<p>The prediction of the dynamic characteristics of vibro-impact oscillators is crucial for vibration analysis and control. Vibro-impact oscillators, which are often modeled as piecewise-linear dynamic systems, represent vibrating structures that interact with elastic or rigid contact boundaries and are widely encountered in mechanical, aerospace, and civil engineering applications. Their complex nonlinear behavior makes resonance prediction both challenging and computationally expensive, as the resulting amplitude-dependent resonances are typically obtained through iterative numerical analyses and continuation procedures. To address the limitations of conventional numerical methods, the generalized bilinear frequency approximation (GBFA), an efficient analytical approach, was recently developed to analyze the backbone curves of high-dimensional vibro-impact systems with bilinear elements. However, the GBFA method is restricted to oscillators with one-sided contact. To overcome this limitation, this study presents a more general approach, the piecewise-linear frequency approximation (PiLFA) method, for analyzing nonlinear resonances in systems with multiple contact boundaries. The PiLFA method relates the nonlinear natural frequency of vibro-impact oscillators to their vibration amplitudes using an algebraic approach, thereby enabling backbone curve analysis without involving any numerical continuation procedures. In this study, the PiLFA method is applied to a single-degree-of-freedom vibro-impact oscillator and a microelectromechanical resonator with two-sided contact. The nonlinear resonances of these systems under varying gap sizes and prestress conditions are investigated. The predicted backbone curves are validated through numerical integrations, experiments, and finite element simulations. The results demonstrate that the PiLFA method accurately captures amplitude-dependent frequencies in vibro-impact systems with multiple contact boundaries while maintaining a low computational cost.</p>