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The blades of helicopters and wind turbines undergo pitch motion in hygrothermal environments. Few works have studied the effect of this movement on blade frequencies. This paper focuses on the bending characteristics of a pitching thin-walled beam, including the effects of hygrothermal environments, rotor speeds, and composite materials. The harmonic pitch function is introduced into the dynamics model of a rotating beam. The method of multiple scales and the Galerkin method are used to solve these equations. Results indicate that the pitch amplitude A dramatically influences natural frequencies. Conclusions are obtained: (1) The flapping frequency varies periodically with pitch amplitude A, and monotonically changes every 2/π. The pitch amplitude A significantly impacts frequencies, while the pitch frequency ωp and pitch phase C don’t influence frequencies. (2) An increase in temperature or humidity will decrease the flapping frequencies of a pitching beam. (3) The ply angle, coupled with the dynamic pitching angle, dramatically influences the flapping frequencies of the composite beam. The larger the ply angle, the greater the effect of pitch amplitude A on frequencies. [ABSTRACT FROM AUTHOR]

Natural vibration characteristics of a cantilever beam that is parametrically excited by pitch motion are theoretically investigated in this work. A partial differential equation governing the parametrically excited bending vibration of the beam is established by employing the generalized Hamiltonian principle. Normal modal functions of the bending vibration are obtained based on the method of separation of variables. It reveals that the dynamic pitch motion cannot change the modal shapes of the bending vibration of a uniform beam. Principal vibrations of the beam are studied by taking into account two cases of E I 1 = E I 2 and E I 1 ≠ E I 2 , where E I 1 and E I 2 are the first and second principal bending stiffness, respectively. The bending stiffness is considered as the superposition of a constant stiffness with a small perturbation. With the aid of the Fourier series theory and the method of multiple scales, the principal vibrations of the parametrically excited system at non-resonant and resonant cases are analyzed by introducing a small natural parameter , while natural vibration characteristics of the beam are obtained and the orthogonal properties of modal functions are illustrated. Theoretical methods provided in this work are verified by using the finite element method, assumed modes method and direct numerical integrations to the governing equation based on a rectangular beam model. It reveals that theoretical results coincide with numerical results very well. Finally, the influences of design parameters including the beam height, beam width, beam length, slender ratio, aspect ratio, pitch amplitude, pitch frequency and pitch phase on natural frequencies of a harmonic pitching beam are discussed. It shows that the width, height, length, slender ratio, aspect ratio and pitch amplitude have dramatic influences on the natural frequencies of the pitching beam, while the pitch frequency and pitch phase have little effect on natural frequencies. [ABSTRACT FROM AUTHOR]

A series of experiments were carried out to investigate the performance of a WEC rotor with platform motion. To achieve platform motion, a forced motion device with a rotor was installed in the Ocean Engineering Basin. In this study, the rotor's performance was examined at various phase stages between incoming waves at three wave heights, and compared to a rotor without a PTO system. The phase stage where the rotor exhibited the largest pitch motion was identified, and the efficiencies of the rotor with the PTO system were analyzed during this stage. Without the PTO system, the rotor experienced its largest pitch motion when the rotating center was positioned at the zero-up crossing point of the incoming waves at three different wave heights. Furthermore, it was observed that in the optimal phase, the rotor's efficiency increased with relatively large platform motion. These findings provide fundamental data for rotor design. [ABSTRACT FROM AUTHOR]

Since a floating solar panel is set above a water surface, the ground effect due to the small gap between the panel and the free surface may be induced by the wind load, in turn causing a high lift force on the panel. In this paper, the wind load on a three-dimensional thin flat plate floating on surface waves is studied analytically under linear assumptions. The clearance between the panel and the free surface is set to be smaller than the panel length and the effects of the base of the floating system are ignored. The pitch motion of the plate due to linear surface waves is considered and the effects of the aspect ratio of the plate, wave number, and wave speed of the free surface are discussed. The analytical solution shows that, if the plate is stationary and the free surface is flat (no waves), then the lift coefficient increases with aspect ratio. For a pitching plate above surface waves, lift coefficient increases with aspect ratio for longer wavelengths, but decreases when the aspect ratio increases for shorter wavelengths. Minimum lift and the associated wave number and aspect ratio for different wave speeds are also discussed. The findings of this study are anticipated to enhance the design of floating solar panels, improving their capacity to withstand substantial wind and waves. [ABSTRACT FROM AUTHOR]

Generally, new and renewable energy systems generate electricity by installing and operating multiple modules simultaneously. In the Republic of Korea, recent studies and developments have focused on asymmetric wave energy converters (hereafter referred to as rotors) suitable for marine environments off the western coast of Jeju. These rotors are arranged on a large floating truss-structure platform and designed to harness electricity from the rotors' pitch motion. However, when multiple rotors operate on a platform, their behavior diverges from that of a single module due to hydrodynamic interactions between them. Moreover, because the rotors are connected to the floating platform, their motion is influenced by the platform's dynamics. In this study, a time-domain multibody motion equation was established to analyze changes in the behavioral characteristics of the rotors, both with and without a floating platform. The hydrostatic and hydrodynamic coefficients were derived in the frequency domain using WAMIT, a commercial code based on linear potential flow theory for three-dimensional diffraction/radiation analyses. The motion equation was then applied under regular and irregular wave conditions using OrcaFlex version 11.3, a marine systems design and analysis program. The resulting behaviors were compared to elucidate the influence of the platform and hydrodynamic interactions on the rotors' performance. [ABSTRACT FROM AUTHOR]

Pitch motion is the key factor affecting the performance characteristics of centrifugal pumps on board ships and exacerbates hydraulic excitation to induce the unsteady vibration of pump units. A hydraulic test platform with swing motion is established to explore the effects of pitch motion on a pump's performance characteristics. An obvious hump zone exists in the head characteristic curve in the low-flow-rate condition due to the pitch motion. The pump head in the shut-off condition has a significant decrease due to the pitch motion, compared to the static state. The head decrease gradually increases as the maximum pitch angle increases or the pitch period shortens. Specifically, the head in the rated flow condition decreases by 6.3 % to reach a minimum at the maximum pitch angle of 20 degrees in a period of 5 s. Based on a multiple-reference coordinate system, a large eddy simulation with a shear-modified eddy viscosity model is employed to simulate inner flow characteristics under the influence of pitch motion. A distinct vortex flow appears near the blade suction surface and becomes increasingly turbulent as the pitch period shortens. The pitch motion intensifies the unsteady stretching and deformation of vortices. The periodic variations in fluid-induced pressure over time present parabolic features, and the amplitude in the frequency domain reaches its maximum value within a pitch period of 5 s. [ABSTRACT FROM AUTHOR]

Pitching mode is more crucial than heaving mode in assessing floating offshore wind turbine (FOWT) motion characteristics, especially the operation of the SPAR substructure. The aim of this paper is to develop an experimental method for improving the SPAR substructure to minimize unnecessary pitch motion. Toward this end, three vertical plate configurations based on the novel SPAR are being developed, known as the 3VP, 4VP, and 5VP models. In consideration of 0⁰, 30⁰, 60⁰, 90⁰-incidence, the pitch response characteristics of the proposed novel SPAR models are comprehensively evaluated in terms of submerged volume ratio, wave-induced motion, non-dimensional damping coefficient, and percentage of motion reduction. The model test results indicate that the 4VP model outperforms the other novel models with respect to dynamic response, particularly the incidence of 0⁰ and 90⁰. This study implies that the novel SPAR development is both feasible and effective in the modification of SPAR-type FOWT substructures.

The motion of small fishing vessels is significantly affected by small waves, leading to accidents, such as capsizing or sinking. This paper presents the results of two types of basin tests. The first test analyzed the characteristics of roll and pitch motions among regular waves with the same wave steepness using the drifting state of three (3G/T, 7G/T, 10G/T) small fishing vessels. The second test analyzed the motion characteristics of the 7G/T fishing vessel under different wave steepness. The first test showed that heave and roll motions are significant in the beam sea, while pitch motion is significant in the bow and stern seas. The second test shows that wave steepness has a linear relationship with roll and pitch motions in the bow and stern seas.

Generally, new and renewable energy systems generate electricity by installing and operating multiple modules simultaneously. In the Republic of Korea, recent studies and developments have focused on asymmetric wave energy converters (hereafter referred to as rotors) suitable for marine environments off the western coast of Jeju. These rotors are arranged on a large floating truss-structure platform and designed to harness electricity from the rotors’ pitch motion. However, when multiple rotors operate on a platform, their behavior diverges from that of a single module due to hydrodynamic interactions between them. Moreover, because the rotors are connected to the floating platform, their motion is influenced by the platform’s dynamics. In this study, a time-domain multibody motion equation was established to analyze changes in the behavioral characteristics of the rotors, both with and without a floating platform. The hydrostatic and hydrodynamic coefficients were derived in the frequency domain using WAMIT, a commercial code based on linear potential flow theory for three-dimensional diffraction/radiation analyses. The motion equation was then applied under regular and irregular wave conditions using OrcaFlex version 11.3, a marine systems design and analysis program. The resulting behaviors were compared to elucidate the influence of the platform and hydrodynamic interactions on the rotors’ performance.

Considering the vibration generated by a propeller-driven UAV or encountering gust, the propeller will perform a very complex follower motion. A pitch and rotating coupled motion is proposed in the present work that can take more complex unsteady performance of follower force than a regular fixed-point rotating motion. In order to evaluate the unsteady follower force and conduct parametric study, an extensive ground test bench was designed for this purpose where the whole test system was driven by a linear servo actuator and the follower force was measured by a 6-component balance. For CFD simulation, coupled motion in particular needs detailed unsteady aerodynamic model; therefore, a high-fidelity CFD-based study integrated with the overset mesh method was complemented to solve the unsteady fluid of varying conditions. The results suggest that a significant influence on unsteady follower force is observed, and the mean value of in-plane force does not equal to zero during the coupled motion process. Compared with the regular fixed-point rotation of propeller, the fluctuation frequency of follower force in present work couples the rotation and pitch motion frequencies. In addition, the oscillation amplitude of out-plane force and torque is positively related with the pitch frequency, pitch amplitude, and relative length from leading edge of wing to the rotation center. For example, the oscillation amplitude of 1-blade’s out-plane force and torque increases by 57.122% and 66.542% for the 5 Hz-5 deg case compared with the 5 Hz-3 deg case, respectively. However, the torque is not sensitive to frequency of pitch motion. The generally excellent agreement evident between the ground test and numerical simulation results is important as guidance for our future investigation on “dynamic” aerodynamic performance of a propeller-driven UAV.

Earlier studies have shown that the pitch motion of the platform can enhance the power coefficient of offshore vertical axis wind turbine (VAWT), particularly in the realm of scaled model. However, there is a shortage of research employing computational fluid dynamics (CFD) to evaluate how that motion affects the aerodynamic performance of full-scale VAWT. Moreover, the differences in aerodynamic characteristics between full-scale and scaled VAWTs are not well-understood. To fill this knowledge gap, we utilize high-fidelity CFD simulations to investigate the aerodynamic performance of a 5.3-MW full-scale offshore H-type VAWT in the presence of pitch motion. Subsequently, we conduct a comparative analysis of the variations between the full-scale VAWT and its scaled counterpart. Furthermore, we explore the influence of pitch amplitude and period on the overall performance. The findings reveal that, with low solidity (i.e., 0.1) and moderate tip speed ratio (i.e., 3.5), periodic pitch motion results in a 16.42% improvement in the power coefficient for the full-scale VAWT. In contrast, the scaled counterpart experiences a significant 56.71% reduction in the power coefficient. Meanwhile, for the full-scale VAWT, selecting a larger pitch amplitude and shorter pitch period holds the potential to enhance the power coefficient; however, the durability concerns stemming from the extensive fluctuations in blade torque need to be addressed. Additionally, it is observed that pitch motion introduces turbulent structures into the wake, facilitating both expansion and recovery. Due to the scale effect (Reynolds number effect), it's crucial to recognize that conclusions drawn about the aerodynamic performance of full-scale VAWT cannot be directly extrapolated from scaled model. • Aerodynamics of full-scale offshore VAWT under pitch motion is studied. • Aero-differences between full-scale and scaled VAWTs are elucidated. • Impact of pitch motion on C P may be contrary for full-scale and scaled VAWTs. [ABSTRACT FROM AUTHOR]

Among the various wave power systems, Salter’s duck (rotor) is one of the most effective wave absorbers for extracting wave energy. The rotor shape is designed such that the front part faces the direction of the incident wave, which forces it to bob up and down due to wave-induced water particle motion, whereas the rear part, which is mostly circular in shape, reflects no waves. The asymmetric geometric shape of the duck makes it absorb energy efficiently. In the present study, the rotor was investigated using WAMIT (a program based on the linear potential flow theory in three-dimensional diffraction/radiation analyses) in the frequency domain and verified using OrcaFlex (design and analysis program of marine system) in the time domain. Then, an experimental investigation was conducted to assess the performance of the rotor motion based on the model scale in a two-dimensional (2D) wave tank. Initially, a free decay test (FDT) was carried out to obtain the viscous damping coefficient. The pitch response was extracted from the experimental time series in a periodic regular wave for two different wave heights (1 cm and 3 cm). In addition, the viscous damping coefficient was calculated from the FDT result and fluid forces, obtained from WAMIT, are incorporated into the final response of the rotor. Finally, a comparative study based on experimental and numerical results (WAMIT & OrcaFlex) was performed to confirm the performance reliability of the designed rotor.

Tuned sloshing dampers (TSDs) are applied to dissipate and absorb vibrational energy in structures. They can become an appropriate candidate for damping vibration in rotating offshore structures. In this study, the TSD systems are utilized in a semi-submersible platform in order to suppress its pitch motion response. First, the hydrodynamic behaviors of two different types of vessels are evaluated including a typical GVA4000 semi-submersible rig, and a floating oil storage tank using a finite element analysis. The results are compared with the available data from previous research, which the agreement is good. Subsequently, the semi-submersible platform equipped with four TSDs, which are located inside the bilge of pontoons and filled with 20% water is analyzed. It is analyzed in the frequency domain by considering the effect of internal fluid sloshing of TSDs. The results show that TSDs play a significant role for reducing the pitch motion response of the semi-submersible platform.

Improving a ship’s stern part could help to reduce greenhouse gases and costs. However, a ship sailing in actual conditions experiences disturbances that can affect its performance. Ship performance is an important aspect of the design process that guarantees ship safety. The heave and pitch motions of an improved fishing boat were predicted numerically by using a hybrid scheme of Eulerian grid-Lagrangian particle, hereinafter improving its stern part and attaching an additional part. The stern part improvement and additional structure attachment affected an increase on the heave amplitude from the ship’s basic form by 5% to 10%. Moreover, the improvement of the stern part in the bottom area contributed to a better heave amplitude than that of the side area. Finally, the pitch amplitude for all forms was relatively small and affected an increase of 5% to 9%, dependent on the form. The improvement had a greater effect on heave motion than pitch.

In this study, vibration control, a behavior which subordinates to stall-induced nonlinear vibration and amplitude control of a wind turbine’s blade section, based on unified pitch motion driven by slider-linkage mechanism, is investigated by using an iterative learning control (ILC) method. The nonlinear dynamical system is a nonlinear aeroelastic system. The aeroelastic system equations consist of three parts: the nonlinear structural equations derived by using Lagrange’s equations, the improved stall-induced nonlinear ONERA (ISNO) aerodynamic equations, and the pitch control equation. The ISNO model is not only suitable for the actual external pitch motion, but also suitable for the solution by using an ILC algorithm due to its fitted nonlinear aerodynamic coefficients. The ILC algorithm used here is an improved iterative learning algorithm (IILC) which considers the large-range, linearized, residual terms, and realizes gain adaptive tuning based on PID controller. On the one hand, it can control the amplitude of an unsteady flutter through trajectory tracking. On the other hand, when the preset value of the amplitude of the ideal trajectory is very small, it can make the system directly tend to convergence and stability of a nonlinear aeroelastic system. To simplify the extremely difficult iterative process, the pitch movement can track the elastic twist displacement in time, thus simplifying the aeroelastic equations and accelerating the IILC iteration process. Therefore, amplitude control for flap-wise/lead-lag displacements is realized by the unified pitch motion and the trajectory tracking controlled by using the IILC algorithm.

In this study, vibration control, a behavior which subordinates to stall-induced nonlinear vibration and amplitude control of a wind turbine's blade section, based on unified pitch motion driven by slider-linkage mechanism, is investigated by using an iterative learning control (ILC) method. The nonlinear dynamical system is a nonlinear aeroelastic system. The aeroelastic system equations consist of three parts: the nonlinear structural equations derived by using Lagrange's equations, the improved stall-induced nonlinear ONERA (ISNO) aerodynamic equations, and the pitch control equation. The ISNO model is not only suitable for the actual external pitch motion, but also suitable for the solution by using an ILC algorithm due to its fitted nonlinear aerodynamic coefficients. The ILC algorithm used here is an improved iterative learning algorithm (IILC) which considers the large-range, linearized, residual terms, and realizes gain adaptive tuning based on PID controller. On the one hand, it can control the amplitude of an unsteady flutter through trajectory tracking. On the other hand, when the preset value of the amplitude of the ideal trajectory is very small, it can make the system directly tend to convergence and stability of a nonlinear aeroelastic system. To simplify the extremely difficult iterative process, the pitch movement can track the elastic twist displacement in time, thus simplifying the aeroelastic equations and accelerating the IILC iteration process. Therefore, amplitude control for flap-wise/lead-lag displacements is realized by the unified pitch motion and the trajectory tracking controlled by using the IILC algorithm. [ABSTRACT FROM AUTHOR]