Experimental and Numerical Validation of an Extended FFR Model for Out-of-Plane Vibrations in Discontinuous Flexible Structures

Toward the innovative design of tunable structures for energy generation, this paper presents an extended Floating Frame of Reference (FFR) formulation capable of modeling slope discontinuities in flexible multibody systems—overcoming a key limitation of conventional FFR methods that assume slope continuity. The model is validated using a spatial double-pendulum structure composed of circular beam elements, representative of out-of-plane energy harvesting systems. To investigate the influence of boundary constraints on dynamic behavior, three electromagnetic clamping configurations—Fixed–Free–Free (XFF), Fixed–Free–Fixed (XFX), and Free–Fixed–Free (FXF)—are implemented. Tri-axial accelerometer measurements are analyzed via Fast Fourier Transform (FFT), revealing natural frequencies spanning from 38.87 Hz (lower frequency range) to 149.01 Hz (higher frequency range). For the lower frequency range, the FFR results (38.76 Hz) show a close match with the experimental prediction (38.87 Hz) and ANSYS simulation (36.49 Hz), yielding 0.28% error between FFR and experiments and 5.85% between FFR and ANSYS. For the higher frequency range, the FFR model (148.17 Hz) achieves 0.56% error with experiments (149.01 Hz) and 0.85% with ANSYS (146.91 Hz). These high correlation percentages validate the robustness and accuracy of the proposed FFR formulation. The study further shows that altering boundary conditions enables effective frequency tuning in discontinuous structures—an essential feature for the optimization of application-specific systems such as wave energy converters. This validated framework offers a versatile and reliable tool for the design of vibration-sensitive devices with geometric discontinuities.