Flexible Plate Research Articles

Wake transition of an unconstrained self-propelled flexible flapping plate

Wake transition of an unconstrained self-propelled flexible flapping plate

New Approach of Normal and Shear Stress Components for Multiple Curvilinear Holes Which Weakened a Flexible Plate

In this article, a thin infinite flexible plate weakened by multiple curvilinear holes is considered. The strength shapes are mapped outside a unit circle with the assistance of particular conformal mapping under certain conditions. The mathematical model that governs the rounded forces of the current physical problem is the boundary value problem of elastic media. This study is applicable to many phenomena throughout nature, like tunnels, caves, and excavations in soil or rock. The Cauchy method for complex variables is used to get the closed forms of Gaursat functions and change the problem to a second-type integrodifferential equation with a Cauchy kernel, which is used for a large area of the contact problems. Then, the normal and shear stress components that act on the model are derived. Afterward, some of the physical applications are studied, and different stress components at specific values in each application are calculated and plotted using Maple 2023.

Comparative analysis of flag based energy harvester undergoing extraneous induced excitation

This study presents a detailed comparative analysis of the piezoelectric flexible plate under the influence of oscillating wakes of different bluff bodies. The piezoelectric plate is tested to determine the optimal configuration for energy harvesting from the wake flow of bluff bodies with different cross-sections in a low-speed closed-circuit wind tunnel. The Reynolds number is varied from 10000 to 75000 and the distance between the bluff body and plate is changed from 1D to 7D (where D is the diameter of the bluff body). The flutter of the plate without a bluff body is considered as a benchmark case and then subsequently the bluff bodies are introduced to see energy generation behavior. The results show that the bluff body caused a significant reduction of 50% in the flow speed as compared to the flutter case along with an improvement of 847% in energy harvesting output. Furthermore, selecting an appropriate bluff body ensures higher peak-to-peak flapping amplitude, which in turn produces a higher amount of electrical energy due to higher bending curvature and resultant strain produced in the piezoelectric plate. An increase of 125% in flapping amplitude is obtained using a bluff body compared to the flutter case. Furthermore, comparison within the various bluff bodies shows that change in cross-section has an enormous impact on output, and an increase of 515% in output power is obtained compared to the typical circular bluff body, which is more often quoted in the literature. Additionally, bending modes are identified and the variation in output power is linked with the flapping behavior of the piezoelectric plate, which is helpful in understanding the energy generation behavior of the piezo plate.

A flexible U-shaped metamaterial terahertz quarter-wave plate with corner design

To overcome the bottleneck problem that the right-angle of metamaterial metal unit cell can’t be perfectly machined in the existing photolithography process, the tangent treatment of U-shaped corners is carried out in this paper. Using two layers of U-shaped metamaterial gold unit cell with corner design sandwiched with three polyimide layers, a flexible terahertz quarter-wave plate (QWP) with polarization conversion efficiency of 0.8 and operating bandwidth of 0.2 THz is obtained. The equivalent dielectric parameter of substrate is proposed to provide the correct dielectric parameter input of polyimide for the precise simulation. The influences of the equivalent dielectric parameter, the corner tangent length and the geometric parameters of the metamaterial metal unit cell on the QWP performance are analyzed. To better understand the effects of these parameters on the QWP performance, an empirical formula for multilayer U-shaped metamaterial is given in this paper. This work has good application potential in terahertz wireless communications, terahertz imaging, and terahertz medical diagnostic systems and other fields.

Flapping vortex dynamics of two coupled side-by-side flexible plates submerged in the wake of a square cylinder

The flapping vortex dynamics of two flexible plates submerged side-by-side in the wake of a square cylinder are investigated through a two-way fluid–structure interaction (FSI) simulation. The gap between the two plates can stabilize wakes, lengthen vortex formation, elongate vortices, suppress vortex shedding, and decrease hydrodynamic forces. The numerical results indicate that the two flexible plates can exhibit four distinct modes of coupled motion: out-of-phase flapping, in-phase flapping, transition flapping, and decoupled flapping, depending on the gap spacing. Additionally, it is discovered that each of the four coupling modes has a unique pattern of vortex development. The findings of this study should proved valuable in the design of FSI-based piezoelectric energy harvesters utilizing cylinder–plate systems.

Theory of nonlocal modal hydrodynamic functions for beam and plate vibrations in viscous fluids

In this paper, we introduce a new nonlocal modal hydrodynamic theory for fluid–structure interactions (FSI) of light, flexible cantilever beams and plates undergoing small amplitude vibrations in Newtonian, incompressible, viscous, heavy fluids otherwise at rest. For low aspect ratio flexible structures and high mode numbers, three dimensional (3D) and nonlocal fluid effects become prominent drivers of the coupled dynamics, to the point that existing local hydrodynamic theories based on two dimensional (2D) fluid approximations become inadequate to predict the system response. On the other hand, our approach is based on a rigorous, yet efficient, 3D treatment of the hydrodynamic loading on cantilevered thin structures. The off-line solution of the FSI problem results in the so-called nonlocal modal hydrodynamic function matrix, that is, the representation of the nonlocal hydrodynamic load operator on a basis formed by the structural modes. Our theory then integrates the nonlocal hydrodynamics within a fully coupled structural modal model in the frequency domain. We compare and discuss our theory predictions in terms of frequency response functions, mode shapes, hydrodynamic loads, quality factors, added mass ratios with the predictions of the classical local approaches, for different actuation scenarios, identifying the limitations of the hypotheses underlying existing treatments. Importantly, we also validate our new model with experiments conducted on flexible square plates. While computationally efficient, our fully coupled theory is exact up to numerical truncation and can bridge knowledge gaps in the design and analysis of FSI systems based on low aspect ratio flexible beams and plates.

Bio-convective maxwell ferrofluid flow over a flexible spinning surface

The current research findings will have potential applications in the development of drug-targeted and self-sterilizing technologies. This research investigates the bio-convective flow of Maxwell ferrofluid over a flexible spinning plate in the presence of a stationary magnetic field in this paper. This theoretical model is based on the CattaneoChristov theories, the Buongiorno microorganism model, and the Shliomis model, and it is solved using the finite element technique. Using the Galerkin weighted residual approach in COMSOL Multiphysics, the non-dimensional equations of this Maxwell ferrofluid model are numerically solved. The concentration and motility of the organism decrease with an increase in the ferromagnetic interaction number, concentration relaxation time parameter, Lewis number, and stretching parameter. In addition to increasing local heat transfer, local mass transfer, and local density of microorganisms, the ferromagnetic interaction number lowers the stress on the surface of the disk.

Flexible structures enhance fluid mixing in a channel flow

Early fluid mixing in channel flows without incurring much drop in the pressure head is desired in industrial applications. This study explores wall-mounted flexible plates as obstacles to enhance mixing in channel flows. Using fluid–structure-scalar interaction simulations, we investigate the oscillations of the flexible plates under the flow, which serve as a vortex generator and help increase the mixing. The channel flow involves a scalar field with distinct concentrations initially separated across the channel, gradually intermixing due to vortical structures of varying scales. We have used the “mixing index” and “head loss” metrics along the channel length to assess the mixing quality when plates with different flexibility (characterized by the Cauchy number, Ca) are used. This study introduces a comprehensive criterion, the “coefficient of performance,” derived by comparing mixing and head loss in the presence and absence of obstacles. Aggregating results across various Ca values reveal that flexible plates substantially improve fluid mixing compared to rigid plates. We have also investigated the effect of the pulsatile fluid inlet (quantified by Strouhal number, Stf) and found that lower inlet flow pulsation (Stf<32) adversely impacts mixing performance, recommending a steady inlet flow. However, at high Stf, specifically in the configuration with Ca = 0.06 and Stf = 32, the best mixing performance is achieved in the channel, which marginally outperforms the steady inlet case. The conclusive takeaways from this study are that the plates with increased flexibility result in better mixing, and high inlet pulsation can be employed to fine-tune the mixing performance for further enhancement.

Experimental study on the flow-induced vibrations of a circular cylinder with a rear flexibly hinged splitter plate

The flow around a circular cylinder is a canonical configuration that may be encountered in many engineering applications, as for instance, civil engineering, architecture, or marine structures. In particular, when bluff bodies are slender and feature low mass-damping characteristics, they may undergo flow-induced vibrations (FIVs), which may result in severe structural fatigue and damage. Here, we present an experimental study on the effect of flexibly hinged splitter plates in the FIV of a flexibly mounted circular cylinder (of diameter D) subject to an uniform cross-flow of velocity u∞. The dynamic response and forcing of the low mass-damping system is characterized for plates of different lengths Lp and different values of the torsional stiffness of the hinge kp. Reductions of the dynamic response of more than 90% can be generally reached at the upper branch, especially when a plate of length l*=Lp/D=2 with intermediate degree of torsional stiffness is attached, which is shown to represent the best solution as it mitigates the oscillations of the system (cylinder and plate) for the whole range investigated of reduced velocity U*=u∞/fnD=[3.9,9.8], where fn is the natural frequency of oscillation. In general, the hinged plates are able to attenuate the vortex-induced vibration system response by increasing shedding frequency, until the ratio f*=f/fn>1 is reached. At high values of U*, a general transition to galloping-like dynamics, characterized by f*<1, occurs. The tested hinged plates modify the transition between regimes, which is associated with shifts in the phase difference between the forcing and response, combining features of the dynamics of both flexible and static rigid plates already reported in the literature. The use of hinged plates has been proven to provide with a significant attenuation of the system response and its associated drag, a feature that can be considered of practical relevance in many engineering applications. In addition, the key aspects for designing these elements as the torsional stiffness and plate length have been analyzed here.

A novel method for predicting fluid–structure interaction with large deformation based on masked deep neural network

Traditional fluid–structure interaction (FSI) simulation is computationally demanding, especially for bi-directional FSI problems. To address this, a masked deep neural network (MDNN) is developed to quickly and accurately predict the unsteady flow field. By integrating the MDNN with a structural dynamic solver, an FSI system is proposed to perform simulation of a flexible vertical plate oscillation in fluid with large deformation. The results show that both the flow field prediction and structure response are consistent with the traditional FSI system. Furthermore, the masked method is highly effective in mitigating error accumulation during temporal flow field predictions, making it applicable to various deformation problems. Notably, the proposed model reduces the computational time to a millisecond scale for each step regarding the fluid part, resulting in an increase in nearly two orders of magnitude in computational speed, which greatly enhances the computational speed of the FSI system.

Guided wave-based crack detection in U-shaped flexural plate butt welds

Based on the guided wave, a crack detection method for U-shaped flexural plate (UFP) butt welds is established to realize damage localization and quantitative identification. Firstly, the semi-analytical finite element (SAFE) method was used to obtain the dispersion curve in a plate with weld by discretizing the cross-section and then solving the characteristic equation. Subsequently, numerical studies were performed to investigate the mode conversion and energy transfer efficiency in weld bending. Then the method was determined after the wave packet analysis of voltage responses under different damage conditions. Finally, a validation experiment was conducted in an actual UFP butt weld. The result indicates that there exist 10 guided wave modes in a plate with weld at 150 kHz, while only 2 modes in a flat plate; For curvature radius of weld bending substantially greater than the weld thickness, the guided wave energy mainly passes through the bending in the form of transmitted waves and the reflected wave formed in the bending can be ignored; The damage can be located with the defect echo of the specific guided wave and the error distance only accounting for 1.5% of the total weld length. It is effective to take wavelet energy as an indicator to characterize the damage degree. The method significantly improves crack detection efficiency and provides a scientific basis for monitoring similar structures.

Wave Dynamics Around a Floating Circular Flexible Plate Over a Permeable Bed

Abstract In this paper, to determine the efficacy of the porous bed on damping far-field wave energy, the wave dynamics around a circular plate is studied. By combining the appropriate boundary conditions, the unknown potential is attained for the free surface and the plate-covered region. The Bessel series solution is attained further, by employing the matched eigenfunction expansion technique. Wave force excitation on the circular plate, deflection of the plate, and flow distribution is calculated and examined to comprehend the efficacy of the current investigation. Moreover, the motion of the plate is assessed in the time domain. The study reveals a substantial reduction in wave amplitude on the plate’s leeward side because of the energy dissipation by the porous bed. Also the study concludes that for intermediate values of porosity with larger wavenumbers, approximately 50% of wave power is dissipated with respect to incident wave power.

Effects of kinematic parameters and corrugated structure on the aerodynamic performance of flexible dragonfly wings

The effects of unsteady motions of flapping flat plates and corrugated structures in different parameters are studied using fluid–solid coupling and overlapping grid methods. Based on the dragonfly’s right forewing and right hindwing model, these actions include sweeping and pitching, take-off acceleration, and tandem wings cruising in the reverse phase at 180°. The results show that when the advance ratio J=0.36, the “inflow deflection” improves the aerodynamic force in two degrees of freedom compared to simple flapping. When considering only the impact of flexibility, the aerodynamic forces of flexible flat plates and corrugated structures are better than those of the rigid wing models. Considering the effect of corrugated structures, the lift of flexible corrugated wings diminishes, but more thrust is generated. From the perspective of vortex street, vortex rings materialize only in the downstroke stage, while the attachment effect of leading-edge vortices is noticeable in several models. In the same phase flapping, the two wings combine to form a giant wing, which generates significant forward flight momentum. In out-of-phase flapping mode, the series wings generate two lifts and two or three thrust peaks to attain the required forward flight speed while sustaining a high lift.

Modeling and vibration control of a rotating flexible plate actuated by MFC

The macro fiber composite (MFC) is a novel piezoelectric intelligent material, which is widely used in the field of vibration control due to its flexibility and larger actuation forces than PZT. In this paper, a laminated plate model considering the anisotropy of MFC is developed and applied to the vibration control of a rotating plate. The laminated plate is defined as a layerwise model, which deformation is described by the Absolute Nodal Coordinate Formulation (ANCF). The MFC laminated plate element contains 48 degrees of freedom (DOFs) where the effect of MFC element can be internally incorporated without increasing the DOFs of system. Simultaneously, a neural network PD control is adopted to control the vibration of the rotating plate. Eventually, static, dynamic, and modal analyses are performed to investigate the effects of different parameters. Several vibration simulations are carried out to illustrate the ability of MFC patches on vibration control. The findings in this article would be applied to mechanical prediction and control for rotor blades of helicopters, solar panels, etc.

Hydroelastic theory for offshore floating plates of variable flexural rigidity

We present a theoretical model of the hydrodynamic behaviour of a floating flexible plate of variable flexural rigidity connected to the seabed by a spring/damper system. Decomposition of the response modes into rigid and bending elastic components allows us to investigate the hydroelastic behaviour of the plate subject to monochromatic incident free-surface waves of constant amplitude. We show that spatially dependent plate stiffness affects the eigenfrequencies and modal shapes, with direct consequences on plate dynamics and wave power extraction efficiency. We also examine how plate length and Power Take-Off (PTO) distribution affect the response of the system and its consequent absorbed energy. This work highlights the need to improve existing models of flexible floating energy platforms, especially given their importance in the Offshore Renewable Energy (ORE) sector.

Acoustic Characteristics of a Plate Silencer with a Flexible Back Cavity Under Arbitrary Boundary Conditions

The flexible back cavity (FBC) plate silencer is composed of an FBC and a flexible inner plate. Through the coupling of the sound field with the flexible inner and outer plates, the transmitted sound energy of the downstream is reduced, and it has a good broadband muffling effect at low frequencies. In order to obtain the transmission loss (TL) of the FBC plate silencer under arbitrary boundary conditions, this paper establishes the acoustic-vibration coupling model of the FBC plate silencer based on the energy principle. Translational restraints and rotational restraints are used to simulate the arbitrary boundary conditions of the flexible plate, and then the influence of the boundary conditions of the flexible plate on the TL is analyzed. The results show that the results of the proposed method are in good agreement with the finite element method (FEM) results. The structural boundary restraint has a significant influence on the acoustic characteristics of the system, and the rotational restraints suppress the muffling effect. By appropriately releasing the translational restraints, a better low-frequency broadband muffling effect can be achieved, with the minimum muffling frequency reduced by 44.8% and the muffling bandwidth broadened by 57.4%.

PREPARATION METHOD AND THERMAL PERFORMANCE OF A NEW ULTRA-THIN FLEXIBLE FLAT PLATE HEAT PIPE

Ultra-thin flat plate heat pipes must provide a degree of flexibility to meet foldable electronics heat dissipation requirements. In this paper, a new flexible ultra-thin flat plate heat pipe with a thickness of 0.75 mm has been designed and fabricated. Compared with the traditional flexible ultra-thin flat heat pipes, the innovation lies in the flexible insulation section formed by epoxy resin pouring of the shell. The design of the shell ensures that the flexible ultra-thin plate heat pipe can respond quickly to the external temperature change, and also has good flexibility, which provides a new choice for the material and structure design of the flexible ultra-thin plate heat pipe shell. The gas-liquid coplanar type mesh is used as the capillary wick to reduce the flow resistance of steam inside the heat pipe, and the wick is hydrophilically modified to improve its capillary pumping performance; a sandwich support structure is used to prevent the steam chamber from collapsing. The thermal performance of the three liquid filling ratios of 0.3, 0.4, and 0.5 was tested at different tilt angles and bending angles. The results show that in the cases of filling ratios of 0.3, 0.4, and 0.5, the ultra-thin flexible flat plate heat pipe with the liquid filling ratio of 0.3 has the best heat transfer performance under different working conditions; the tilt angle has different effects on the heat transfer performance and starting speed of the ultra-thin flexible flat plate heat pipe with different filling ratios, and the bending angle changes the steam condensation position inside the ultra-thin flexible flat plate heat pipe and increases the thermal resistance.

Measurements of flow-induced vibration of a flexible splitter plate mounted on a cylinder in free stream flow

We experimentally study flow-induced vibration (FIV) of a thin, cantilevered, flexible plate attached on the lee side of a circular cylinder in a free stream airflow. The Reynolds number (ReD) based on the diameter of the cylinder was varied in the range of (4 × 103, 5×104). The plates of different lengths and the same span were tested with varying airflow velocities (U) in a wind tunnel. The reduced velocity (UR) based on the length and the second natural frequency of the plate was in the range of (1, 11). We describe the plate dynamics showing displacement, frequency, phase plane, amplitude spectral density (ASD), oscillation envelope, modal energy contribution, and flow structures. Based on the motion of the plate, three FIV regimes are observed, namely, initial excitation, transition, and lock-in. During lock-in, the plate attains self-sustained limit cycle oscillation. We observe the presence of small-amplitude higher harmonics in the ASD plot. The second mode is dominant around the onset of lock-in, while the first mode is dominant later in the lock-in regime. The dimensionless displacement increases with an increase in mass ratio (Ms) in the lock-in regime. With a decrease in Ms, the slope of the dimensionless frequency with UR increases. To explain measurements, we develop a wake oscillator model (WOM) in which the plate and fluctuating lift force are modeled as an Euler–Bernoulli cantilever beam and van der Pol oscillator, respectively. The coupled WOM qualitatively and quantitatively predict the measured amplitude and frequency response, respectively, in the lock-in regime.

EQUILIBRIUM OF A NORMALLY LOADED ELASTIC SHALLOW CYLINDRICAL SHELL WITH DISLOCATIONS AND DISCLINATIONS

We consider the problem of the equilibrium of a normally loaded elastic shallow rectangular circular cylindrical shell, which contains sources of internal stress in the form of fields of continuously distributed edge dislocations and wedge disclinations or other sources, for example, thermal ones. Based on the modified system of Karman equations for the equilibrium of an elastic plate with dislocations and disclinations, a system of nonlinear equilibrium equations for the shell was constructed. The resulting system of equations differs from the Karman system of equilibrium equations for an elastic shallow cylindrical shell under the action of a normal load by the presence on the right side of the continuity equation of a nonzero function, called the incompatibility function, which is expressed through the densities of edge dislocations and wedge disclinations. The edges of the shell are freely clamped or hinged. In the absence of internal stress sources, this system transforms into a system of equilibrium equations for a shallow shell, and in the case of an infinitely large radius of curvature (and the presence of internal stress sources) into a modified system of Karman equilibrium equations for a flexible elastic plate with dislocations and disclinations. To solve the system of nonlinear shell equilibrium equations, the Newton – Kantorovich method in combination with the difference method is proposed. For the case of small values of the normal load and small values of the incompatibility function, linearization is carried out with respect to the deflection and stress function. As a result, a linear boundary value problem was obtained in the form of a system of differential equations for the deflection and the stress function, which is solved by the difference method. The solution of the linearized system is used as an initial approximation in the implementation of the Newton – Kantorovich method. Examples of numerical calculations of deflection and stress function for given values of normal load and incompatibility function are given, and corresponding graphs are constructed.

Vibration vision measurement and wavelet neural network control of flexible hinged plate

Vibration vision measurement and wavelet neural network control of flexible hinged plate