RU2011599C1 - Semisubmersible base for sea structure - Google Patents

Abstract

FIELD: shipbuilding. SUBSTANCE: flat or volumetric passive-active damper 2 made in form of plate of circular vertical or horizontal cylinder is mounted in floating bases containing vertically oriented semisubmersed displacement columns 1 near free surface in area of active action of waves at a depth of 1.25 of the working amplitude of waves. This damper reduces self-disturbing action of waves on floating base. Form and geometric sizes of passive-active dampers for rated frequency and amplitude of wave are obtained from the conditions of minimization of total disturbing action of waves on the column and passive-active damper of forces of the static and hydrodynamic wave nature. Floating base also has device for minimization of disturbing action of waves at unrated swell which includes incoming wave parameter meter 3, unit 4 for processing these parameters and obtaining most probable length and amplitude, meter 5 for determination of submergence of semisubmersible base, electric power source 6, optimization unit 7, ballast tank 8 and automatic ballasting unit 9. EFFECT: enhanced reliability. 5 cl, 4 dwg

Description

 The invention relates to shipbuilding, in particular to means of developing the ocean and hydraulic structures, and is intended to reduce the disturbing effects of water on semi-submerged floating structures such as drilling and oceanological stabilized platforms, freely drifting and anchored buoys, as well as reducing their vertical pitching.

 A device is known for reducing pitching parameters by increasing the resistance coefficient of an object. It is implemented in devices such as the Froude milestone, which must float in a semi-submerged state. It contains a long semi-immersed vertical cylinder of small diameter, to the lower part of which a hydrodynamic damper with a load is suspended on a long cable [1].

 The milestone of Froude works with respect to the wave as a filter of high-frequency oscillations.

 The problem of decreasing vertical oscillations in a cylindrical vertical buoy of the Woods Hole Oceanographic Institute is similarly solved.

 Distinctive features of the technical solution used in the milestone and buoy: a semi-immersed vertical cylinder of small cross section with a length not less than the expected wave height in the region is used; at a depth of at least 0.5 the wavelengths expected in the region (the waves no longer penetrate to such depth) a damper (canvas sheet in a rigid frame) with an area of 30-40 times the cross-sectional area of the pole is suspended on the cable. The entire structure in a semi-dead state is maintained due to the positive buoyancy of the vertical cylinder and the negative buoyancy of the damper with suspended ballast; reduction of the disturbing effect of waves on a vertical cylinder is achieved only by reducing the diameter of the cylinder; the principle of operation of the design is passive filtering of vibrations due to a sharp increase in the inertia of the entire system.

 This technical solution, with all its simplicity, has several disadvantages: limited applicability for buoys that do not require large usable volumes and masses to accommodate equipment and crew; the technical complexity of the application for oceanological and drilling platforms, because when the diameter of the vertical column is 1.5-2 m, the damper area is very large.

 Known oceanological stations and platforms, which are vertical structures. Such, for example, platforms such as "Buoy Laboratory", "Spar", "Flip" [2]. They represent towed in a horizontal position structures, consisting of two cylindrical parts of different sections. For translation in working condition, the thicker part is filled with water ballast, and the platform takes a vertical position. The surface is crossed by a narrow part with a diameter of 1.8-4.5 m. Ballast tanks, fuel reserves, mechanisms, etc. are located in the lower part with a diameter 2-3.5 times larger. The passive quenching damping principle is also used in these structures: pear-shaped lower part has a large attached mass, and the surface crosses a cylinder of small diameter. Due to this, as in the case of the Froude milestone, conditions are created when the object (platform) weakly reacts to a disturbing force having a frequency 2-3 times higher than the frequency of natural vibrations.

 Compared to the buoys and the milestone of Frud, the increase in the period of natural vibrations of these structures is achieved by increasing the virtual mass attached (the mass of water displaced by the submerged volume, plus the mass added), by choosing the shape of the underwater part. But at the same time, hydraulic resistance to platform vibrations is small, they do not have dampers. Therefore, under non-wave disturbance (for example, at a high filling speed of the main ballast tanks), long-term oscillations of large amplitude are possible.

 The disadvantage of the device for stabilizing such platforms is also that it requires a depth of 40-60 m in the center of the stabilizing volume. Therefore, platforms can only be used at great depths. As before, the restriction applies - a small area of the waterline and a large diameter of a deeply submerged thickening. The principle of pitch reduction is passive filtering.

 The prototype of the invention is the semi-submerged base of the offshore structure, containing a water-changing cylindrical column crossing the free surface of the water, a work platform above it and a damper located on it under free surface [3].

 A disadvantage of the known device is that the calculated expressions for the pressure field in the waves, as well as the forces that form the basis of the known solution, are too simplified. Therefore, minimizing the vertical roll on their basis cannot give an accurate result. The simplified representation of forces (only pressure forces are taken into account) has limited the constructive ways of solving the problem only due to pressure forces at displacement volumes.

 The purpose of the invention is the expansion of the functionality of the structural ways of dealing with wave loads and improving the accuracy of stabilization of floating structures from vertical rolling on waves.

 The technical result of this invention is achieved in that in a semi-submerged base of a marine structure containing at least one displacement cylindrical column intersecting the free surface of the water, the work platform above it and a damper located on it under the free surface of the water, the length of the immersed part of the column and its surface height parts to the working area is at least 1.25-1.5 of the estimated wave amplitude, the damper is installed at a depth of 1.25 of the calculated wave amplitude and is passively active. The invention is provided with a device for minimizing the disturbing effect of waves on off-design waves.

In addition, the passive-active damper (PAD) is made in the form of a flat disk, and its area S _{PAD is} ≈0.137-0.147 / xS ₁ ˙λ _p , where S ₁ is the cross-sectional area of the column, determined from the buoyancy condition of the whole structure, λ _p - estimated wavelength.

In addition, PAD is made in the form of a volumetric cylindrical ring, and its volume V _{PAD is} ≈ (0.148-0.151) (1 + K ₂₂ ) ^-1 ˙ S ₁ ˙λ _p , where K ₂₂ ≈ 0.7-0.9 is the coefficient of the attached the mass of bulk PAD, depending on the shape and ratio of the difference between the outer and inner diameters and its heights.

= /0,256-0,266/·S₁·λ_p
Кроме того, устройство минимизации возмущающего воздействия волн на полупогруженное основание включает в себя электрический измеритель параметров набегающих волн, блок их обработки и получения наиболее вероятной длины и амплитуды, измеритель заглубления полупогруженного основания источник электоэнегии, блок оптимизации, балластную цистену с клапанами ее заполнения и осушения и блок автоматической балластировки. Измеритель параметров волн электрически связан с блоком оптимизации и измерителем заглубления, а блок оптимизации связан с блоком автоматической балластировки, при этом последний связан с клапанами заполнения и осушения балластной цистерны.In addition, the PAD is made in the form of a cylinder, the longitudinal axis of which is oriented horizontally, and its radius r ₂ and length l _{2 are} determined by the ratio
r $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ L ₂ e

= / 0.256-0.266 / S ₁ λ _p
In addition, the device for minimizing the disturbing effect of waves on a semi-submerged base includes an electric meter of incoming wave parameters, a unit for processing and obtaining the most probable length and amplitude, a deepening meter for a semi-submerged base, an electro-energy source, an optimization unit, a ballast cyst with valves for filling and draining it, and automatic ballasting unit. The wave parameter meter is electrically connected to the optimization unit and the depth meter, and the optimization unit is connected to the automatic ballasting unit, the latter being connected to the ballast tank filling and draining valves.

 In FIG. 1 shows a semi-submerged base of an offshore structure; in FIG. 2 - milestone with a passive active damper; in FIG. 3 - milestone with a flat passive-active damper; in FIG. 4 - milestone with a passive-active damper in the form of a cylinder.

 The semi-submerged base contains a displacement column 1, intersecting the free surface of the water, located on it under the free surface of the water damper 2. The length of the immersed part is at least 1.25-1.5 of the estimated wave amplitude. Damper 2 is installed at a depth of 1.25 of the estimated wave amplitude and is passively active. It also contains a device for minimizing the disturbing effect of waves on a semi-submerged base on an off-design wave, including an electric meter 3 of incoming wave parameters, a processing unit 4, a meter 5 for deepening a semi-submerged base, an electric power source 6, an optimization unit 7, a ballast tank 8 and an automatic block 9 ballasting.

, длины набегающих волн

, измерителя 5 заглубления вехи и других схем и систем вехи. Сигналы от блоков 4 и 5 поступают в блок 7 оптимизации режима позиционирования вехи и выработки управляющего сигнала для блока 9 автоматической балластировки вехи.The device operates as follows. Before setting the buoy or milestone from the carrier vessel, the parameters of the waves and the optimal depth of the PAD are determined, the necessary amount of ballast is provided, which ensures the necessary draft T of the buoy. In this state, the buoy is dropped from the vessel and it starts to work. The energy source 6 begins to generate electricity, which will go to the work of meter 3, unit 4 for determining the mathematical expectation of amplitude

, incident wavelengths

, milestone deepening meter 5 and other milestone circuits and systems. The signals from blocks 4 and 5 are received in block 7 optimization of the milestone positioning mode and generate a control signal for block 9 automatic ballasting milestones.

и

получаемых от блока 4, оптимальное заглубление ПАД или осадку вехи

.In block 7, for the already known dimensions of the milestone (radius of the vertical cylinder r, its length l, area S of the _PAD and volume V _{2 of the} PAD, inertia coefficients) and based on the following expressions (1) for the volumetric PAD (2) for the plane side mini Computer look for specific

and

obtained from block 4, the optimal deepening of the PAD or draft of the milestone

.

, получаемой из блока 5 и Т_орt, получаемой из блока оптимизации 7 и вырабатывается сигнал на прием (откачку) воды Δ Q.In block 9, the current draft is compared

obtained from block 5 and T _opt obtained from optimization block 7 and a signal is generated to receive (pump) water Δ Q.

=

-

.In accordance with this signal, the ballast water is received (pumped out) into the tank 8. In order for the system not to work continuously in block 9, a signal deepening from the difference must be provided

=

-

.

 The invention relies on the complete structure of the perturbing effect of waves on semi-immersed vertical cylindrical bodies and fully immersed flat or volumetric dampers, which act as unloading elements.

-

-
-

+

+ (1)
+

-

-
-

, где V₁ и V₂ - объемы погруженной части вертикального цилиндра и объемного демпфера;
S₁ - площадь поперечного сечения цилиндра;
l_1п и Y_o - длина погруженной части вертикальной цилиндра и заглубление центра его плавучести;
Y_ПАД - заглубление центра плавучести ПАД;
k = 2π/λ ; ω =

- волновое число и частота волны;
ε₁(y₀) = e

, ε₂(y_ПАД) = e

- коэффициенты ослабления амплитуды волны на горизонтах Y_o и Y_ПАД;
λ₁= K₁ρV₁; λ₂= K₂ρV₂ - присоединение массы цилиндра и демпфера;

и

- безразмерные коэффициенты демпфирования цилиндра и демпфера, отнесенные к массам ρV₁ и ρV₂ и частоте волны ω;
κ₁иκ₂- редукционные коэффициенты, определяемые соотношением размеров цилиндра и демпфера, и длиной волны.The full structure of the perturbing effect of the harmonic wave Y _b = A ˙cos ωt on a statically balanced vertically oriented cylinder 1 with a volumetric passively active damper 2 (Fig. 2) has the form:
F _y ≈

-

-
-

+

+ (1)
+

-

-
-

where V ₁ and V ₂ are the volumes of the submerged part of the vertical cylinder and the volume damper;
S ₁ - the cross-sectional area of the cylinder;
l _1p and Y _o - the length of the immersed part of the vertical cylinder and the deepening of the center of its buoyancy;
Y _PAD - deepening of the center of buoyancy of PAD;
k = 2π / λ; ω =

- wave number and wave frequency;
ε ₁ (y ₀ ) = e

, ε ₂ (y _PAD ) = e

- attenuation coefficients of the wave amplitude at the horizons Y _o and Y _PAD ;
λ ₁ = K ₁ ρV ₁ ; λ ₂ = K ₂ ρV ₂ - joining the mass of the cylinder and damper;

and

- dimensionless damping coefficients of the cylinder and damper, referred to the masses ρV ₁ and ρV ₂ and the wave frequency ω;
κ _{1 and} κ ₂ are reduction coefficients, determined by the ratio of the dimensions of the cylinder and the damper, and the wavelength.

, а для горизонтального радиуса r₂κ₂ = 1-

Структурное выражение (1) включает четыре составляющие: F_1г.ст - гидростатическую силу, связанную с изменением заглубления вертикального цилиндра. Эта сила изменяется в фазе с волной и пропорциональна площади сечения s₁; F_1ив и F_2ив - инерционно-волновые силы вместе с динамической частью сил давления, действующих на вертикальный цилиндр и объемный демпфер. Инерционно-волновые силы F_1ив и F_2ив пропорциональны массовому водоизмещению и присоединенным массам вертикального цилиндра и объемного демпфера, а также вертикальному ускорению частиц в волне на уровне Y_o и Y_ПАД. Эти силы опережают волну на π и действуют в противофазе в ней; F_1п и F_2п - силы присоса вертикального цилиндра и ПАД и поверхности, которые не зависят от времени. Эти силы с учетом ω²= gr пропорциональны квадрату угла волнового склона (2π/λ˙A˙ε₁) на уровне Y_o и Y_ПАД и водоизмещениям V₁ и V₂. Обычно эти силы учитываются лишь при изучении движения подводных лодок вблизи свободной поверхности. В задачах воздействия волн на буи и платформы этими силами можно пренебречь. Их, однако, в общем случае легко и учесть или компенсировать приемом водяного балласта; силы демпфирующей природы F_1д и F_2д, выразающиеся через размерные коэффициенты демпфирования V_yi =

V₁ и вертикальную скорость v_y2= A ˙ε_i˙ω˙ sinω˙ t на горизонтах Y_o и Y_ПАД. Эти силы опережают волну на π /2.For a vertical cylinder, κ ₁ = 1 -

, and for the horizontal radius r ₂ κ ₂ = 1-

Structural expression (1) includes four components: F _1g.st - hydrostatic force associated with a change in the depth of the vertical cylinder. This force varies in phase with the wave and is proportional to the cross-sectional area s ₁ ; F _1iv and F _2iv - inertial-wave forces together with the dynamic part of the pressure forces acting on the vertical cylinder and the volume damper. The inertial-wave forces F _1iv and F _{2iv are} proportional to the mass displacement and the attached masses of the vertical cylinder and the volume damper, as well as the vertical acceleration of particles in the wave at the level of Y _o and Y _PAD . These forces are ahead of the wave by π and act in antiphase in it; F _H1 and F _2n - suction force and a vertical cylinder and the surface of the PAD, which do not depend on time. These forces, taking into account ω ² = gr, are proportional to the square of the angle of the wave slope (2π / λ˙A˙ε ₁ ) at the level of Y _o and Y _PAD and displacement V ₁ and V ₂ . Usually, these forces are taken into account only when studying the movement of submarines near a free surface. In problems of the effect of waves on buoys and platforms, these forces can be neglected. However, they are generally easy to take into account or compensate for by the use of ballast water; damping forces F _1d and F _2d expressed in terms of damping dimensional coefficients V _yi =

V ₁ and the vertical velocity v _y2 = A ˙ε _i ˙ω˙ sinω˙ t at the horizons Y _o and Y _PAD . These forces are ahead of the wave by π / 2.

V₁sinωt-A²ε₂(y_ПАД)ω²C_yρS_ПАДsinωt
В отличие от (1) в структуре (2) объем демпфера полагается равным нулю, поэтому объемных сил давления он не доставляет, однако плоский демпфер имеет присоединенную массу, и возникающая на нем инерционная сила разгружающе действует на F_1г.ст. Коэффициент демпфирования плоского ПАД нормируется в этом случае на его площадь S_ПАД и ρ V_y ²/2. Как и в случае (1), демпфирующие силы вертикального цилиндра и ПАД опережают волну по фазе на π /2. Силы присоса здесь создаются лишь на вертикальном цилиндре, и силы эти малы.For the case of a vertical cylinder with a flat PAD (Fig. 3), the structure of the perturbing action of the wave on it has the form:
F _y ≈ gρS ₁ Acosωt-Aε ₁ (y ₀ ) ω ² κ ₁ (ρV ₁ + λ ₁ ) cosωt-
- Aε ₂ (y _PAD ) ω ² κ ₂ λ ₂ cosωt + kA ² ε $\genfrac{}{}{0ex}{}{\text{2}}{\text{1}}$ (y ₀ ) ω ² ρV ₁ - (2)
- Aε ₁ (y ₀ )

V ₁ sinωt-A ² ε ₂ (y _PAD ) ω ² C _y ρS _PAD sinωt
Unlike (1) in structure (2), the damper volume is assumed to be zero, therefore, it does not deliver volumetric pressure forces, however, the flat damper has an attached mass, and the inertial force arising on it acts unloading on F _{1 g.st.} PAD damping coefficient plane in this case is normalized to an area S _PAD and ρ V _y ^2/2. As in case (1), the damping forces of the vertical cylinder and PAD are ahead of the wave in phase by π / 2. The suction forces here are created only on a vertical cylinder, and these forces are small.

-

_

+

+ (3)
+

-

→

.Consider also the composite structure (Fig. 4), consisting of a vertical column or wall with a section S ₁ , and a horizontal cylinder with a section S2. This design can be a calculated component of submersible drilling platforms, consisting of many vertical columns and 2-3 horizontal cylinders. The length of the vertical column l ₁ , the length of the element of the horizontal cylinder l ₂ , the deepening of the centers of their buoyancy Y ₁₀ and Y _{20 The} structure of the perturbing effects of waves on this composite structure has the form:
F _y ≈

-

_

+

+ (3)
+

-

→

.

In contrast to structures (1) and (2), the role of PAD here is played by a horizontal cylinder. On it, inertial-wave forces F _{2iv are formed} , which together with F _1iv unload the action of F _1g.st.

 As experiments show, the perturbing forces of a damping nature are small compared with hydrostatic and inertial-wave ones, especially for a vertical cylinder. As for the suction forces, in both cases they can be compensated by the use of additional water ballast and therefore they can be excluded from consideration. The remaining terms allow explicit minimization of the amplitude of the total effect of the wave on the composite structure by selecting the appropriate volume (area), shape and depth of the PAD.

 Let us show by examples how at the stage of design and operation of floating structures (Figs. 2, 3, 4) the disturbing effect of waves can be minimized and their vertical pitch can be significantly reduced.

PRI me R 1 implementation of the present invention for milestones and buoys (Fig. 3). At the design stage, it is necessary to perform the following operations: retrieve the calculated area for the milestone or buoy and the mode of their operation. For a given wave intensity, select the most probable wavelength π _p and its amplitude A _p ; assign the length of the immersed part of the milestone l _1g ≥1.5 A _p and the entire milestone l ₁ ≥ (2.75-3) A _p for reasons so that during excitement all its upper part does not sink into the water and the damper, which should be immersed to a depth of Y _PAD ≈ 1.25 A _p from the waterline of the static equilibrium of the milestone in the absence of unrest; for reasons of ensuring the necessary buoyancy and useful volume of the milestone in a semi-submerged state, it is necessary to find the cross-sectional area s _{1 of the} milestone:
m _o + m _b + m _d = ρ˙ (s ₁ l _1n + V _b + V _d ) (4),
where m _o - net weight of the milestone together with devices, mechanisms, systems, housing;
m _b and m _d - mass of ballast and damper;
V _b and V _d - the volume of ballast and damper.

To solve equation (4), in a first approximation, neglected V _b and V _d from V ₁ = s ₁ l _1P, and then refine the value s _1.

·3 = 0.79; ε₂(y_ПАД) = exp -

·5 = 0.675.4. Find the attenuation coefficients of the amplitude at the level of the center of buoyancy of the milestone and damper. If for a numerical example we take λ _p = 80 m and A _p = 4 m, then l _p = 6 m, Y ₁₀ = 3 m, Y _PAD = 5, l ₁ = 12 m. For this data, ε ₁ (y ₁₀ ) = exp -

3 = 0.79; ε ₂ (y _PAD ) = exp -

5 = 0.675.

·60 = 0.009 и, следовательно, волна на пассивный демпфер не воздействует. Он работает только на пассивное сопротивление в уравнении колебательного звена.Here it is necessary to note the fundamental difference between the PAD and the massive damper of the Froude milestone, which is located at a depth of 60-70 m. For it, ε = exp -

· 60 = 0.009 and, therefore, the wave does not affect the passive damper. It works only on passive resistance in the equation of the vibrational link.

и V₁= s₁ l_1п и, считая, что силы присоса уравновешены приемом водяного балласта и главное воздействие на веху дают статические и инерционно-волновые компоненты, можно получить условия их взаимной компенсации:
F_1г.ст + F_1ub + F_2ub = 0 или
S₁-

· ε₁(l_1П·S₁+λ₁) -

· ε₂·λ_ПАД= 0.5. Using the conditions ω ² = g

and V ₁ = s ₁ l _1п and, considering that the suction forces are balanced by the reception of ballast water and the main impact on the milestone is provided by static and inertial-wave components, we can obtain the conditions for their mutual compensation:
F _1g.st + F _1ub + F _2ub = 0 or
S ₁ -

Ε ₁ (l _1P · S ₁ + λ ₁ ) -

Ε ₂ · λ _PAD = 0.

For a vertical cylinder, λ ₁ = = K ₁ ˙ρ˙V ₁ = K ₁ ˙ρ˙ l _1п˙ s ₁ , where:
K ₁ - the coefficient of the attached mass, changing at different frequencies in the range of 0.02-0.06. For a flat plate with area λ = π˙ρ˙ S, where K ≈1. Therefore, λ _{PAD is} ≈ρ˙S _PAD . This implies the condition for the area of a plane passive-active damper that neutralizes the calculated static effect of the wave on the pole.

- ε₁(y₁₀)l_1п(1+K₁)

(5)
Для принятых выше численных данных S_пад ≈ 11,6 s₁, и наружный радиус кольцевого демпфера К ≈3,54 r, где r - радиус самой вертикальной вехи. И если r = 0,20 м, то R ≈ 0,70 м размеры вполне технически реализуемые.S _PAD ≈ S ₁ ε $\genfrac{}{}{0ex}{}{\text{-}}{\text{2}}$ ¹ (y _PAD )

- ε ₁ (y ₁₀ ) l _1p (1 + K ₁ )

(5)
For the numerical data adopted above, S _pad ≈ 11.6 s ₁ , and the outer radius of the annular damper K ≈ 3.54 r, where r is the radius of the most vertical milestone. And if r = 0.20 m, then R ≈ 0.70 m dimensions are technically feasible.

, а высота волны h= 2 А при 3% обеспеченности составляет 0,06

, а при 1% обеспеченности - 0,1

(5). Отсюда ожидаемые амплитуды волн должны укладываться в диапазон

= /0.03-0.05/

. С учетом всего этого на основе (5) можно получить выражения для выбора S_ПАД для высот волн 1- и 3% -ной обеспеченности:
S $\genfrac{}{}{0ex}{}{\text{1\%}}{\text{ПА}}$ _Д ≈ S₁e

_ e

·1,5·0,05·1,04

≈ S₁·1,48

[0,159-0,0616] = 0,144S

S $\genfrac{}{}{0ex}{}{\text{3\%}}{\text{ПА}}$ _Д ≈ S₁e

_ e

·1,5·0,03·1,04

≈ S₁·1,26

[0,159-0,041] = 0,149·S

.Based on the expressions (5), said selection conditions previously magnitude submerged part milestones l _1H ≥1,5 A _p calculated wave amplitude and desensitization incident plane Y _PAD Ar ≈ 1.25, and the average values of coefficients associated mass vertical cylinder ₁ ≈ K 0.04 and K ≈ 1 plate, you can get a general expression for choosing the area of a flat PAD. In accordance with the statistical theory of sea waves, each score corresponds to its own mathematical expectation of wavelength

and the wave height h = 2 A at 3% coverage is 0.06

, and at 1% security - 0.1

(5). Hence, the expected wave amplitudes should fall within the range

= /0.03-0.05/

. With all this taken into account, on the basis of (5), it is possible to obtain expressions for choosing S _PAD for wave heights of 1- and 3% coverage:
S $\genfrac{}{}{0ex}{}{\text{1\%}}{\text{PA}}$ _D ≈ S ₁ e

_ e

1.5 · 0.05 · 1.04

≈ S ₁ · 1.48

[0.159-0.0616] = 0.144S

S $\genfrac{}{}{0ex}{}{\text{3\%}}{\text{PA}}$ _D ≈ S ₁ e

_ e

1.5 · 0.03 · 1.04

≈ S ₁ · 1.26

[0.159-0.041] = 0.149 · S

.

Thus, the area of a flat PAD to minimize vertical disturbing forces should lie within:
S _PAD ≈ (0.144-0.149) ˙s ₁ ˙λ _p , where s ₁ is the cross-sectional area of the vertical cylinder, and
λ _p is the calculated wavelength.

, κ₁≈κ₂≈1 λ₂= K₂ρ˙V₂ и λ₁= К₁˙ρ˙V= K₁˙ρ˙s₁˙l_1п можно также получить условие выбора элементов ПАДа:

· S₁ - e

S₁·l_1n(1+ K₁) - e

V₂(1+ K₂) = 0
С учетом l_1п= 1,5 А, y₁₀= l_1п/2, y₂₀= 1,25 А_р и А_р= (0,03-0,05)˙λ_pполучаем условие выбора объемного ПАДа:
V₂(1+K₂)= (0,144-0,149) s₁ ˙λ.For bulk PAD on the basis of (3) by mutual compensation F _1g.st. , F _1iv and F _2iv taking into account ω ² = g

, Κ ₁ ≈κ ₂ ≈1 λ ₂ = ₂ ρ˙V the K ₂ and lambda = ₁ To ₁ ˙ρ˙V = K _{1 1} ˙ρ˙s ˙l _1P can also be a condition item selection PAD:

S ₁ - e

S ₁ l _1n (1+ K ₁ ) - e

V ₂ (1+ K ₂ ) = 0
Taking into account l _1p = 1.5 A, y ₁₀ = l _1p / 2, y ₂₀ = 1.25 A _p and A _p = (0.03-0.05) ˙λ _p we obtain the condition for the choice of volume PAD:
V ₂ (1 + K ₂ ) = (0.144-0.149) s ₁ ˙λ.

Следует иметь в виду, что ПАД работает двояко: и как пассивный демпфер, и как разгрузочный элемент. Поэтому уравнение вертикальной качки вехи или буя с ПАД при условии компенсации силы присоса на волне Y_b= A˙ cos ω t имеет вид:
(ρ·V₁+λ_В+λ_Б+λ_ПД+λ_ПАД)

+(N_В+N_ПД+N_ПАД)

+gρ·S₁·y =
= A [gρ·S₁-ε₁(y₁₀)ω²κ₁(ρ·V₁+λ_В)-ε₂(y_ПАД)·ω²·λ_ПАД] ·cosωt - (6)
- Aω²[ε (y₁₀)

V_В+A·ε $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ (y_ПАД)·C_y·ρ·S_ПАД] ·sinωt.The value of K ₂ depends on the geometric shape of the PAD. If this is a cylindrical ring with an outer radius r ₂ , inner r ₁ , area π (r ₂ ² -r ₁ ² ) and thickness t, then K ₂ ≈ 1. In this case, taking into account s ₁ = π˙ r ₁ ² , we obtain the condition of choice:
r ₂ ≈ r

It should be borne in mind that the DAD works in two ways: both as a passive damper and as an unloading element. Therefore, the equation of the vertical roll of a milestone or buoy with a PAD subject to compensation of the suction force on the wave Y _b = A˙ cos ω t has the form:
(ρ · V ₁ + λ _B + λ _B + λ _PD + λ _PAD )

+ (N _B + N _PD + N _PAD )

+ gρ · S ₁ · y =
= A [gρ · S ₁ -ε ₁ (y ₁₀ ) ω ² κ ₁ (ρ · V ₁ + λ _В ) -ε ₂ (y _PAD ) · ω ² · λ _PAD ] · cosωt - (6)
- Aω ² [ε (y ₁₀ )

V _B + A $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ (y _PAD ) · C _y · ρ · S _PAD ] · sinωt.

 For experimental verification of the proposed technical solution, 3 cylindrical foam milestones with a length of l = 40 cm and a radius of r = 2 cm were made. These milestones were balanced and ballasted for swimming in a stable vertical semi-submerged state. In the upper part, they had light wooden rods with flags for visualizing their vertical pitching: milestone 1 - with ballast suspended from below and without a damper, milestone 2 - with ballast suspended from below and a deeply located damper (model of Froude milestone) with a diameter of 24 cm, milestone 3 - with a passive-active damper with a diameter of 12 cm; located in the area of active influence of waves. (its area is determined for a laboratory wave with a length of λ = 1.6 m).

 The wave producer was launched and it was established that milestone 1 has a very intense vertical pitching, milestone 2 is well self-stabilizing on waves, but milestone 3 with a much smaller area of the damper raised below the surface to a depth of 15 cm stabilizes even better. This experience indicates that the theory is fundamentally true.

 PRI me R 2. The implementation of the principle of dynamic compensation in the stabilization of floating platforms, consisting of vertical and horizontal cylinders. The design element of such platforms is shown in FIG. 4.

. Пренебрежем силами присоса или компенсируем их приемом водяного балласта. В этом случае уравнение (3) для суммарной силы принимает вид:
F_yΣ ≈ gρS₁Acosωt-g

S₁l₁(1+K₁)Aε₁(y₁₀)cosωt-
- g

S₂l₂(1-K₂)Aε₂(y₂₀)cosωt - g

S₁l₁× (7)
× Aε₁(y₁₀)sinωt-g

S₂l₂Aε₂(y₂₀)sinωt.We assume that the length of the immersed part of the vertical cylinder is l ₁ , and the cross-sectional area is s ₁ , the length of the horizontal cylinder is l ₂ , and the cross-sectional area is s ₂ . We take into account that V ₁ = s ₁ ˙ l ₁ ; V ₂ = s ₂ ˙ l ₂ , λ ₁ = K ₁ ˙ρ˙s ₁ ˙l ₁ ˙λ ₂ = K ₂ ˙ρ˙s ₂ ˙l ₂ , where K ₁ and K ₂ are the coefficients of the attached masses of the cylinders, and also that ω ² g

. We neglect the forces of the suction cup or compensate for them by the use of ballast water. In this case, equation (3) for the total force takes the form:
F _yΣ ≈ gρS ₁ Acosωt-g

S ₁ l ₁ (1 + K ₁ ) Aε ₁ (y ₁₀ ) cosωt-
- g

S ₂ l ₂ (1-K ₂ ) Aε ₂ (y ₂₀ ) cosωt - g

S ₁ l ₁ × (7)
× Aε ₁ (y ₁₀ ) sinωt-g

S ₂ l ₂ Aε ₂ (y ₂₀ ) sinωt.

AS₁l₁ за скобку и сгруппировать подобные члены, получим следующее условие для возмущающей силы от волны на составную конструкцию.If we take out the common factor g in (7)

AS ₁ l ₁ for the bracket and group similar terms, we obtain the following condition for the disturbing force from the wave to the composite structure.

S₁l

- (1+K₁)ε₁(y₁₀)κ₁-
- (1+K₂)

(y

cosωt-

(y₁₀ε₁(y₁₀)κ₁- (8)
-

(y

sinωt

.F _yΣ ≈ g

S ₁ l

- (1 + K ₁ ) ε ₁ (y ₁₀ ) κ ₁ -
- (1 + K ₂ )

(y

cosωt-

(y ₁₀ ε ₁ (y ₁₀ ) κ ₁ - (8)
-

(y

sinωt

.

This expression is subject to minimization, since the main term in it is the value of the square bracket before cosωt, and inside the bracket there are terms subtracting from each other. The task of this minimization should be solved first at the stage of designing platforms for the design wave, and then at the stage of their operation, with the difference between the real wave and the calculated one. We show how it can be solved at the design stage. Let us choose the wavelength λ _p = 100 m and the amplitude A _P = 5 m as the calculated parameters of the wave.

In this case, it is necessary to find the required depth of the vertical column l ₁ ≥1.25 A so that the horizontal cylinder is not exposed. Let l ₁ = 6.5 m and the length of the entire column 13 m. Based on the payload of the platform per one calculating element (all necessary masses without ballast water) and ensuring buoyancy conditions, the minimum necessary diameter of the vertical column s ₁ , area s ₂ and the length l _{2 of the} horizontal column:
ρ˙s ₁ ˙l ₁ + ρ˙s ₂ ˙l ₂ = m.

Let, for example, the diameter of the vertical column d ₁ = 2 m and s ₁ = 3.14 m ² . Then expression (10) determines the minimum buoyancy required s ₂ ˙ l ₂ = m ¹ / ρ -s ₁ l ₁ , and for design reasons, s ₂ or l ₂ that satisfy this condition can be selected. This is a necessary condition, and all decisions on optimizing the force impact should be decided for large s ₂ l ₂ . The problem in the future should be solved by methods of variations and successive approximations.

3. For design reasons, we determine the length of the calculated horizontal cylinder l ₂ (most often the total length of the platform is determined by the restriction of overall dimensions and the number of vertical columns, which are selected from other considerations). Then we can find in the first approximation s ₂ = (m ¹ / ρ -s ₁ l ₁ ): l ₂ , and from s ₂ go to the minimum diameter d ^o ₂ . The accepted value must be greater than d ^o ₂ . Suppose, for example, that we have chosen, as a first approximation, d ¹ ₂ = 3 m and then s ₂ = 7.07 m ² .

l₁ и y₂₀= l₁+

; ε₁= exp -

·3,25= 0,815
ε₂= exp -

(6,5+1,5)= 0,605. (9)
5. Необходимы редукционные коэффициенты для вертикального цилиндра κ₁= 1-

= 0,994 и горизонтального цилиндра κ₂= 1-

≈ 1,0. Они оказались близкими к единице.4. The required attenuation coefficients of the amplitude at the level
y ₁₀ =

l ₁ and y ₂₀ = l ₁ +

; ε ₁ = exp -

3.25 = 0.815
ε ₂ = exp -

(6.5 + 1.5) = 0.605. (9)
5. The necessary reduction factors for the vertical cylinder κ ₁ = 1-

= 0.994 and horizontal cylinder κ ₂ = 1-

≈ 1.0. They turned out to be close to unity.

 6. Neglecting, to a first approximation, the influence of the damping components as terms of the second order of smallness compared with the pressure and inertial-wave forces, we write down the condition that the term vanishes before cosω t.

For the first approximation, we take the value of the coefficients of the attached masses for the vertical cylinder K ₁ = 0.04 for the horizontal K ₂ = 0.8. Then (10) can be solved with respect to the length l ₂ .

и коэффициентов присоединенных масс общее выражение для стабилизирующего горизонтального цилиндра. Будем считать κ₁≈κ₂≈1, среднее значение К₁≈ 0,04, К₂ ≈ 0,8, а положение центра плавучести вертикальной колонны посередине ее высоты, т. е. Y₁₀= 1/2; l₁= 0,625 (0,03-0,05)

, а горизонтального цилиндра на глубине Y₂₀= l₁+r₂= 1-25 (0,03-0,05)

+r₂. В этом случае можно записать для 3 и 1% -ной обеспеченности следующие условия выбора оптимальных соотношений в первом приближении:

× e

S₂l₂

(10)
× S₂l₂
Из этих выражений можно получить условия на выбор длины горизонтального цилиндра и его радиуса, обеспечивающие минимальные вертикальное воздействие морских вол на составную конструкцию:
r $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ l₂ε

= /0,256÷0,266/S₁λ_р.We obtain on the basis of (10) and previously formulated recommendations on the length of the vertical column l ₁ = 1.25 A = 1.24 (0.03-0.05) /

and the coefficients of the attached masses are a general expression for a stabilizing horizontal cylinder. We assume that κ ₁ ≈κ ₂ ≈1, the average value of K ₁ ≈ 0.04, K ₂ ≈ 0.8, and the position of the center of buoyancy of the vertical column in the middle of its height, that is, Y ₁₀ = 1/2; l ₁ = 0.625 (0.03-0.05)

and a horizontal cylinder at a depth of Y ₂₀ = l ₁ + r ₂ = 1-25 (0.03-0.05)

+ r ₂ . In this case, we can write for the 3 and 1% coverage the following conditions for choosing optimal ratios in a first approximation:

× e

S ₂ l ₂

(10)
× S ₂ l ₂
From these expressions, one can obtain conditions for the choice of the length of the horizontal cylinder and its radius, ensuring the minimum vertical effect of sea waves on the composite structure:
r $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ l ₂ ε

= / 0.256 ÷ 0.266 / S ₁ λ _p .

и

зависят (хотя и не очень сильно) от чисел Рейнольдса: Re= Aω˙ε₁˙d₁˙ν^-1 и Re= Aω˙ε₁˙d₁˙ν^-1 и безразмерных частот

= ω(l₁g^-1)^0,5 и σ₂ = ω(d₂·g^-1)^0,5 =

то необходимо найти Re_i и σ_i и после этого вычислить значения k₁, k₂,

и

для вертикального и горизонтального цилиндров. Для конкретно принятых выше размеров имеем:
Re= 14,8 ˙10⁶; Re₂= 5,41˙ 10⁶; σ₁= 0.64; σ₂= 0.60.Based on this expression, for the calculated wavelength and assigned from other considerations s ₁ , the optimal combination of r ₂ and l ₂ can be selected. If, for example, the radius r _{2 is} specified, then the optimal length l ₂ can be calculated or vice versa. 7. Next, it is necessary to clarify the obtained values. Since the coefficients of the attached masses K ₁ and K ₂ and damping

and

depend (although not very strongly) on the Reynolds numbers: Re = Aω˙ε ₁ ˙d ₁ ˙ν ^-1 and Re = Aω˙ε ₁ ˙d ₁ ˙ν ^-1 and dimensionless frequencies

= ω (l ₁ g ^-1 ) ^0.5 and σ ₂ = ω (d ₂ · g ^-1 ) ^0.5 =

then you need to find Re _i and σ _i and after that calculate the values of k ₁ , k ₂ ,

and

for vertical and horizontal cylinders. For the specifically adopted above sizes, we have:
Re = 14.8 ˙10 ⁶ ; Re ₂ = 5.41 · 10 ⁶ ; σ ₁ = 0.64; σ ₂ = 0.60.

/-14.5+11

/;

≈ 1.23-1.9δ а для горизонтального К≈ Rе: (-658+1,5 Re); r ≈

: /0.28+3.69/.Based on our studies, it was found that for a vertical cylinder K ≈

/-14.5+11

/;

≈ 1.23-1.9δ and for horizontal K≈ Re: (-658 + 1.5 Re); r ≈

: /0.28+3.69/.

 8. Now let us draw from (8) the condition for minimizing the force action of the wave on the composite structure, taking into account the damping terms.

- (1+K₁)ε₁(y₁₀)κ₁-(1+K₂)ε₂(y₂₀)

cosωt-
-

0,815+r_2y0,605

sinωt

. (11)
Искомым параметром при выбранном диаметре d₂ является l₂. При учете синусной и косинусной составляющей нужно минимизировать функцию:
Φ =

- (1+K₁)ε₁(y₁₀)κ₁- (1+K₂)ε₂(y₂₀)×
×

+

(y₁₀)+

(y₂₀)

. (12)
Ее минимуму соответствует значение s₂l₂, определяемое равенством:
S₂l₂= { [

- (1+K₁)ε₁(y₁₀)κ₁] [(1+K₂)ε₂(y₂₀)κ₂(S₁l₁)^-1] -
- r

(y

(y₂₀)κ₂} : { [(1+K₂)ε₂(y₂₀)κ₂(S₁l₁)^-1]²+ (13)
+ [

(y₂₀)κ₂(S₁l₁)^-1] ²} .min

- (1 + K ₁ ) ε ₁ (y ₁₀ ) κ ₁ - (1 + K ₂ ) ε ₂ (y ₂₀ )

cosωt-
-

0.815 + r _2y 0.605

sinωt

. (eleven)
The desired parameter for the selected diameter d ₂ is l ₂ . When taking into account the sine and cosine components, it is necessary to minimize the function:
Φ =

- (1 + K ₁ ) ε ₁ (y ₁₀ ) κ ₁ - (1 + K ₂ ) ε ₂ (y ₂₀ ) ×
×

+

(y ₁₀ ) +

(y ₂₀ )

. (12)
Its minimum corresponds to the value of s ₂ l ₂ defined by the equality:
S ₂ l ₂ = {[

- (1 + K ₁ ) ε ₁ (y ₁₀ ) κ ₁ ] [(1 + K ₂ ) ε ₂ (y ₂₀ ) κ ₂ (S ₁ l ₁ ) ^-1 ] -
- r

(y

(y ₂₀ ) κ ₂ }: {[(1 + K ₂ ) ε ₂ (y ₂₀ ) κ ₂ (S ₁ l ₁ ) ^-1 ] ² + (13)
+ [

(y ₂₀ ) κ ₂ (S ₁ l ₁ ) ^-1 ] ² }.

Obtained from (14), the optimal value of s ₂ l ₂ makes it possible to clarify the length l ₂ or diameter d ₂ .

 Thus, this principle of creating floating foundations can be widely used for a wide variety of floating marine structures.

 The examples considered relate to issues of making architectural decisions at the stage of designing floating foundations. They allow you to choose the shape and optimal aspect ratio for the calculated wave. As the calculated wave, the most dangerous wave of a given point and security is usually selected. However, excitement is a random process. And at a given specific time and location of the offshore structure (for example, wave milestone), the most likely characteristics of the waves can differ significantly from the calculated ones. At such a wave, the calculated elements of the PAD do not adequately compensate for the static components of the wave action. However, in the case of the already selected PAD, it remains possible to minimize the disturbing effect of the wave by changing its displacement along the vertical column or by changing the draft of the entire structure so that conditions (4), (5) are satisfied for the most probable wave characteristics measured during operation.

e

S_ПАДe

, (14)
где λ₁ - новая длина волны;
Y_o и Y^о _ПАД - исходные углубления центров плавучести вехи и ПАД.Let us show by the example of a wave-milestone how technically this possibility can be realized. By changing the frequency (length) of the wave with the already chosen calculated area S of the _PAD and the deepening of Y ^{about the} _{PAD by} changing the milestone draft (and, at the same time, the depth of the PAD), condition (5) can be satisfied. In this case, the change in the precipitation of the milestone ΔY should be determined from the solution of the transcendental equation:
S ₁ - (l ₁ + Δy) S ₁ (1 + K ₁ )

e

S _PAD e

, (14)
where λ ₁ is the new wavelength;
Y _o and Y ^o _PAD - the initial deepening of the centers of buoyancy milestones and PAD.

 If the wave frequency increases (its length decreases), then the inertial-wave action increases, and to neutralize the hydrostatic component, the pole with the damper must sink deeper to weaken the inertial-wave forces. If the wavelengths increase, the milestone should emerge.

Claims (5)

 1. SEMI-LOADED BASE OF MARINE CONSTRUCTION, containing at least one vertical displacement cylindrical column crossing the free surface of the water, a working platform above it and located on the column under the free surface of the water damper, characterized in that the length of the immersed part of the column and the height of its underwater part to the working area is less than 1.25 - 1.5 of the calculated wave amplitude, and the damper is installed at a depth of 0.25 of the calculated wave amplitude and is passively active, while it is equipped with on a device for minimizing the disturbing effect of waves on off-design waves. 2. The basis of claim. 1, characterized in that the passive-active damper is made in the form of a flat disk, and its area
S _pad ≈ (0.137-0.147) ˙S ₁ ˙λ _p ,
where S ₁ - the cross-sectional area of the column, determined from the conditions of buoyancy of the entire structure,
λ _p is the calculated wavelength. 3. The basis of claim. 1, characterized in that the PAD is made in the form of a volumetric cylindrical ring, and its volume
V _pad ≈ (0.148-0.151) ˙ (1 + K ₂₂ ) ^-1 ˙ S ₁ ˙λ _p , where K ₂₂ ≈ 0.7 - 0.9 is the coefficient of the attached mass of the volume PAD, depending on the shape and ratio of the difference between the external and internal diameter and its height. 4. The basis of claim. 1, characterized in that the PAD is made in the form of a cylinder whose longitudinal axis is oriented horizontally, and its radius r ₂ and length l _{2 are} determined by the ratio
r $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ L ₂ e

= /0.256right0.266/S ₁ λ _p .  5. The basis of paragraphs. 1 to 4, characterized in that the device for minimizing the disturbing effect of waves on a semi-submerged base on an off-design wave includes an electric meter of incoming wave parameters, a unit for processing and obtaining the most probable length and amplitude, a depth meter for a semi-submerged base, an electric power source, an optimization unit, a ballast tank with valves for filling and draining and an automatic ballasting unit, the wave parameter meter being electrically connected to the optimization unit and and a depth gauge, and the optimization unit is connected to the automatic ballasting unit, while the latter is connected to valves for filling and draining the ballast tank.

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