Predicting dynamic response of stiffened-plate composite structures in a wide-frequency domain based on Composite B-spline Wavelet Elements Method (CBWEM)

Due to the mid-frequency problem, the Hybrid Statistical Energy Analysis (SEA) / Traditional Finite Element Methods (TFEMs) methods still cannot provide the dynamic responses of the stiffened-plate composite structures in a wide frequency domain. The main reason is that all of the SEA and TFEMs cannot provide the reliable numerical solutions in the middle frequency domain when simulating the thin plate substructures. In order to solve the problem, this paper proposes the Composite B-spline Wavelet Elements Method (CBWEM) based on the c₁ type wavelet plate and beam elements for modeling the stiffened-plate composite structures and predicting its dynamic responses in a wide frequency domain. Unfortunately, due to the complex interpolation functions and transformation matrices of these c₁ type wavelet elements, the existing numerical scheme to construct the constraint matrix will be invalid when modeling the coupling relationship between the c₁ type wavelet plate and beam elements. To solve the problem, this study deduces and gives the formulas of the new numerical scheme for constructing the constraint matrix and modeling the stiffened-plate composite structures based on the CBWEM. Besides, the numerical and experimental studies are carried out to verify the CBWEM, respectively. On the one hand, the numerical study displays that the proposed method can solve the mid-frequency problem and provide reliable dynamic responses in a wide frequency domain within an acceptable computational cost. On the other hand, the experimental study shows that the Central Processing Unit (CPU) time to predict the dynamic response in a wide frequency domain is less than 3.5 s only based on the proposed method and the personal computers, and the corresponding numerical solutions are in good agreement with the experimental results. Thus, we can easily conclude that the proposed method can be taken as one useful numerical technique to solve the mid-frequency problem and predict the dynamic responses of the stiffened-plate composite structures in a wide frequency domain.