Resonators are often used to reduce low-frequency vibrations in shell and plate structures. Understanding the interaction mechanisms between resonators and host structures is crucial for effective vibration control. Although numerous theoretical models for such coupled systems have been developed in recent decades, a universal and precise dynamic modeling framework has not yet been established. This study proposes a unified dynamic stiffness (DS) model for shell or plate structures with resonators. The proposed model derives the stiffness matrices for shell and plate structures from their governing differential equations. The resonator is treated as an external excitation acting on the host structure. By formulating the resonator's kinematic equations, its displacement is related to that of the host structure, resulting in an equivalent DS matrix for the resonator. The resonator's equivalent stiffness matrix is further transformed into a projected DS matrix that matches those of the host structure using the Dirac delta function. The global DS matrix of the coupled system is assembled using a similar approach to the finite element method (FEM). The accuracy and applicability of the model are verified by comparing the present results with those from ANSYS simulations. Furthermore, the model is extended to the vibration control of coupled shell-plate structures, where the effects of resonator parameters on the vibration characteristics of the system are investigated. The results show that the proposed model not only has great accuracy and applicability, but also significantly reduces the computational degrees of freedom compared to traditional FEM.

The jet in crossflow describes a unique flow characteristic, which involves the injection of a fluid jet into a turbulent boundary layer. This flow structure is significant for applications in vibration reduction, noise suppression, and cooling and heat transfer. In this study, a numerical model for jet-in-crossflow was established using Large Eddy Simulation, and the accuracy of simulation results was validated by comparison with experimental data. On the basis of maintaining the same jet exit flow rate, the study investigated the differences in fundamental flow characteristics, wall pressure fluctuations, and flow noise among jet-in-crossflow cases with circular, square, and elliptical orifices. The distribution of sound sources for the three cases was identified using vortex sound theory. The study shows that the elliptical orifice case did not develop a jet blockage effect similar to the other cases. All three orifice cases generated counter-rotating vortex pairs, although the vortex core positions varied. For the circular and square orifices, the root mean square pressure along the lower edge of the orifice exhibited a symmetric distribution, while the elliptical orifice case showed no clear symmetry. In the downstream region, spanning 2–10 orifice diameters, a stable dominant frequency was observed for all three cases, which is attributed to vortex transport. The elliptical orifice demonstrated significant noise reduction performance, with a noise reduction of 3–8 dB, mainly concentrated in the downstream region up to 10 orifice diameters. Using Proper Orthogonal Decomposition and Dynamic Mode Decomposition, the relationship between vortex transport and wall pressure fluctuations for the three cases was explained. The analysis revealed the fundamental reason behind the noise reduction capabilities of the elliptical orifice and the vortex structures responsible for generating the dominant frequency.

This work presents a unified dynamic stiffness modeling for the vibration analysis of multi-plate coupled systems with discrete spring connections (MPCS-DSC). First, based on the governing differential equation of the plate, the dynamic stiffness matrix (DS) of transverse and in-plane vibration for a completely free rectangular plate is separately derived by combining the generalized superposition method and the projection method. Then, according to the continuity of displacements at the connection point between the spring and the plate, the projected DS matrix of the discrete spring is developed. Then, using an element assembly concept similar to that in the finite element method (FEM), global DS matrices of various coupled systems are determined by assembling the spring's DS matrice and the transverse or in-plane DS matrices of the plate. In order to verify the accuracy and applicability of the proposed method, the free and forced vibration analysis of four types of coupling systems is carried out. The reliability and applicability of the proposed method are confirmed by comparing the present results with those from open literature and the finite element solutions. This study not only expands the application range of DS modeling theory but also provides a powerful tool to investigate the vibration characteristics of the MPCS-DSC.

This paper presents a unified vibration modeling for free and forced vibration analysis of coupled open cylindrical shell-plate structures (COSPS). In the model, the coupled structure is first split into several open cylindrical shells and rectangular plates, and then based on Kirchoff's thin plate theory and Flugge's thin shell theory, the dynamic stiffness (DS) matrix of each substructure is separately established by applying the generalized superposition method and the projection method. Subsequently, according to the continuity and equilibrium conditions of the coupled boundary, the coordinate transformation matrix of each substructure is derived. After obtaining fundamental DS matrices and their coordinate transformation matrices, global DS matrices of various COSPS are assembled using a strategy similar to the finite element method (FEM) without repeating the theoretical derivation. To verify the convergence and reliability of the current formulation, free vibration and forced vibration analysis of three types of coupled structures are carried out, and the results are compared with those from published works and FEM solutions. In addition, an experimental model of a coupled structure is established and an experimental test is performed. The comparison results show that the proposed model is reliable and effective, and its modeling process is more direct and convenient. This work not only greatly expands the application scope of the DSM but also provides a new idea for the vibration analysis of COSPS.

A hybrid analytic-numerical formulation is developed to study the vibration behaviors of a cylindrical shell coupled with an internal flexural floor structure. The full structure is divided into a cylindrical shell, axisymmetric annular plates and a non-axisymmetric floor structure. The cylindrical shell and annular plates are analyzed by the analytic dynamic stiffness method (DSM) while the floor is modeled by the finite element method (FEM), so the line connections between the cylindrical shell and interior floor degrade into discrete point connections. At each coupling point, virtual springs are used to couple the cylindrical shell and interior floor, and coupling conditions at six Dofs are fully taken into consideration. In DSM, the displacement solutions of the cylindrical shell and annular plate are described by exponential functions and Bessel functions, respectively. In FEM, the dynamic condensation technique is adopted to reduce the model Dofs, while the main dynamic characteristic of the FEM model is preserved as much as possible.To verify the accuracy and effectiveness of present formulation, vibration results calculated by present method are compared with those obtained from FEM and a test experiment. Moreover, the effects of ribs, bulkheads, coupling conditions, boundary conditions of the shell and structural damping on the vibration responses are also investigated.

This paper presents a dynamic stiffness formulation for free vibration analysis of open cylindrical shells and their coupling structures. Based on the Flugge's thin shell theory, the dynamic stiffness matrix of an open cylindrical shell is derived by employing the projection method and a newly developed superposition method, which considers the entire domain of the system as a whole part instead of dividing it into small subdomains in the traditional Gorman's superposition method. By doing this, the derivation process of the dynamic stiffness formulation is much easier and the analytical model has a significantly lower order than the traditional dynamic stiffness formulation. The presented dynamic stiffness formulation is then extended to the vibration analysis of coupled shell structures. To achieve this goal, the coupled shell structures are divided into several sub-shells, and the global dynamic stiffness matrices are assembled according to the geometrical coupled conditions between them. Several typical coupled shell structures are taken as examples and their vibration characteristics are studied by the present formulation. The convergence and accuracy of the present formulation are verified by comparing present results with those obtained by literature and the finite element method (FEM). Parameter studies for the vibration analysis of the coupled shell structures are presented, indicating that the circumference angles, length-toradius ratios, and thickness-to-radius ratios have significant influences on the dynamic characteristics of the coupled shell structures.