This paper extends the inverse substructuring (IS) approach to the state-space domain and presents a novel state-space substructuring (SSS) technique that embeds the dynamics of connecting elements (CEs) in the Lagrange Multiplier State-Space Substructuring (LM-SSS) formulation via compatibility relaxation. This coupling approach makes it possible to incorporate into LM-SSS connecting elements that are suitable for being characterized by inverse substructuring (e.g. rubber mounts) by simply using information from one of its off diagonal apparent mass terms. Therefore, the information obtained from an in-situ experimental characterization of the CEs is enough to include them into the coupling formulation. Moreover, LM-SSS with compatibility relaxation makes it possible to couple an unlimited number of components and CEs, requiring only one matrix inversion to compute the coupled state-space model (SSM). Two post-processing procedures to enable the computation of minimal-order coupled models by using this approach are also presented. Numerical and experimental substructuring applications are exploited to prove the validity of the proposed methods. It is found that the IS approach can be accurately applied on state-space models representative of components linked by CEs to identify models representative of the diagonal apparent mass terms of the CEs, provided that the CEs can be accurately characterized by the underlying assumptions of IS. In this way, state-space models representative of experimentally characterized CEs can be found without performing decoupling operations. Hence, these models are not contaminated with spurious states. Furthermore, it was found that the developed coupling approach is reliable, when the dynamics of the CEs can be accurately characterized by IS, thus making it possible to compute reliable coupled models that are not composed by spurious states.

翻译：本文扩展了逆子结构（IS）方法至状态空间领域，并提出一种新颖的状态空间子结构（SSS）技术，该技术通过相容性松弛将连接元件（CEs）的动力学特性嵌入到拉格朗日乘子状态空间子结构（LM-SSS）公式中。这种耦合方法使得仅需利用连接元件的一个非对角视在质量项信息，即可将通过逆子结构方法表征的CEs（例如橡胶支座）纳入LM-SSS公式。因此，通过原位实验表征获得的CEs信息足以将其包含在耦合公式中。此外，采用相容性松弛的LM-SSS方法能够耦合无限数量的组件和CEs，仅需一次矩阵求逆即可计算耦合状态空间模型（SSM）。本文还提出了两种后处理流程，用于通过该方法计算最小阶耦合模型。通过数值和实验子结构应用验证了所提方法的有效性。研究发现，若CEs的动力学特性可被IS的基本假设准确表征，则IS方法可精确应用于由CEs连接的组件状态空间模型，以识别CEs对角视在质量项的代表模型。由此可无需进行解耦操作即可获得表征实验表征CEs的状态空间模型，从而避免模型被伪态污染。进一步研究表明，当CEs的动力学特性可被IS方法准确表征时，所提出的耦合方法具有可靠性，能够计算不含伪态的可靠耦合模型。