doi:
UDK: 629.12.073.243.4

INVESTIGATION OF SECOND-ORDER ACCELERATIONS ON BIHARMONIC WAVES

Семенова В. Ю., Жукова А. М. Article language: English

Annotation

In this article, the study of nonlinear forces and accelerations of the second order, due to the difference and the sum of frequencies, is carried out on a biharmonic wave. The article describes a method for determining nonlinear second-order hydrodynamic forces and moments due to the sum and difference of frequencies, based on the solution of a second-order plane hydrodynamic problem. To solve this problem, the small parameter method is used using the Green function, as well as the combined method of Helmholtz integral equations. The determination of accelerations due to the action of nonlinear forces has not been considered before. The results of calculations of the horizontal and vertical components of acceleration for various combinations of frequencies on biharmonic waves for various types of vessels are presented. Also, the influence of nonlinear forces on accelerations for points on board, the bow perpendicular and the waterline of each vessel is considered. An algorithm for calculating the components of nonlinear accelerations on bichromatic waves has been developed. The calculations were carried out using a program written in the FORTRAN 90 programming language, which allows calculating nonlinear forces and accelerations due to the difference and sum of frequencies. Keywords: nonlinear forces, second-order accelerations, Green’s function, biharmonic wave, small parameter method, Helmholtz integral equation method.

Bibliography

1. KiavThura. Razrabotka metoda rascheta nelinejnyh sil vtorogo poryadka, obuslovlennyh summoj i raznost’yu, voznikayushchih pri kachke sudna na volnenie: dis. … kand. tekhn. nauk. [Development of a method for calculating nonlinear forces of the second order due to the sum and difference arising from the rolling of the vessel on the wave]. Diss. for the degree of Candidate of Technical Sciences of SPbGMTU, 2018. (In Russ.).
2. SemenovaV.Yu. Nelinejnaya teoriya kachki: Uchebnoe posobie. [Nonlinear theory of pitching, textbook of SPbGMTU], 2014. (In Russ.).
3. SemenovaV.Yu. Razrabotka metoda rascheta nelinejnoj kachki sudov: dis. … d-ra tekhn. nauk. [Development of a method for calculating the nonlinear pitching of ships”]. Diss. for the degree of Doctor of Technical Sciences of SPbGMTU 2005. (In Russ.).
4. SemenovaV.Yu. Raschet nelinejnyh sil vtorogo poryadka, obuslovlennyh summoj i raznost’yu chastot i voznikayushchih pri difrakcii neregulyarnogo volneniya ot shpangoutnogo kontura [Calculation of second-order nonlinear forces caused by the sum and difference of frequencies and arising from diffraction of irregular waves from the frame contour]. Journal Marine Bulletin N3(6) 2007, pp.43-47. (In Russ.).
5. SemenovaV.Yu. Gidrodinamicheskaya teoriya linejnoj kachki korablya [Hydrodynamic theory of linear ship pitching St. Petersburg], 2014. (In Russ.).
6. So Zho Tu. Razrabotka metoda rascheta nelinejnyh sil vtorogo poryadka, voznikayushchih pri kachke sudna na melkovod’e: dis. … kand. tekhn. nauk. [Development of a method for calculating nonlinear forces of the second order that occur when a ship is pitching in shallow water]. 2014, Diss. for the degree of Candidate of Technical Sciences B-kaSPbGMTU. (In Russ.).
7. Joao Pessoa, Carlos GuedesSoares, Marc Le Boullec. [Experimental Study of the Slowly Varying Wave Exciting Drift Forces On a Body of Simple Geometry]. Proceedings of the HYDRALAB III Joint User Meeting, Hannover, February 2010.
8. Kim M.H. [Second-order sum-frequency wave loads on large-volume structures]. Applied Ocean Research, 1991, Vol. 13, No. 6. pp.287-296.
9. Lee C.M. [The second-order theory for no sinusoidal oscillations of a cylinder in a free surface] “8th Symposium of Naval Hydrodynamics», Pasadena, 1970, pp. 905–950.
10.Papanikolaou A. [On the solution of the quasi-third order problem of two-dimensional cylinders in Forced –Motion]. Journal of the Kansai society of Naval Architecture, Japan N 210, 1988, pp. 121–133.
11. Pinkster I.A. [Low Frequency Second-Order Wave Exciting Forces on Floating Structures, Netherlands Ship Model Basin], Wageningen-Netherlands N 650, p.240.