Frequency-Domain Analysis of Inequality-Constrained Structural Systems via a Stabilized Generalized Inverse Method

This paper presents a frequency-response formulation for inequality-constrained structural systems based on a stabilized generalized inverse method (SGIM). The proposed approach operates directly in the frequency domain, embedding constraint-aligned stiffness and damping into the dynamic stiffness operator and thereby producing projection-type frequency response functions (FRFs) that explicitly reveal the influence of constraints on structural vibration. An active-set strategy is employed to handle displacement and contacttype inequality constraints on a frequency-by-frequency basis, resulting in piecewisesmooth FRFs that capture constraint activation without introducing artificial dynamics. The role of stabilization parameters is examined in terms of resonance attenuation, constraint satisfaction, and numerical robustness. A series of representative vibration problems, including a two-degree-of-freedom pounding surrogate, multi-DOF structural chains, and a finite-element beam with localized stiffness reduction, are used to demonstrate the behavior of the method. The results show that the SGIM formulation effectively suppresses spurious amplification near resonances while preserving the natural frequencies and off-resonant FRF characteristics of the underlying unconstrained structure. The proposed framework provides a transparent and robust tool for frequency-domain analysis in structural dynamics, with potential applications to pounding mitigation, interstory drift control, and damage-sensitive FRF-based assessment.