Flexible Plate Research Articles

Dynamics of a hot flexible cantilever plate under natural convection heat transfer in a square cavity

This study investigates the fluid-structure interactions of a flapping plate within a square cavity under four distinct boundary conditions, where two opposing walls are heated isothermally, and the others are adiabatic. These configurations are defined as case 1 (cooled side walls), case 2 (cooled top and bottom walls), case 3 (heated bottom and cooled top wall), and case 4 (heated top wall and cooled bottom wall). The effects of non-dimensional parameters, including Rayleigh number (Ra), Cauchy number (Ca), and mass ratio (β) on plate dynamics and convective heat transfer are analyzed. Numerical investigations are executed utilizing the SU2 open-source multi-physics computational fluid dynamics solver, with a fixed Prandtl number (Pr) set at 0.71 and dimensionless temperature difference (ϵ) established at 0.6. The results show that in cases 1 and 4, the plate exhibits no observable unsteadiness, while cases 2 and 3 reveal different oscillatory behavior within certain parameter ranges, including static mode, periodic flapping mode, quasi-periodic flapping mode, and chaotic flapping mode. In particular, the configuration in case 3 possesses higher inherent instability than case 2, causing the earlier onset of Hopf bifurcation. These findings provide valuable insights into the influence of boundary conditions on the behavior of flexible structures in fluid environments, highlighting the critical role of flow instabilities and boundary conditions in determining the dynamic response of the system.

Comparative Analysis of Surgical Techniques for Pediatric Diaphyseal Forearm Fractures: A Focus on Titanium Flexible Nails versus Plates and Screws

Comparative Analysis of Surgical Techniques for Pediatric Diaphyseal Forearm Fractures: A Focus on Titanium Flexible Nails versus Plates and Screws

Hydroelastic responses of a multi-modular very large floating structure on a flexible bottom with lateral stress in a two-layer fluid

Based on the small-amplitude water wave theory, an analytical investigation is performed for the interaction between incident waves and a multi-modular very large floating structure (VLFS) in a two-layer fluid with a flexible seabed. A vertical porous flexible plate is fixed in the center of each floating plate to suppress the hydroelastic response. A key innovation is the modeling of both the VLFSs and the seabed as thin elastic plates with the lateral stress. The analytical expressions for dispersion relationships and vertical eigenfunctions are exactly derived in the water regions with a flexible seabed. The series solution of the velocity potential is obtained through the combination of inner product and the least squares approximation method. The study uniquely illustrates the impact of lateral stress and flexible seabeds on wave propagation, revealing that at low frequencies, waves in both open water and plate-covered regions with a flexible seabed exhibit the similar propagation characteristics. At higher frequencies, however, the propagation characteristics of the waves in the open water regions remain unaffected by the presence of a flexible seabed. The lateral stress has significant effects on the roots of dispersion relationships and the hydroelastic responses. The influences of other physical parameters of the fluid and structures are also displayed graphically. The results demonstrate that the increasing number of modules and extending the vertical plates effectively suppress hydroelastic responses and reduce wave transmission. The porous barriers can reduce the stress on the vertical plates and weaken the effect of barriers for suppressing hydroelastic response.

Simplified inverse distance weighting-immersed boundary method for simulation of fluid-structure interaction

When simulating fluid-structure interaction (FSI) problems involving moving objects, the implicit inverse distance weighting-immersed boundary method (IDW-IBM) developed by Du et al. [1] has to construct a large square correlation matrix and solve its inversion at each time step. In this work, a simplified inverse distance weighting-immersed boundary method (SIDW-IBM) is proposed to eliminate the intrinsic limitations in the original implicit IDW-IBM. Through error analysis using Taylor series expansion, a second order approximation can be derived, which allows us to approximate the large square correlation matrix into a diagonal matrix; thereby, we proposed the SIDW-IBM based on this second order approximation to explicitly evaluate the velocity corrections, where the needs to assemble the large correlation matrix and inverse it are circumvented. Owing to the fact that the inverse distance weighting interpolation removes the limitations in the Dirac delta function, the proposed SIDW-IBM has been successfully implemented on the non-uniform meshes to further improve the computational efficiency. The proposed SIDW-IBM is integrated with the reconstructed lattice Boltzmann flux solver (RLBFS) [2] to simulate some classic incompressible viscous flows, including flow past an in-line oscillating cylinder, flow past a heaving airfoil, and flow past a three-dimensional flexible plate. The good agreement between the present results and reference data demonstrates the capability and feasibility of the SIDW-IBM for simulating FSI problems with moving boundaries and large deformations.

Parametric study of traveling wave motion in energy absorption mode

There are two modes of traveling wave motion, traveling wave propulsion and traveling wave energy absorption. In this paper, a two-dimensional flexible traveling wave plate is taken as the research object. The characteristic length and characteristic parameter of traveling wave motion are determined by numerical simulation, and the parametric study of the traveling wave motion in energy absorption mode is conducted. The effects of dimensionless amplitude and dimensionless wave velocity on the energy absorption characteristics of flexible traveling wave plate are analyzed, and the mechanism of traveling wave energy absorption is revealed. The results show that the larger the dimensionless amplitude is, the stronger the work capacity of the traveling wave plate becomes, while the absolute amplitude or absolute wavelength has little effect on the work capacity of the traveling wave plate. Under different waveforms, the work capacity of the traveling wave plate increases first and then decreases as the dimensionless wave velocity increases. Within the parameter range studied in this article, when the dimensionless amplitude is 0.2 and the dimensionless wave velocity is 0.5, the traveling wave plate can achieve an energy absorption efficiency of about 40 %.

Elastic nail versus plate for treatment of single close fracture of femur shaft

This study aims to describe the outcome of pediatric flexible nails versus plates for the treatment of femur fracture. We reviewed the medical records of 28 femur fractures in children treated with flexible nail insertion and 26 children treated with plate fixation from January 2017 to December 2019. The mean age of the children was 8.88 ± 1.86 years. Data were obtained from patient charts. Union of bones was found in all the operated children, 28 (51.9%) of the group flexible nails, while no union was found in 3 (5.6%) of the group plate with screws. Delay union was found in 5 (9.3%) of the plate with screws, while in the group of flexible nails was in 2 (3.7%). Malrotation was found in 2 (3.7%) of the flexible nails and in 1 (1.9%) in the plate and screw. Bursa was found only in the flexible nails with 7 (13%) (p = 0.007). Re-fracture was found only in the group of plates with screws with 5 (9.3%) (p = 0.021). The limbs were shortened only in 1 (1.9%) patient with flexible nails. Superficial infection was high in the group plate with screws group 4 (7.4%). Deep infection was found to be high among 3 (5.6%) of the group plate & screw. We conclude that flexible intramedullary nail fixation of fracture shaft femur in children is a very acceptable way of treatment and is associated with minimal complications.

Finite-Element Validation of U-Shaped Flexural Plates Integrated into a Novel Brace Dissipator

Finite-Element Validation of U-Shaped Flexural Plates Integrated into a Novel Brace Dissipator

Improving the energy harvesting performance of clamped flexible plates using vortex shedding behind bluff bodies: A computational study

This study assesses flow-induced vibrations of clamped flexible plates with the objective of improving their energy harvesting performance. Toward this, a rectangular bluff body is placed between the two clamped flexible plates to harness the vortices generated behind the bluff body. The strain energy of the plate is used as a measure of energy harvesting performance. Computational studies are performed for different parameters of interest, such as dimensions and material properties of the plate and dimensions and locations of the bluff body. The effects of these stated parameters on flow-induced vibration response and vortical structures are investigated, and the optimal values for the location and geometry of the bluff body, as well as the aspect ratio and Young's modulus of the plate for energy harvesting performance, are determined. The results show that vortex shedding from the bluff body strongly influences the dynamic behavior and energy output of the flexible structures inside the wake region of the bluff body at different locations. Additionally, the aspect ratio and its effect on vorticity and energy harvesting are discussed in detail, along with the average displacement and average lift force experienced by the plates. The outcomes of this work offer significant insights into optimizing the design of clamped flexible plates for optimal energy generation by cleverly exploiting the vortex shedding behind fixed bluff bodies.

Particle motion in a bed under a rigid plate, submerged and oscillated over its surface, and bed morphologies induced by flexible plates

Particle motion in a bed under a rigid plate, submerged and oscillated over its surface, and bed morphologies induced by flexible plates

The perpendicular gyroscope: modal analysis of plate, beam and gyroscope multistructures.

This paper presents a study of the perpendicular gyroscope, which is formed of two orthogonal beams, a flexural plate and a gyroscope. Two sets of chiral-torsional boundary conditions are derived to analytically model the dynamic effects of the gyroscope while taking into account the broken symmetries of the system. The perpendicular junction causes the coupling of the compressional, flexural and torsional displacements in the system. This complex behaviour is accounted for with a comprehensive set of kinematic and dynamic junction conditions. Modal analysis demonstrates the fully coupled system and reveals how the spinning gyroscope induces dynamic chiral Chladni patterns in the plate.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Exploiting interfacial instability during peeling a flexible plate from elastic films

Adhesive interactions between soft materials are prevalent in both biological systems and various engineering applications, including soft robots, flexible electronics, and antifouling coatings. Many studies have demonstrated that cavitation and fingering instabilities emerge at the adhesive interface between rigid objects and soft films, owing to the geometric attributes of the contact region. However, in the context of peeling configurations, defining the geometric features is challenging, resulting in relatively scant exploration of interfacial instabilities. Hence, the modulation of instability patterns during the peeling process of a flexible plate from a thin elastic film, alongside the consequential effects on mechanical responses, remains poorly understood. To elucidate the mechanisms underlying interfacial instability during peeling process and its impacts on peel-off force, we use finite element methods to simulate the evolution of interface separation. Consistent with previous experimental observations, we find that the interfacial instability will occur when the bending stiffness of the flexible plate is bigger than a critical value. We show that the interfacial instability is mainly induced by the competition between the adhesion energy and the strain energy of the film, and the incompressibility of the thin film is critical for the appearance of the interfacial instability. Combining theory and finite element simulation, we propose the scaling laws for the critical peel-off force for stable and unstable peelings, respectively, and show that the critical peel-off force will decrease when the interfacial instability occurs. Finally, we demonstrate that weakening the tangential adhesion strength and loosening the constraints between the film and the rigid substrate effectively suppress fingering instability. Collectively, our findings elucidate the pivotal factors influencing interfacial instability, offering invaluable insights for the design of structures or systems involving soft materials.

A flexible piezoelectric energy harvester featuring an eccentric pendulum via frequency up-conversion for human motion

This paper presents an innovative design of a flexible piezoelectric energy harvester featuring an eccentric pendulum (FPEH-P), which has two major characteristics: frequency up-conversion and large deformation that can improve output capacity. To clarify operational principles, we establish a dynamic model of the pendulum, and the vibration of the flexible piezoelectric plate is analyzed. Then, the two major characteristics of the FPEH-P are verified by experiments and simulations. Furthermore, it is verified that the FPEH-P can work at a low frequency (about 2 Hz) experimentally. Due to the large deformation of the piezoelectric plate, the maximum peak open-circuit voltage can reach 6.82 V. At an excitation frequency of 1.9 Hz and amplitude of 100 mm, the maximum average power can reach 6.06 μW. The FPEH-P can efficiently harvest energy from individuals engaged in walking, jogging, and running, as evidenced by the output load voltage and average power. Moreover, it can also output voltage under multiple motion actions. Finally, it has been verified that the high-instantaneous voltage characteristic of the harvester can provide sustainable power to a timer.

Constructive interaction in an array of flexible energy-harvesting plates in oscillatory cross flow

Constructive interaction in an array of flexible energy-harvesting plates in oscillatory cross flow

Outcome of Flexible Intramedullary Nailing versus Plating in Treatment of Diaphyseal Femur Fractures in Paediatrics: Systematic Review and Meta-analysis

Abstract Background Pediatric femoral fractures are the most the common long bone fracture in children, with one third of these occurring between ages 5 to 12. These injuries are usually the result of road traffic accidents, sports and non-accidental injury. Different modalities exist for managing these fractures, often stratified according to the age of the patient. Aim of the Work The aim of this work is to provide a complete overview of the optimal surgical treatment of diaphyseal femur fractures in children by evaluating and comparing the clinical and functional outcomes of flexible intramedullary nailing versus plating for such fractures. Patients and Methods This review followed the Cochrane Handbook's standard methodology and reported the findings in accordance with the Preferred Reporting Items for Systematic Reviews and Meta- analyses (PRISMA) statement guidelines. Result In patients undergoing flexible nailing, the surgical variable data found this treatment modality to be superior in terms of certain operative features: shorter operative duration times (p = 0.00001), smaller volumes of estimated blood loss (p = 0.00001). There was no difference regarding length of hostital stay (p = 0.59). This suggests that flexible nailing may offer increased safety to patients in terms of duration of anesthesia, volume of blood loss, and cost of surgery when compared to plating. However, Secondary outcome analysis also found a statistically significant increased risk of malunion (p = 0.002) and metalwork irritation (p = 0.00001) when using FIN compared to plating techniques. There was no difference regarding risk of infection (p = 0.53) and developing leg length discrepancy (p = 0.44). Conclusion Options for stabilization and fixation in this age group include flexible nailing, plating (open or sub-muscular), external fixation, or hybrid techniques.

Wake-induced response of a flexible splitter plate detachedly placed downstream of a circular cylinder

A fluid–structure interaction numerical investigation was conducted on the flow past a circular cylinder with a detached flexible plate at a low Reynolds number Re = 160. A broad gap ratio range of 0–6.0 is examined at three plate lengths. Numerical results indicated that the vortex formation is closely related to the position of the plate with respect to the recirculation region behind the cylinder. Three wake interference regimes are identified, including the extended-body, continuous reattachment (CR), and alternate reattachment (AR). Taking into account the wake interference and vortex shedding modes and the response order, six wake flow patterns are observed. The CR regime shifts to AR at a critical gap G/D = 3, where both the vibration amplitude and frequency sharply increase. The sizes of vortex spacing and plate length determine the response mode of the flexible plate. Compared to an isolated cylinder, the optimal reduction percentages in drag and lift coefficients are around 90% and 20%, respectively.

Bio-inspired compensatory strategies for damage to flapping robotic propulsors.

Natural swimmers and flyers can fully recover from catastrophic propulsor damage by altering stroke mechanics: some fish can lose even 76% of their propulsive surface without loss of thrust. We consider applying these principles to enable robotic flapping propulsors to autonomously repair functionality. However, direct transference of these alterations from an organism to a robotic flapping propulsor may be suboptimal owing to irrelevant evolutionary pressures. Instead, we use machine learning techniques to compare these alterations with those optimal for a robotic system. We implement an online artificial evolution with hardware-in-the-loop, performing experimental evaluations with a flexible plate. To recoup thrust, the learned strategy increased amplitude, frequency and angle of attack (AOA) amplitude, and phase-shifted AOA by approximately 110°. Only amplitude increase is reported by most fish literature. When recovering side force, we find that force direction is correlated with AOA. No clear amplitude or frequency trend is found, whereas frequency increases in most insect literature. These results suggest that how mechanical flapping propulsors most efficiently adjust to damage may not align with natural swimmers and flyers.

Dynamics of a wall-mounted flexible plate in oscillatory flows

Dynamics of a wall-mounted flexible plate in oscillatory flows

A two-way coupled fluid–structure interaction method for predicting the slamming loads and structural responses on a stiffened wedge

Ships navigating through rough seas are subjected to slamming loads from waves, which can lead to structural damage and maritime accidents. The wedge model is commonly employed to investigate slamming loads and structural responses. While a stiffened wedge closely resembles a real ship hull plate, incorporating it into fluid–structure interaction simulations presents challenges. This paper proposes a two-way coupled fluid–structure interaction method to examine slamming loads and structural responses of a free fall non-prismatic stiffened steel wedge. Hydrodynamic loads are determined through Reynolds-averaged Navier–Stokes computations using OpenFOAM, while structural responses are predicted using the finite element analysis (FEA) software Calculix. To achieve two-way coupling between computational fluid dynamics and FEA simulations, a coupling library for partitioned multi-physics simulations, preCICE, is introduced. The computed impact pressure and stress align well with available experimental data. Various free fall heights are investigated in the numerical simulations. The results indicate that elastic deformation mitigates impact pressure, while the presence of transverse ribs enhances the rigidity of the flexible plate. The duration of pressure and the peak slamming pressure exhibit an inverse correlation. Greater free fall heights result in shorter pressure duration times, and smaller free fall heights may reduce rise time. Three-dimensional effects cause pressure to decrease along the midpoint of the plate toward both sides. Additionally, structural stress in the central area exceeds that in the areas on both sides at the same height. In conclusion, the proposed two-way coupled model proves suitable for accurately and efficiently computing hydroelastic slamming on flexible wedges.

Out-of-plane interactive behavior and design of novel T-hooked buckling-restrained steel plate shear walls

To eliminate the use of a large number of connecting bolts for the cover panels in conventional buckling-restrained steel plate shear walls (BRSPSWs), T-hooked BRSPSW was proposed by using T-sectional stiffeners for restraining the out-of-plane deformation of the cover panels. With larger-sized flexural cover panels that provide confinement effects to the infilled steel plate, the out-of-plane interactive behavior between the infilled steel plate and each cover panel is greatly concerned for safe designs of the T-hooked BRSPSW. In this paper, a refined finite element (FE) model was established for evaluating the out-of-plane restraining effects in the T-hooked BRSPSW. The key parameters affecting the high-order buckling modes of the infilled steel plate were analyzed. The average spacing between adjacent buckling half-waves varied from 0.15 to 0.7 times the height of the steel sub-plate across common parameter ranges. Furthermore, a formula that estimates the total extrusion force produced by the buckled steel plate was corrected. By simplifying the cover panels into one-way flexural plates under uniform force, a flexural moment amplification coefficient in the range of 1.11 − 9.74 was defined to consider the difference between the actual strip-shaped interaction forces and the simplified model. Finally, a formula to calculate the bending moment of cover panels was proposed to safely design the T-hooked BRSPSWs.

Semi-analytical approach to study wave interaction with a pair of obliquely submerged heterogeneous flexible structures

ABSTRACT Analyzing inclined flexible plates of varying thickness is crucial for optimising and attaining precise control over wave reflection and transmission. This is particularly significant in the context of breakwater construction. In contrast to horizontal breakwaters, inclined barriers can penetrate multiple layers of fluid with varying particle velocities, facilitating interactions and causing wave breaking, which results in the dissipation of wave energy. Moreover, compared to vertical structures, inclined ones demonstrate more effective wave attenuation. In the context of the present study, we investigate the interaction of water waves with a pair of obliquely submerged flexible thin plates characterised by non-uniform thickness. In order to model this complex physical scenario, we employ the principles of linear water wave theory in conjunction with Kirchhoff's thin plate theory. By employing repeated integration and Green's integral theorem, we reduce the boundary value problem to a system of coupled integral equations. Through appropriate approximations, we solve this system and obtain numerical values for various hydrodynamic quantities. This model provides comprehensive results for both horizontal and vertical plates, making it highly versatile. We examine the impact of varying thickness and the inclination of the two flexible plates to understand their roles in the wave scattering process and the associated physical parameters. The results obtained from this study shed light on the intricate dynamics involved in wave-structure interactions and can inform the design and optimisation of breakwater systems.