Hybrid Methods For The Mid-Frequency Vibration Analysis Of Built-up Plate Structures

Built-up plate structures are widely used in the aerospace, automotive and ship industries. These engineering structures are subjected to broadband dynamic loads during their operation. Consequently, in order to preserve the safety, reliability and riding comfort of the whole system it is essential to study the forced response of plate structures for improving the design. For the structural vibration analysis at low frequencies and high frequencies, the finite element method and the statistical energy analysis can be used separately. However, when a built-up system is excited in a mid-frequency environment, some components will vibrate deterministically at low frequency, while others will undergo statistical vibration at higher frequency. For this mid-frequency vibration behavior of the built-up system, the finite element analysis will incur a prohibitive time cost, and the statistical energy analysis is inappropriate due to the insufficient modal overlap. Methods with more effectiveness are provided in this thesis for the mid-frequency vibration analysis of the built-up plate structures.The main idea of the proposed approaches is to divide the whole structure into uniform rectangular plate regions and non-rectangular regions. The vibration behavior of the rectangular regions is described by using symplectic waveshape expansion; the other non-rectangular regions of the structure are modeled by the conventional finite element method; and the plate components with sufficient randomness are described by statistical energy analysis. The details can be summarized as:1) A symplectic waveshape expansion method is developed for the mid-frequency vibration analysis of systems comprising rectangular thin plates. The wave propagation parameters and waveshapes are obtained using the symplectic method and thus eliminate the boundary condition limitation of the traditional analytical waveshape expansion method and avoid the numerical issues encountered frequently in the numerical waveshape expansion methods. The sympectic analytical solution of the dispersion relation is obtained from the the sympectic analytical solution of the wave propagation parameters. Considering the displacement continuity and equilibrium of force, the directly excited waves, the waveshape compatibility at junctions are obtained respectively, based on which the forced response of the structure can be computed. The expressions for plate energy and power flow between plates are also derived in terms of waveshape expansion. The results show that the in-plane behavior for the energy transmission among plate components at high frequencies is essential.2) A hybrid symplectic waveshape expansion and finite element method is developed for the mid-frequency vibration of built-up plate structures. The main idea of the proposed approach is to divide the whole structure into uniform rectangular plate regions and others. The vibration behavior of the rectangular regions is described by using symplectic waveshape expansion and the other non-rectangular regions of the structure are modeled by conventional finite element method. This hybrid analysis formulation makes full use of the advantages of the two methods. The present method shows great advantage of high accuracy and high efficiency in the analysis of mid and high frequency vibration of built-up plate structures. A modal expansion technique is provided for reducing the computational time of the inversing operation. In addition, the waveshape compatibility relationship at the junction is obtained by the hybrid formulation, based on which the finite element modeling can be avoided in a new analysis which significantly improves the efficiency.3) An energy flow analysis for the mid-frequency vibration of built-up plate structures is proposed based on symplectic waveshape subsystem description. This method considers the propagative waveshapes as subsystems that carry and spread energy. The system equations are established based on the equilibrium between the input and transmission and dissipation of energy of each waveshape subsystem. And thus this method can be regarded as an extension of the framework of the statistical energy analysis to the mid-frequency vibration of structures. The symplectic analytical solutions for mode count, modal density and group velocity of each waveshape subsystem are obtained. Unlike the power injection method, the proposed method can provide coupling factors that fully consider the medium frequency characteristics for both the weak coupling and strong coupling systems. Compared to the displacement based method, the present method uses the energy as degree of freedom and hence can provide more efficiency. Compared to the statistical energy analysis, the present method can accurately obtain the energy of each waveshape which can further provide a useful reference for the control of structural vibration.4) A hybrid symplectic waveshape expansion and statistical energy analysis method is provided for the mid-frequency vibration of built-up plate systems. When a built-up plate structure is excited in a mid-frequency environment, some components will vibrate deterministically at low frequency, while others will undergo statistical vibration at higher frequency. The deterministic plate component of the system is described in terms of symplectic waveshapes, and the statistical plate component is described by the statistical energy analysis. Comprared to the hybrid FE-SEA method, the proposed method can provide more accuracy and more efficiency. In addition, it is found that the proportionality coefficient between the coupling power and the difference of the energy of each component is constant when the external force is applied at different locations on the same line perpendicular to the waveshape propagation direction, based on which a fast solution technique is established.