Abstract The present article deals with the development and validation of a hybrid finite element-statistical energy analysis (FE-SEA) formulation employed to obtain the ensemble-average of the time-averaged vibrational energy response of dynamic systems with nonlinear joints. The proposed FE-SEA formulation is validated via a nonlinear stochastic benchmark model. The theoretical formulation related to the latter, is entirely derived by employing a variational approach. The weak-form of the governing equations, for each of the sample in the ensemble, is based on Kirchhoff’s thin-plate assumptions and is restricted to the out-of-plane motion only. The classical Lagrange-Rayleigh-Ritz method (LRRM), combined with the Monte Carlo simulation (MCS), is used as solution technique. An appropriate degree of uncertainty is introduced into the model in order to break the system symmetries ensuring transition from an exponential to a Rayleigh distribution of the modal spacing. Both in the hybrid FE-SEA and in the LRRM+MCS the localised nonlinearities are linearised by means of the method of harmonic balance. Various built-up plate systems, consisting of rectangular isotropic, homogeneous and linear elastic plates, elastically coupled by virtue of nonlinear translational and/or torsional springs and subjected to harmonic point loads are investigated.

中文翻译：

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非线性节点组合系统动态响应的混合有限元-统计能量分析方法

摘要 本文涉及混合有限元-统计能量分析 (FE-SEA) 公式的开发和验证，该公式用于获得具有非线性关节的动态系统的时间平均振动能量响应的整体平均。提出的 FE-SEA 公式通过非线性随机基准模型进行验证。与后者相关的理论公式完全是通过采用变分方法推导出来的。对于集合中的每个样本，控制方程的弱形式基于 Kirchhoff 的薄板假设，并且仅限于平面外运动。经典的 Lagrange-Rayleigh-Ritz 方法 (LRRM) 与蒙特卡罗模拟 (MCS) 相结合，用作求解技术。模型中引入了适当程度的不确定性，以打破系统对称性，确保模态间距从指数分布到瑞利分布的过渡。在混合 FE-SEA 和 LRRM+MCS 中，局部非线性通过谐波平衡方法线性化。研究了各种组合板系统，包括矩形各向同性、均匀和线性弹性板，通过非线性平移和/或扭转弹簧弹性耦合并承受谐波点载荷。