discussed. The boundary conditions affect the vibration response by controlling the system stiffness of the plate. Moreover, the influences of turbulent flow speed and direction under different boundary conditions are studied. It is found that the increasing turbulent flow speed leads to the increase of the vibration level, and the growth rate is similar under different boundary conditions. The velocity power spectral densities are slightly different when a turbulent flow along the short side and long side of the plate. [Display omitted]