Heave Force Research Articles

Energy extraction properties of a flapping wing with a deformable airfoil

Flapping wing devices have attracted considerable attention as a new means of power extraction. The present study applies transient numerical calculations based on the dynamic mesh technique to investigate the influences of leading edge, trailing edge, or overall circular arc airfoil deformations on the power extraction efficiencies of a flapping wing device under the condition of maintaining a constant arc length along the mean camber line of the foil. The results indicate that airfoil deformations can improve the power extraction efficiency of the flapping wing device. The primary reason is that the active synchronised deformation of the foil increases the effective curvature and the velocity circulation around the foil. In addition, the performance curve of the flapping wing device exhibits two frequency ranges with relative high efficiency. In the low frequency region, if the leading edge vortex (LEV) detaches from the trailing edge just as the foil reverses its heaving direction, the foil will gain much more energy due to the positive power extraction of the pitching moment. In the high frequency region, a small steady body-attached vortex (BAV) maintains a high lift, and, thus, the device extracts more power due to the enhanced heaving force.

Computational research on a combined undulating-motion pattern considering undulations of both the ribbon fin and fish body

In this work, the combined undulating-motion pattern (CUMP) of the undulatory ribbon-fin propulsion is numerically investigated, inspired by the swimming of the large-mouthed catfish (Silurus soldatovi meridionalis Chen). The swimming of a juvenile large-mouthed catfish is observed and recorded to study the undulation of its elongated anal fin, commonly known as the “ribbon fin”. Compared with the knifefish, which undulates the ribbon fin to swim while maintaining a relatively rigid fish body, the large-mouthed catfish performs a CUMP propulsion, which comprises the undulation of the fish body and the active undulation of the ribbon fin. Accordingly, a fin–body fish model is used to study the effect of the CUMP propulsion on the swimming performance. Simulation results show that the phase-angle difference between the undulations of the fish body and the ribbon fin has a significant impact on the thrust and heave forces. More specifically, an in-phase CUMP propulsion, which is commonly found in the swimming of actual large-mouthed catfish, can dramatically improve the thrust. In addition, the effects of the angular amplitude of ribbon fin and the swimming frequency are considered as well. Finally, the reasons for the thrust augmentation in the in-phase CUMP propulsion are detailed and analyzed.

Experimental studies of a damaged ship section in forced heave motion

This work documents a detailed series of experiments performed in a wave flume on a thin walled prismatic hull form. The model consists of a rectangular opening located on the side. The length of the model is slightly smaller than the flume breadth to achieve two-dimensional (2D) behavior in the experiments. Forced oscillatory heave tests in calm water have been carried out by varying the model-motion parameters and examining both intact and damaged conditions. Video recordings, measurements of the wave elevation inside the damaged compartment and of the force on the model were performed in all the experiments. The effect of damage opening in the model on hydrodynamic loads is examined by comparing with an intact section. A theoretical analysis is used to explain the behavior of added mass and damping coefficients in heave for a 2D damaged section. The presented results demonstrate occurrence of sloshing and piston mode resonances in the tests and their influence on the hydrodynamics loads of a damaged ship. Detailed physical investigations are presented at these resonance frequencies for the damaged section. Effect of filling level in the damage compartment, damage-opening length and air compressibility in the airtight compartment is examined. Nonlinear effects are documented and appear dominant, especially, for lowest filling level where we have shallow-water depth conditions in the damaged compartment. Resonance phenomena that can lead to significant local loads are identified for the shallow water condition. Air compressibility in the airtight compartment and floodwater act as a coupled system and influence inflow/outflow of floodwater in the compartment. It has a significant effect on local floodwater behavior in the damaged compartment.

Analysis of Temperature Field of Tunnel Surrounding Rocks in Freezing-Thawing Environment

On the background of large scale rocks engineering in cold regions, Temperature Field and Stress Field of Tunnel Surrounding Rock under the freeze-thaw environment are numerically analysed. According to the single temperature field equation of tunnel surrounding rock and Da Ban mountain tunnel project in Qinghai province as an example, large scale finite element software is used to simulate temperature distribution under freeze-thaw cycles, which is from the rising temperature to the decreasing temperature and from the rising temperature to the decreasing temperature again. The frost heaving force of the tunnel in the cold region is introduced and the mathematical model about rocks temperature field is also researched. Finally, finite element method is used to calculate the frost heaving force of rock tunnel in the cold regions. The results show that in the freezing and thawing environment, the area near the inner wall of the tunnel is more likely to be affected by the ground temperature and the effect of open ventilation and convection, and the temperature and stress changes more violently. In the design and construction of the cold regions, the influence of the frost heave force of the surrounding rock must be considered. Because freeze-thaw circles could cause the destruction of the tunnel structure, convective heat transfer will occur between tunnel mouth and walls and the environment, resulting in large temperature difference. Therefore, in order to reduce freeze-thaw disasters in the cold regions, we should consider the Protection measures about the hole and the wall. In this way, it reduces the range of freeze-thaw circles and prevent the convective heat transfer effectively.

Numerical modelling of forced heaving of mono hull and twin hull in particle method

In this paper, the particle method for handling oscillation of floating body using variable particle spacing is reported. Heave oscillation of floating mono hull and twin hull on the free surface in a viscous fluid is performed using Improved Meshless Local Petrov-Galerkin method based on Rankine Source function (IMLPG_R). The IMLPG_R method is a particle-based method that will solve the interaction between fluid and floating body using Navier-Stokes equation. The pressure at each time step is estimated from Pressure Poisson equation, in order to incorporate the heaving of the floating bodies, some improvements like free surface identification, gradient calculations has been introduced in the present paper to handle the variable resolutions in modelling. Simulations are performed for different frequency and amplitude of oscillations for mono and twin hull forced motions to show the robustness of the developed model to handle both small and steep oscillations.

Experimental and numerical investigation of wave induced forces and motions of partially submerged bodies near a fixed structure in irregular waves

This paper is the third of a series covering investigations of the wave induced force and motion behavior of ice masses near a fixed structure. The objective of this phase of the study was to determine whether the effects observed in regular waves (Sayeed et al. (2017b, 2018)) still held in irregular seas. In the present case, wave characteristics measured in front of the fixed structure showed that the significant wave heights follow a standing wave pattern generated by the superposition of the incident and reflected peak frequency wave. Thus it may be inferred that the significant surge and heave forces and motions will be increased or decreased at the node and antinode locations in front of the structure as previously observed for regular waves. Force spectra generated from regular wave force data (Sayeed et al. 2017b) and wave measurements from the present study showed that beyond the nodal location at Dλp=0.25, the significant surge force goes down and significant heave force goes up as the body gets close to the structure. Direct measurements of irregular wave forces on a fixed berg model at different proximity to the fixed structure demonstrate the change in significant wave forces based on the ratio of separation distance to peak wavelength. When the berg body is positioned closer to the fixed structure, the normalized significant forces in the horizontal direction decrease, and the normalized significant forces in the vertical direction increase. Significant differences were found between the directly measured force spectra and those produced by linear superposition of regular wave force transfer functions. This is attributed to non-linear effects arising from the iceberg profile and low freeboard.Free floating motion experiments showed smaller differences in the surge and heave velocity spectra due to the presence of the structure. This is because there is insufficient motion data at any specific location to capture the motion responses for all the frequencies in the spectrum. The proximity effect on wave loads and wave induced motions in the vertical direction is found to be more pronounced than the same in the horizontal direction.Numerical simulations using RANS based commercial CFD code Flow3D© are compared to the experimental results. Selected test cases from both force and motion experiments are simulated in irregular waves generated from selected experimental wave spectra. Numerical results for irregular waves demonstrate the ability to simulate random waves and resulting forces and motions with trends comparable to the experimental results.

An open frozen–heave test on the pipeline foundation soils in the permafrost regions

In the Da Hinggan Mountains, the safe and smooth operation of shallowly buried oil pipelines is threatened greatly by the frozen–heave damage derived from frozen soil. At present, a closed frozen–heave simulation test is often carried out in China, with water content and dry density of samples being assumed to be constant. However, an open frozen–heave test, all the factors of which change as the test goes on, can reflect the real frozen–heave damage more accurately. In this paper, the open frozen–heave test was carried out on five types frozen soil along the China–Russia Crude Oil Pipeline to measure the frozen–heave factor and water content of each soil sample and accordingly analyze their relationship. Besides, its test results were compared with that of the closed frozen–heave test. Then, the normal frozen–heave force was measured by using the displacement limiting method, and this measurement was compared with the result of the static equilibrium test. Finally, a difference significance test was conducted. It is shown that the frozen–heave factor of the open test is higher than that of the closed test; the frozen–heave factor of fine grained soil has a significant effect on the frozen–heave factor of soils, and the frozen–heave factor increases as the capillary effect or the swabbing action of soil increases; the frozen–heave factor of coarse grained soil is mainly dependent on the mud content, and it is lower than that of fine grained soil; the value of frozen–heave force is in close relation with the test methods and the sample height; it is indicated that the open frozen–heave test is more applicable to the investigation on the frozen–heave of the foundation soils of pipelines in the Da Hinggan Mountains. It is concluded that the soils for the cushion and digging/packing layers of the pipelines in the permafrost regions shall be acted by the gravel or detritus with lower mud content, and waterproof and draining pipeline jetty shall be made from the clay soils with a higher plasticity.

A new URANS based approach on the prediction of vertical motions of a surface combatant in head waves

In this study, wave excitation and radiation terms in 2DOF equations of vertical ship motion are obtained by using a URANS solver based on the finite volume method. The DTMB 5512 hull form is chosen for the calculations at the Froude number of 0.41. Numerical simulations are performed for 7 different regular wave conditions. First, in the regular wave, the excitation heave force and pitch moment with the related phase angle are computed while the ship is fixed to heave and pitch motions. Then, the body is forced to oscillate in the heave and pitch directions with a certain frequency and the radiation coefficients are obtained. After finding the excitation and radiated terms, the 2DOF vertical ship motion equations are solved in the frequency domain, and motion transfer functions are plotted. The results are compared with those obtained through strip theory, fully nonlinear URANS approach and experiments. The new URANS based approach presented in this paper offers a more accurate prediction of vertical ship motions compared to strip theory outputs because it takes the viscous effects and free surface nonlinearities into account. The new URANS based approach can be considered as a better alternative to the fully nonlinear URANS approach.

Energy harvesting properties of a flapping wing with an adaptive Gurney flap

Flapping wing structures have drawn increasing attention for harvesting energy from flowing fluids. This work proposes the application of an adaptive Gurney flap to the trailing end of a flapping wing foil, which actively adjusts the position of a single Gurney flap to be consistently employed on the foil pressure side. The transient two-dimensional numerical simulations are conducted to compare the energy harvesting efficiency of the proposed adaptive flapping wing structure with that of a conventional flapping wing structure and the one with fixed Gurney flaps. In addition, the effects of wing oscillation frequency, Gurney flap length, and the position of the flap relative to the trailing edge of the foil were also considered. The results demonstrate that the adaptive Gurney flap provides greater energy harvesting efficiency for the oscillating wing primarily by increasing the heave force through the synchronous switching of the flap from one side to the other within the period of motion. Compared with fixed Gurney flaps, the adaptive flap can accommodate greater flap lengths and operation over a wider oscillation frequency range. The results indicate that the optimum position of the Gurney flap is as near as possible to the trailing edge of the foil. The results also reveal two relatively high harvesting efficiency oscillation frequency regions. In the low frequency region, if the leading edge vortex detaches from the trailing edge just when the foil exchanges the heaving direction, the foil can gain much more energy due to the positive power extraction contributed by the pitching moment. In the high frequency region, a small steady attached vortex maintains a high lift force on the foil, and, thus, the enhanced heaving force harvests more power.

Semi-active flapping foil for marine propulsion

The present study deals with numerical investigation of a semi-active flapping foil of which the kinematics is characterized by an imposed heave motion and a free pitch motion. A torsion spring is attached to the foil and acts to restore the foil parallel to the advance velocity. The prescribed flapping foil has been simulated using a boundary element method in combination with a Newton-Euler solver in order to study the influence of flapping frequency and spring stiffness on the propulsive performance. The spring stiffness has strong influence on the induced pitch angle and the effective angle of attack which consequently determines the openwater characteristics. The stiff spring resists the foil from pitching resulting in high heave force, while the more elastic hinge leads to drag generation at the end of each stroke. The results demonstrate that the semi-active flapping foil attached to an appropriate torsion spring performs efficiently over a wide range of advance ratio like a controllable-pitch propeller. The best efficiency is found for a Strouhal number and a pitch amplitude as reported in biological researches. The numerical results also imply that the resonance seems to have less influence on the propulsive performance.

CALCULATION OF TANGENTIAL FROST HEAVE STRESSES BASED ON PHYSICAL, MECHANICAL AND STRESS-STRAIN BEHAVIOR OF FROZEN SOIL

Development of northern territories opens up new opportunities for social and economic development of the society. However, designing construction facilities in such areas is complicated by special features of the severe climate; frost heave of soils is one of its manifestations. Normal frost heave forces under the foundation base can be neutralized by foundation embedment below the seasonal frost line. In these conditions, tangential heave stresses will act on the lateral surfaces of foundations, causing uneven lifting of structures, which will lead to the violation of the structure integrity. Regulatory and technical literature recommends determination of tangential frost heave stresses on the basis of generalized tabular data or experimentally, which is not always possible. A relevant technique for calculating tangential stresses is required, which takes into account climatic and hydrogeological conditions of the construction site. In this article, an attempt is made to reveal those aspects of originating and development of tangential frost heave stresses, which would allow carrying out their calculation. To solve this problem, the existing research experience, features of the cryogenic structure, mechanical and stress-strain behavior of frozen soils were analyzed. A relationship of tangential frost heave stresses with specific cohesion and moisture of frozen soil was revealed on the basis of the analysis. A point of view, according to which tangential frost heave stresses are a result of maximum compressive heave stresses, directed along the normal to the lateral surface of the foundation, was emphasized too; this allowed relating tangential heave stresses with the frozen soil deformation modulus. Based on the above statements, formulas for calculating tangential frost heave stresses were obtained. The calculation method for determining these stresses would provide the possibility of designing cost-effective and safe structures in areas with the severe climate.

3D numerical parametric study of the influence of open-pit mining sequence on existing tunnels

The development of open-pit mines can adversely affect and even damage existing access tunnels. To ensure the safety and serviceability of them, it is essential to know potential adverse effects of the mining sequence on existing tunnels such as displacements of the lining and additional loads on the lining. In this paper, three-dimensional numerical parametric study is performed to explore this complex interaction. This study investigates the effects of different parameters that may affect the tunnel response. These parameters are: excavation sequence method, horizontal/vertical stress ratio, slope angle, and tunnel diameter. This study shows that the mining sequence affects the stability of the tunnels. The open-pit mining activities lead to both higher axial forces in rock bolts and normal forces and bending moments in the lining. The results of the analysis also demonstrate that the mining sequence causes tunnel heave and significant tensile forces in the lining. Based on the study in this paper a better understanding of the interaction between open-pit mining sequence and tunnels will be obtained.

Finite water depth effect on wave-body problems solved by Rankine source method

Finite water depth effect for wave-body problems are studied by continuous Rankine source method and non- desingularized technique. Free surface and seabed surface profiles are represented by continuous panels rather than a discretization by isolated points. These panels are positioned exactly on the fluid boundary surfaces and therefore no desingularization technique is required. Space increment method is applied for both free surface source and seabed source arrangements to reduce computational cost and improve numerical efficiency. Fourth order Runge-Kutta iteration scheme is adopted on the free surface updating at every time step. The finite water depth effect is studied quantitatively for a series of cylinders with different B/T ratios. The accuracy and efficiency of the proposed model are validated by comparison with published numerical results and experimental data. Numerical results show that hydrodynamic coefficients vary for cylinder bodies with different ratios of B/T. For certain set of B/T ratios the effect of finite water depth increases quickly with the increase of motion frequency and becomes stable when frequency is relatively large. It also shows that water depths have larger hydrodynamic effects on cylinder with larger breadth to draft ratios. Both the heave added mass and damping coefficients increase across the frequency range with the water depths decrease for forced heave motion. The water depths have smaller effects on sway motion response than on heave motion response.

Research on the mechanism of power extraction performance for flapping hydrofoils

Utilizing the UCFD (Unified Computational Fluid Dynamics) software, this paper describes simulation of the extraction of marine tidal energy using a flapping hydrofoil. Firstly, the validity of the numerical simulation was confirmed, where the time signal of heave force coefficient agreed well with the experimental result. Secondly, a parameter optimization study was conducted under different influence factors, results such as heaving force and work done by the heaving and pitching motions were analyzed and compared. When the quarter-period effective angle of attack is 34.4°, the heaving amplitude is 1.0c or the Strouhal number is 0.36, the power efficiency of the flapping foil was found maximized. Finally, by combining the vortex variation and pressure coefficient distribution on the hydrofoil surface at different moments, it was found that if there is a relatively large leading edge vortex at the bottom surface of the foil at 0.25T, and also if the difference between the pressure coefficients for top and bottom surfaces is relative large, then a high power efficiency could be achieved. This result could be used as a necessary, but not precisely sufficient condition for evaluating the power extraction, since the pitching amplitude should also be considered for analysis.

Reliability research on the 5-cm-thick insulation layer used in the Yuximolegai tunnel based on a physical model test

The Yuximolegai tunnel was built in the Tianshan mountain of Xinjiang. A 5-cm-thick insulation layer designed by engineering analogy was laid to project the surrounding rocks. To investigate the reliability of the design, a model test, primarily including a refrigeration system, a circulation system and a temperature control system, was developed. Two tests were designed and conducted: (1) a tunnel without insulation layer is studied using the freezing test; (2) a tunnel with a 5-cm-thick insulation layer is studied using the same test. The results show that the 5-cm-thick insulation layer employed in the field can only stop 86.5% of the lowest temperature to transfer to the surrounding rocks on average. On the basis of the analysis for the temperature law from in situ monitoring results and the model test results, the freezing depth is approximately 1.5–2m away from the lining. When the 5-cm-thick insulation layer is laid, the freezing depth still reaches 0.5m, which indicates that the preservation measure cannot fully protect the rocks surrounding the tunnel against freezing damage. In addition, comparing the frost heave force from the model test is found to have good consistency with the in situ test. The results obtained can serve as a guide for the design and the numerical simulation research of cold-region tunnels.

Wave interaction with a surface-piercing body in water of finite depth: a parametric study

ABSTRACTThe wave–body interactions for a surface-piercing body in water of finite depth are studied using a potential-theory-based, two-dimensional, fully nonlinear numerical wave tank. A parametric study was conducted in order to investigate the effects of the non-dimensional water depth, wave steepness, wave frequency, and beam–draft ratio on the wave-exciting forces acting on a fixed surface-piecing barge. It was found that a reduction of the water depth from deep to finite enhances all the wave-exciting forces. In all water depths, the second-order harmonics of the heave force and pitch moment are significantly large, although they can generally be neglected for the surge force. The barge was then allowed to move and the influence of the water depth on its wave forces is investigated. It was found that with the body motion involved, the surge force and the heave force reduce in the first-order harmonics while the pitch moment increases. In addition, a peak appears at finite water depth for the first-order harmonics of the heave force as well as for the heave displacement, indicating the great impact of water depth on the motions experienced by the floating barge.

Study of the foundation design for a linear generator wave energy converter using stochastic methods

This paper presents design studies of the gravity-based foundation for a linear generator wave energy converter. The wave energy converter is based on a direct driven generator mounted on the gravity-based foundation located at the seabed. The linear generator is connected to a point absorbing buoy on the sea surface via a connection rope. Such a device, developed at Uppsala University, has been in operation on the Swedish west coast since 2006. Study is focused on the analysis of the impact from undesirable motions of the gravity-based foundation, particularly the study of the tip and lifts phenomena with regard to the heave and surge forces. Long-term extreme significant wave heights are extrapolated from the statistical analysis of the measured wave climate data in the test site where the wave energy converter is deployed. The joint distribution of the significant wave height and the zero-crossing period from the measured wave climate is also analyzed to estimate the associated periods with respect to the long-term extreme significant wave height. The 25 years return extreme significant wave height 4.8 m which is associated with its mean zero-crossing period 8.25 s from the joint distribution is chosen to determine the characteristics of the possible maximum wave for the Lysekil test site. The estimated maximum wave 9.2 m is used to estimate the extreme values of the heave and surge forces on the wave energy converter and the gravity-based foundation. The results with respect to the foundation of a new generation wave energy converter about 35 tons with the presented methodology indicate that a heavier foundation which is about 70 tons needs to be designed in terms of considering the stability of the mooring foundation for long term real sea operation. The purpose of this paper is to propose a reliable approach to estimate the appropriate dimensions for gravity-based foundation of the linear generator wave energy converter and provides a theoretical reference to the construction of the gravity-based foundation.

Stress and deformation characteristics of transmission tower foundations in permafrost regions along the Qinghai–Tibet Power Transmission Line

A transmission tower foundation embedded in frozen soil is subject to both the wind-induced uplift and frost heave forces. The frost heave results in an upward force acting on the foundation, while additional stress induced by the structure load may compress the underlying soils. The freezing- and thawing-induced deformations tend to cause further structural loads and lead to instability problems within the structure. To evaluate the engineering risk and ensure the safety of the Qinghai–Tibet Power Transmission Line (QTPTL) system, stress sensors were installed at the bases of two test tower foundations to investigate the stress state of the tower foundations. Using data on air and ground temperatures, and the deformation of tower foundations, we analyzed the stress variation, and the causes were discussed here. The results showed that the stresses at the bases of tower foundations had a close relationship with air and ground temperatures. The cooling of the underlying soils led to the occurrence of frost heave, which pushed the foundations upward and caused a significant stress bulb under the bases of tower foundations. Seasonal variations in the contact stress depended on the seasonal freezing and thawing of foundation soil. The contact stress increased with the cooling of the underlying soils and decreased with the warming of the underlying soils. The results also showed that the contact stress was free of the wind influence, i.e., the wind-induced uplift force was minor for the contact stress. To fully understand the influences of freezing and thawing on the stress state of tower foundations, a thermal–elasto-plastic finite element model for the tower foundation–soil system was established, and the stresses and deformations of a tower foundation subject to frost heave and thaw settlement were simulated. The results showed that the frost heave force induced by soil freezing potentially threatens the safety and normal operation of the QTPTL. Thaw settlement may lead to harmful deformation of tower foundations if global warming is considered in the numerical model. The remedial measure with thermosyphons only can reduce the settlement of the foundation and will increase the frost jacking risk of the foundation.

Design and Experiment on a Biomimetic Robotic Fish Inspired by Freshwater Stingray

Freshwater stingrays undulate their flexible disc-like pectoral fins to perform cruising, manoeuvring, and other motions. This undulatory propulsion has a higher propulsive efficiency and more precise manoeuvrability than most other species at low swimming velocity. In the current study, a new robotic fish inspired by the freshwater stingray was developed and tested. First, the morphology and kinematic patterns of the freshwater stingray were presented. A kinematic model of the pectoral fin was established based on several assumptions. Then a robotic stingray with an undulatory pectoral fin was designed and developed. Experiments were conducted to investigate the effects of various fin actuation parameters on its linear swimming velocity and the forces generated by the robotic stingray. The controllable fin parameters include oscillation frequency, wave number, maximal angular deflection of the fin rays, and the amplitude pattern of the pectoral fin. The experimental results indicate that the developed prototype is able to generate adequate thrust for self-propulsion. Linear swimming velocity and surge force increase rapidly with oscillation frequency, angular deflection, and wave number. A maximum velocity of 4.3 cm·s−1 (nearly 0.18 Body Lengths per second (BL·s−1)) and a maximum surge force of 102 mN are achieved at an oscillation frequency of 0.5 Hz, a wave number of 1, a maximum angular deflection of 30°, and an equal amplitude pattern. The sway force of the robotic fish fluctuates around 0 mN. The heave force varies with wave number and reaches its minimum at a wave number of 1.

Viscosity and nonlinearity effects on the forces and waves generated by a floating twin hull under heave oscillation

Nonlinear hydrodynamics of a twin rectangular hull under heave oscillation is analyzed using numerical methods. Two-dimensional nonlinear time-domain solutions to both inviscid and viscous problems are obtained and the results are compared with linear, inviscid frequency-domain results obtained in [26] to quantify nonlinear and viscous effects. Finite-difference methods based on boundary-fitted coordinates are used for solving the governing equations in the time domain [2]. A primitive-variables based projection method [6] is used for the viscous analysis and a mixed Eulerian–Lagrangian formulation [11] for inviscid analysis. The algorithms are validated and the order of accuracy determined by comparing the results obtained from the present algorithm with the experimental results of Vugt [22] for a heaving rectangle in the free surface. The present study on the twin-hull hydrodynamics shows that at large and non-resonant regular frequencies, and small amplitude of body oscillation, the fluid viscosity does not significantly affect the wave motion and the radiation forces. At low frequencies however the viscosity effect is found to be significant even for small amplitude of body oscillation. In particular, the hydrodynamic force obtained from the nonlinear viscous analysis is found to be closer to the linear inviscid force than the nonlinear inviscid force to the linear inviscid force, the reason for which is attributed to the wave dampening effect of viscosity. Since the wave lengths generated at smaller frequencies of oscillation are longer and therefore the waves could have a more significant effect on the dynamic pressure on the bottom of the hulls which contribute to the heave force, the correlation between the heave force and the wave elevation is found to be larger at smaller frequencies. Because of nonlinearity, the wave radiation and wave damping force remained nonzero even at and around the resonant frequencies – with the resonant frequencies as determined in [26] using linear potential flow theory. As to be expected, the nonlinear effect on the wave force is found to be significant at all frequencies for large amplitude of oscillation compared to the hull draft. The effect of viscosity on the force, by flow separation, is also found to be significant for large amplitude of body oscillation.