Modal Analysis of Parabolic Trough Solar Collectors Based on Mode Participation Factors
Modal analysis of parabolic trough solar collectors (PTCs) is critical for structural dynamic design under field operating conditions, yet the rational truncation of modal extraction orders remains inadequately addressed. This study derives theoretical expressions for mode participation factors and cumulative effective mass participation ratios from the differential equations of motion for proportionally damped systems under base excitation. Finite element modeling of a full-scale PTC (19.5 m length, 5.1 m rotational axis height, 8.5 m aperture width) was performed with mesh independence verification. Using a modal truncation criterion requiring cumulative effective mass participation ratio ≥90%, the first 15 modes were extracted, achieving 91.20% cumulative effective mass participation with numerical fluctuation below 0.10% across pitch angles. Computational modal parameters were solved for varying pitch angles, and field modal tests were conducted on the outermost purlin using impulse hammer excitation. Results demonstrate that pitch angle variation exerts minimal influence on modal parameters, with maximum natural frequency relative error of 0.57% and consistent mode shapes. Experimental and computational modal comparisons show high similarity in corresponding mode shapes, with maximum natural frequency relative error of 3.86%. Despite loss of modes 4–7 due to modal density and excitation limitations, the high-fidelity agreement of low-order modes validates the finite element model's applicability. The established methodology provides quantitative support for dynamic design of PTCs and offers generalizable reference for modal truncation and dominant mode selection in complex structures.