• Advances in aircraft and spacecraft science
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• v.5 no.3
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• pp.335-348
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• 2018

The structural dynamics (SD) behavior of Elastic Flapping Wings (EFWs) is investigated analytically as a novel approach in EFWs analysis. In this regard an analytical SD solution of EFW undergoing a prescribed rigid body motion is initially derived, where the governing equations are expressed in modal space. The inertial forces are also analytically computed utilizing the actuator induced acceleration effects on the wing structure, while due to importance of analytical solution the linearity assumption is also considered. The formulated initial-value problem is solved analytically to study the EFW structural responses, where the effect of structure-actuator frequency ratio, structure-flapping frequency ratio as well as the structure damping ratio on the EFW pick amplitude is analyzed. A case study is also simulated in which the wing is modeled as an elastic beam with shell elements undergoing a prescribed sinusoidal motion. The corresponding EFW transient and steady response in on-off servo behavior is investigated. This study provides a conceptual understanding for the overall EFW SD behavior in the presence of inertial forces plus the servo dynamics effects. In addition to the substantial analytical results, the study paves a new mathematical way to better understanding the complex role of SD in dynamic EFWs behavior. Specifically, similar mathematical formulations can be carried out to investigate the effect of aerodynamics and/or gravity.

• 한국가시화정보학회:학술대회논문집
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• 2007.11a
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• pp.134-137
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• 2007

The temporal evolution of wake behind a circular cylinder oscillating rotationally with a relatively high forcing frequency has been investigated experimentally using a dynamic PIV technique. Experiments were carried out with varying the frequency ratio $F_R\;(=f_f/f_n)$ in the range from 0.0 (stationary) to 1.6 at oscillation amplitude of ${\theta}_A=30^{\circ}$ and Reynolds number of $Re=4.14{\times}10^3$. Depending on the forcing condition ($F_R$), the flow was divided into three regimes; non-lock-on ($F_R=0.4$), transition ($F_R=0.8$, 1.6) and lock-on regimes ($F_R=1.0$) with markedly different flow structure in the near-wake region behind the cylinder. When the frequency ratio was less than 1.0 ($F_R{\le}1.0$), the rotational oscillatory motion of the cylinder decreased the length of the vortex formation region and enhanced the mutual interaction between large-scale vortices across the wake centerline. The entrainment of ambient fluid seemed to play an important role in controlling the near-wake flow and shear-layer instability. However, the flow characteristics changed markedly beyond the lock-on flow regime ($F_R=1.0$) due to high-frequency forcing. At $F_R=1.6$, the mutual interactions between the vortices shed from both sides of the cylinder were not so strong. Thereby, the flow entrainment and momentum transfer into the wake center region were reduced. In addition, the size of the large-scale vortices decreased since the lateral extent of the wake was suppressed.

• Journal of computational fluids engineering
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• v.6 no.4
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• pp.26-34
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• 2001

The flow past a circular cylinder forced to vibrate transversely is numerically simulated by solving the two-dimensional Navier-Stokes equations modified by the vibration velocity of a circular cylinder at a Reynolds number of 164. The higher-order finite difference scheme is employed for the spatial discretization along with the second order Adams-Bashforth and the first order backward-Euler time integration. The calculated cylinder vibration frequency is between 0.60 and 1.30 times of the natural vortex-shedding frequency. The calculated oscillation amplitude extends to 25% of the cylinder diameter and in the case of the lock-in region it is 60%. It is made clear that the cylinder oscillation has influence on the wake pattern, the time histories of the drag and lift forces, power spectral density and phase diagrams, etc. It is found that these results include both the periodic (lock-in) and the quasi-periodic (non-lock-in) state. The vortex shedding frequency equals the driving frequency in the lock-in region but is independent in the non-lock-in region. The mean drag and the maximum lift coefficient increase with the increase of the forcing amplitude in the lock-in state. The lock-in boundaries are also established from the present direct numerical simulation.

• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.181-188
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• 2001

The flow past a circular cylinder forced to vibrate transversely is numerically simulated by solving the two-dimensional Wavier-Stokes equations modified by the vibration velocity of a circular cylinder at a Reynolds number of 164. The higher-order finite difference scheme is employed for the spatial discretization along with the second order Adams-Bashforth and the first order backward-Euler time integration. The calculated cylinder vibration frequency is between 0.60 and 1.30 times of the natural vortex-shedding frequency. The calculated oscillation amplitude extends to $25\%$ of the cylinder diameter and in the case of the lock-in region it is $60\%$. It is made clear that the cylinder oscillation has influence on the wake pattern, the time histories of the drag and lift forces, power spectral density and phase diagrams, etc. It is found that these results include both the periodic (lock-in) and the quasi-periodic (non-lock-in) state. The vortex shedding frequency equals the driving frequency in the lock-in region but is independent in the non-lock-in region. The mean drag and the maximum lift coefficient increase with the increase of the forcing amplitude in the lock-in state. The lock-in boundaries are also established from the present direct numerical simulation.

• Journal of Mechanical Science and Technology
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• v.20 no.11
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• pp.1993-2001
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• 2006

The piezoelectric bimorph film, which, as an actuator, can generate more effective displacement than the usual PVDF film, is used to control the turbulent boundary-layer flow. The change of wall pressures inside the turbulent boundary layer is observed by using the multi-channel microphone array flush-mounted on the surface when actuation at the non-dimensional frequency $f_b^+$:=0.008 and 0.028 is applied to the turbulent boundary layer. The wall pressure characteristics by the actuation to produce local displacement are more dominantly influenced by the size of the actuator module than the actuation frequency. The movement of large-scale turbulent structures to the upper layer is found to be the main mechanism of the reduction in the wall- pressure energy spectrum when the 700$700{\nu}/u_{\tau}$-long bimorph film is periodically actuated at the non- dimensional frequency $f_b^+$:=0.008 and 0.028. The biomorph actuator is triggered with the time delay for the active forcing at a single frequency when a 1/8' pressure-type, pin-holed microphone sensor detects the large-amplitude pressure event by the turbulent spot. The wall-pressure energy in the late-transitional boundary layer is partially reduced near the convection wavenumber by the open-loop control based on the large amplitude event.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.2
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• pp.193-199
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• 1988

The forced vibrations of nondissipative nonlinear two-degree-of-freedom system, subjected to periodic forcing functions, are investigated by use of the method of slowly changing phase and amplitude. The first order differential equations are derived for nonrationally solutions and the coupled nonlinear algebraic equations for stationary solutions. Through investigating the response curves of the system, which are obtained numerically by using Newton-Raphson method, it is found that the resonances can occur at more than the number of degree-of-freedom of the system depending on the relation between the nonlinear spring parameters, which has no counterpart in linear systems.

• Structural Engineering and Mechanics
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• v.55 no.2
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• pp.281-298
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• 2015

In this study, nonlinear transverse vibrations of tensioned Euler-Bernoulli nanobeams are studied. The nonlinear equations of motion including stretching of the neutral axis and axial tension are derived using nonlocal beam theory. Forcing and damping effects are included in the equations. Equation of motion is made dimensionless via dimensionless parameters. A perturbation technique, the multiple scale methods is employed for solving the nonlinear problem. Approximate solutions are applied for the equations of motion. Natural frequencies of the nanobeams for the linear problem are found from the first equation of the perturbation series. From nonlinear term of the perturbation series appear as corrections to the linear problem. The effects of the various axial tension parameters and different nonlocal parameters as well as effects of different boundary conditions on the vibrations are determined. Nonlinear frequencies are estimated; amplitude-phase modulation figures are presented for simple-simple and clamped-clamped cases.

• Structural Engineering and Mechanics
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• v.27 no.3
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• pp.333-345
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• 2007

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Forcing and damping terms were also included in the equations. The dimensionless equations were solved for six different set of boundary conditions. A perturbation method was applied to the equations of motions. The first terms of the perturbation series lead to the linear problem. Natural frequencies for the linear problem were calculated exactly for different boundary conditions. Second order non-linear terms of the perturbation series behave as corrections to the linear problem. Amplitude and phase modulation equations were obtained. Non-linear free and forced vibrations were investigated in detail. The effects of the position and magnitude of the step, as well as effects of different boundary conditions on the vibrations, were determined.

• Ocean and Polar Research
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• v.28 no.3
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• pp.245-258
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• 2006

We investigated seasonal variations of the upper ocean temperature and the mixed layer depth (MLD) in an eddy-permitting global ocean general circulation model (OGCM) to assess the OGCM perfermance. The OGCM is based on the GFDL MOM3 which has a horizontal resolution of 0.5 degree and 30 vertical levels. The OGCM was integrated for 68 years using a monthly-mean climatological wind stress forcing. The model sea surface temperature (SST) and sea surface salinity were restored to the Levitus climatology with a time scale of 30 days. Annual-mean model SST shows a cold bias $(<\;-2^{\circ}C)$ in the summer hemisphere and a warm bias $(>\;1^{\circ}C)$ in the winter hemisphere mainly due to the restoring boundary condition of temperature. The model MLD captures well the observed features in most areas, with a slightly deep bias. However, in the Ross Sea and Weddell Sea, the model shows significantly deeper MLD than the climatology-mainly due to weak salinity stratifications in the model. For amplitude of seasonal variation, the model SST is smaller $(1{\sim}3^{\circ}C)$ than the observation largely due to the restoring surface boundary condition while the model MLD has larger seasonal variation $({\sim}50m)$. It is suggested that for more realistic simulation of the upper ocean structure in the present eddy-permitting ocean model, more refinements in the surface boundary condition for the thermohaline forcing and parameterization for vertical mixing are required, together with the incorporation of a sea-ice model.

• Ocean Systems Engineering
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• v.6 no.1
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• pp.23-60
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• 2016

The major objective of this study was to develop further understanding of 3D nearshore hydrodynamics under a variety of wave and tidal forcing conditions. The main tool used was a comprehensive 3D numerical model - combining the flow module of Delft3D with the WAVE solver of XBeach - of nearshore hydro- and morphodynamics that can simulate flow, sediment transport, and morphological evolution. Surf-swash zone hydrodynamics were modeled using the 3D Navier-Stokes equations, combined with various turbulence models (${\kappa}-{\varepsilon}$, ${\kappa}-L$, ATM and H-LES). Sediment transport and resulting foreshore profile changes were approximated using different sediment transport relations that consider both bed- and suspended-load transport of non-cohesive sediments. The numerical set-up was tested against field data, with good agreement found. Different numerical experiments under a range of bed characteristics and incident wave and tidal conditions were run to test the model's capability to reproduce 3D flow, wave propagation, sediment transport and morphodynamics in the nearshore at the field scale. The results were interpreted according to existing understanding of surf and swash zone processes. Our numerical experiments confirm that the angle between the crest line of the approaching wave and the shoreline defines the direction and strength of the longshore current, while the longshore current velocity varies across the nearshore zone. The model simulates the undertow, hydraulic cell and rip-current patterns generated by radiation stresses and longshore variability in wave heights. Numerical results show that a non-uniform seabed is crucial for generation of rip currents in the nearshore (when bed slope is uniform, rips are not generated). Increasing the wave height increases the peaks of eddy viscosity and TKE (turbulent kinetic energy), while increasing the tidal amplitude reduces these peaks. Wave and tide interaction has most striking effects on the foreshore profile with the formation of the intertidal bar. High values of eddy viscosity, TKE and wave set-up are spread offshore for coarser grain sizes. Beach profile steepness modifies the nearshore circulation pattern, significantly enhancing the vertical component of the flow. The local recirculation within the longshore current in the inshore region causes a transient offshore shift and strengthening of the longshore current. Overall, the analysis shows that, with reasonable hypotheses, it is possible to simulate the nearshore hydrodynamics subjected to oceanic forcing, consistent with existing understanding of this area. Part II of this work presents 3D nearshore morphodynamics induced by the tides and waves.