title: Linear/nonlinear statistical energy analysis-based hybrid models for mid-frequency dynamic analysis of complex structures
Creators: name: Tan, Puxue
Publisher: name: University of Liverpool Repository
Year: 2023

description: Hybrid finite element - statistical energy analysis model has shown its distinct advantages in mid-frequency vibrational prediction of complex structures with uncertainties. This thesis, by extending existing the hybrid finite element-statistical energy analysis model, devotes to develop four new formulations. The initial two formulations broaden the linear applicability of the hybrid deterministic-statistical energy analysis model, while the latter two consider the presence of nonlinearity which is likewise a pivotal factor in the complex structure. The first formulation introduces a meshless method by modelling the deterministic components substituting the FE method. The meshless method-moving least square-Ritz is applied; the moving least square is used to construct the shape functions and to build the discrete model; the Ritz method allows to obtain variational formulation of the deterministic components. The penalty method or Lagrange multipliers can be used to enforce the boundary conditions when deriving the governing equations. These two different methods result in the moving least square-statistical energy analysis formulation with different complexity. The second formulation is proposed to target the structural global/local modes which have different sensitivities to uncertainties. A reduced-order method is employed to achieve good separations of the global/local elastic modes. This work respectively applies (parametric) perturbation method and (non-parametric) frequency-band-averaged technique, to global and local fields.
This formulation can achieve smooth energy response transition from low-frequency range to mid-frequency range. The third hybrid formulation is developed to target dynamic complex structures with nonlinear joints based on classic finite element-statistical energy analysis formulation. In the nonlinear hybrid finite element-statistical energy analysis formulation, the localized nonlinearities are linearized by using the method of harmonic balance for harmonic loads or statistical linearization for random loads. The proposed nonlinear finite element-statistical energy analysis formulation is validated by developing a nonlinear benchmark model combining the Lagrange-Rayleigh-Ritz method with the Monte Carlo simulation. The fourth formulation improves the work of the third one on the occasion of harmonic loads, by considering the energy scattering between the frequency bands. The equivalent stiffness of deterministic components in frequency domain is determined by using the method of harmonic balance with the Galerkin method. In linearized formulation, the diffuse fields at
selected frequencies are assumed to be the statistical subsystems. This increases the number of subsystems in comparison to the system under the linear consideration. For these four formulations, cases and numerical results are studied in order to validate the developed formulations and to investigate their performance.