doi: 10.52899/24141437_2026_03_299
UDK: 531.391.1:532.5.011

Determination of Second‑Order Nonlinear Forces Due to Sum and Difference of Frequencies Arising From Ship Motions in Irregular Waves

Семенова В. Ю., Чжан С. .
Article language: русский
Citation Link: Semenova VYu, Zhang X. Determination of Second‑Order Nonlinear Forces Due to Sum and Difference of Frequencies Arising From Ship Motions in Irregular Waves. Transactions of the Saint Petersburg State Marine Technical University. 2026;5(3):299–310. DOI: 10.52899/24141437_2026_03_299 EDN: ZMGSLM

Annotation

BACKGROUND: The importance of calculating high-order nonlinear forces has been confirmed by numerous theoretical and experimental studies. Of particular importance are nonlinear forces caused by the sum and difference of frequencies, which can cause long-period oscillations of ships and offshore structures and lead to fatigue stress. Therefore, determining these forces under natural irregular wave conditions is a pressing issue. AIM: To develop a method for calculating nonlinear forces caused by the sum and difference of frequencies under irregular wave conditions. METHODS: To calculate nonlinear forces, the integral equation method and the spectral method are used. RESULTS: A method for calculating nonlinear forces caused by the sum and difference of frequencies in irregular waves has been developed and validated. Calculations of nonlinear forces induced by the sum and difference of frequencies were performed for various types of vessels under irregular wave excitation. The results obtained for different vessel types and various frequency combinations are analyzed. CONCLUSION: The paper describes a methodology for calculating nonlinear forces due to the sum and difference of frequencies in irregular waves. An increase in nonlinear force values in irregular waves is demonstrated with increasing wave severity. Itis shown that nonlinear forces due to the sum of frequencies under irregular wave conditions exceed those due to the difference. Keywords: nonlinear forces; frequency difference; frequency sum; small parameter method; integral equation method; irregular waves.

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