Determination of nonlinear second-order diffraction forces acting on a ship in shallow water conditions based on the use of three-dimensional potential theory

В статье рассматривается метод определения нелинейных дифракционных сил, действующих на судно в условиях мелководья на основании трехмерной потенциальной теории. Производится оценка влияния относительной глубины водоема Н/Т на данные нелинейные силы. Для нахождения нелинейных сил, требуется определение потенциалов второго порядка малости. Решение основано на методах малого параметра, интегральных уравнений Фредгольма и функции Грина для случая мелководья. Данное решение является новым для отечественной практики. При определении потенциалов второго порядка учитываются нелинейные граничные условия на свободной поверхности жидкости и на смоченной поверхности судна. На основании изложенного метода разработана программа расчета нелинейных сил при различных Н/Т. Приводятся результаты расчетов сил и моментов для трех различных типов судов. Приведено сравнение с расчетами, основанными на двумерной теории. Особое внимание уделяется учету потенциала набегающего волнения второго порядка. Учитывается его вклад в образовании нелинейных дифракционных сил. Приводится сравнение расчетов с учетом влияния данного потенциала и без него. The article discusses a method for determining nonlinear diffraction forces acting on a ship in shallow water conditions on the basis of a three-dimensional potential theory. The influence of the relative depth of the fluid Н/Т on these nonlinear forces is assessed. To determine them, it is necessary to calculate the potentials of the second order of smallness. The solution of the problem is carried out on the basis of small parameter methods, Fredholm’s integral equations and Green’s function for a fluid of limited depth. The presented solution in national practice is new. During the determination of the second order potentials, nonlinear boundary conditions on the free surface of the liquid and on the wetted surface of the ship are taken into account on the basis of methods program was developed, considering various Н/Т. The results of calculations of the forces and moments for three types of different ships are presented. Comparison with calculations based on two-dimensional theory is given. Special attention is paid to taking into account the potential of the second-order of incoming wave. Its contribution to the formation of nonlinear diffraction forces is taken into account. A comparison of calculations with and without the influence of this potential is given

The Determination of nonlinear second-order diffraction forces acting on a ship based on three-dimensional theory

В статье рассматривается определение нелинейных дифракционных сил второго порядка, на основании применения трехмерной потенциальной теории. Для их определения необходимо вычисление потенциалов второго порядка малости. Представленное решение в отечественной практике является новым. Решение задачи осуществляется на основании методов малого параметра и интегральных уравнений с учетом нелинейного граничного условия на свободной поверхностью жидкости. В работе показана возможность расчета интегралов по свободной поверхности напрямую за счет их сходимости на бесконечном удалении от судна. Нелинейные дифракционные силы и моменты определяются в работе с использованием различных функций Грина: для бесконечно-глубокой жидкости и жидкости ограниченной глубины, когда H→∞. Полученные результаты практически полностью согласуются между собой. Приводятся результаты расчетов дифракционных сил и моментов для четырех разных судов. Расчеты представлены в сравнении с расчетами по двумерной теории, выполненными также для случая бесконечно глубокой жидкости и жидкости ограниченной глубины при больших значениях отношения глубины к осадке H/T. Показано хорошее согласование результатов между собой. Показана возможность расчета нелинейных дифракционных сил на произвольных курсовых углах. The article discusses the definition of nonlinear diffraction forces of the second order, based on the application of three-dimensional potential theory. To determine them, it is necessary to calculate the potentials of the second order of smallness. The presented solution is new in domestic practice. The problem is solved on the basis of small parameter methods and integral equations taking into account the nonlinear boundary condition on the free surface of the liquid. The paper shows the possibility of calculating the integrals over the free surface directly due to their convergence at an infinite distance from the ship. Nonlinear diffraction forces and moments are determined in the work using various Green's functions: for an infinitely deep fluid and a fluid of limited depth when H → ∞. The results obtained are in almost complete agreement with each other. The results of calculations of diffraction forces and moments for four different ships are presented. The calculations are presented in comparison with the calculations according to the two-dimensional theory, performed also for the case of an infinitely deep liquid and a liquid of limited depth at large values of ratio H / T. Good agreement of the results with each other is shown. The possibility of calculating nonlinear diffraction forces at arbitrary heading angles is shown.

Mathematical Models of Microwave and Photonic Devices Engaging Strong Nonlinearities Using Decomposition on Nonlinear Autonomous Blocks

Mathematical modeling technique based on solving the nonlinear Maxwell’s equations (Eqs.) rigorously using the decomposition approach on nonlinear autonomous blocks partially filled by the nonlinear media with a “strong” nonlinearity (NABs) and reliable engineering method for numerical computation of microwave and photonic nonlinear 3D devices engaging strong nonlinearities, applicable in CAD, were developed. To determine the NAB descriptors the iterative computational process for solving the nonlinear 3D diffraction boundary problems with the non-asymptotic radiation boundary conditions on the NAB bounds was performed using the projection method. The iteration method of recomposition of NABs is developed using the linearization of its descriptors. Using the computational algorithm for solving nonlinear diffraction boundary problems performed as NABs and improved computation algorithm of determination of bifurcation points the nonlinearity thresholds in the magnetic nanoarrays at microwaves were numerically simulated.

Генерация третьей гармоники терагерцовых волн нелинейной графеновой многослойной метаповерхностью

The nonlinear diffraction of an electromagnetic wave by multilayer nonlinear metasurfaces consisting of rectangular graphene finite length ribbons array located on dielectric layers is studied at terahertz (THz) frequencies. It is shown that the third harmonic generation efficiency increases by several orders of magnitude at surface plasmon-polariton resonance frequencies, which can be controlled by dynamic tuning the chemical potential without changing the geometry and dimensions of the nonlinear graphene metasurface.

Air Gap Assessment of Semi-Submersibles: Efficient Utilization of Model Test Data

In linear air gap analysis of semi-submersibles, the surface elevation is modified by an asymmetry factor to account for the crest-to-trough asymmetry related to wave nonlinearity and the effect of nonlinear diffraction. The asymmetry factor varies with numerous conditions including the position relative to the semi-submersible, the sea state, the relative wave direction and the semi-submersible’s loading condition. Although simplified values for the asymmetry factor are suggested in rules and guidelines such as DNVGL-OTG-13, model tests should ideally be performed in order to get accurate values for each specific design. When considering nonlinear responses, model tests are generally done according to the contour line approach, where several realizations (seeds) of a few critical sea states are performed using the 3-hour maximum from each of these to fit a Gumbel distribution. We here seek to explore if the number of seeds can be optimized when considering the relative wave elevation (upwell) by using the less data-wasteful Peaks-Over-Threshold method.

Experimental observation of the far field diffraction patterns of functionalization single and multi-walled carbon nanotubes using nonlinear diffraction technique

Nonlinear diffraction pattern can be induced by focusing CWlaser into a thin quartzes cuvette containing nanofluid. The numberof revealed pattern rings indicates to the nonlinear behavior of fluid.Here, the nonlinear refractive index of each of functionalized singlewall carbon nanotube (F-SWCNTs) suspention and multi wall carbonnanotube (F-MWCNTs) suspention have been investigatedexperimentally .Each of CNTs suspention was at volume fraction of13×10−5 and 6×10−5. Moreover the laser source at wavelength of473 nm was used. The results show that SWCNTs suspentionpossesses higher nonlinearty than other at the same volume fraction