Traditional approaches to analyzing nonlinear systems often involve assuming a specific model form and model order for the nonlinearity. These nonlinearities in a system could instead be modeled as a nonlinear force applied to an underlying linear system. Force reconstruction methods can be used to recreate this nonlinear force from measured data, allowing the system change to be quantified. A modal based force reconstruction technique has proven capable of recreating force inputs at unmeasured locations and has been successfully applied to nonlinear intermittent external contact forces in previous studies. To extend these findings, a two-beam system was designed such that intermittent contact occurs near the joint locations, resulting in correlated forces. Previous work with this methodology has not addressed correlated loading conditions, so this work extends these techniques to the localization of correlated forces beyond measured points. The methodology is first demonstrated using analytical case studies, then performed experimentally. Acceleration responses are obtained from a sparse measurement grid which does not include the contact points, so the forces are reconstructed at unmeasured locations. Estimates of the nonlinear contact forces are calculated using the force reconstruction process, which are then compared to the measured force values. Cases are presented which address intermittent contact, loosening of preloaded connections, and the reconstruction of multiple connections simultaneously. Reconstructing correlated forces beyond measured points allows for the ability to locate and estimate forces without needing to assume the locations of these forces prior to acquiring data, extending the range of applications for these techniques.

传统的分析非线性系统的方法通常涉及假设特定的模型形式和非线性的模型顺序。可以将系统中的这些非线性建模为施加到基础线性系统的非线性力。可以使用力重建方法从测量数据中重新创建该非线性力，从而可以对系统变化进行量化。基于模态的力重建技术已被证明能够在无法测量的位置重建力输入，并且在先前的研究中已成功地应用于非线性间歇性外部接触力。为了扩展这些发现，设计了两束系统，使关节位置附近发生间歇性接触，从而产生相关的力。以前使用此方法的工作尚未解决相关的加载条件，因此，这项工作将这些技术扩展到了相关测力之外的相关力的本地化。该方法首先使用分析案例研究进行演示，然后通过实验进行。加速度响应是从不包含接触点的稀疏测量网格中获得的，因此在未测量位置重建了力。使用力重建过程来计算非线性接触力的估计值，然后将其与测得的力值进行比较。提出了解决间歇性接触，松开预紧连接以及同时重建多个连接的情况。