Fluid-structure Interaction Technique Research Articles

Exploring arteriolar atherosclerosis: laminar blood flow across stenosis with fluid-structure interaction and gravitational effects

Abstract In response to the unanswered relevant questions surrounding atherosclerosis, it becomes imperative to investigate arterioles using sophisticated mathematical modelling techniques to shed light on critical stress and strain patterns influenced by gravity. The primary objective of this study is to scrutinize flow characteristics and probe stress and strain distributions experienced by the intima layer of arterioles, encompassing coronary, renal, cerebral, mesenteric, and pulmonary arteries, under gravitational forces. This investigation employs a fluid-structure interaction methodology utilizing arbitrary Eulerian–Lagrangian formulation. The study delves into blood flow characteristics within coronary, renal, cerebral, mesenteric, and pulmonary arterioles using the fluid-structure interaction technique, employing an arbitrary Eulerian–Lagrangian formulation. It thoroughly examines various biomechanical parameters such as the Cauchy–Green stress tensor, Principal strain, Piola–Kirchoff stress tensor, deformation tensor, and volume strain along the intima layer under the gravitational influence, elucidating vulnerable regions prone to endothelial dysfunction. Higher values of δV are found at the left shoulder and in the intima’s post stenosis area due to the pressure gradient along the flow channel, whereas other intima regions show a null volume strain. A thorough understanding of stress distribution is essential to create focused therapies to lessen vascular health problems. The stress in the post-stenosis region seems to affect the endothelial layer to a significant extent.

Nonlinear biomechanical behaviour of extracranial carotid artery aneurysms in the framework of Windkessel effect via FSI technique

Extracranial carotid artery aneurysms (ECCA) lead to rupture and neurologic symptoms from embolisation, with potentially fatal outcomes. Investigating the biomechanical behaviour of EECA with blood flow dynamics is crucial for identifying regions more susceptible to rupture. A coupled three-dimensional (3D) Windkessel-framework and hyperelastic fluid-structure interaction (FSI) analysis of ECCAs with patient-specific geometries, was developed in this paper with a particular focus on hemodynamic parameters and the arterial wall's biomechanical response. The blood flow has been modelled as non-Newtonian, pulsatile, and turbulent. The biomechanical characteristics of the aneurysm and artery are characterised employing a 5-parameter Mooney-Rivlin hyperelasticity model. The Windkessel effect is also considered to efficiently simulate pressure profile of the outlets and to capture the dynamic changes over the cardiac cycle. The study found the aneurysm carotid artery exhibited the high levels of pressure, wall shear stress (WSS), oscillatory shear index (OSI), and relative residence time (RRT) compared to the healthy one. The deformation of the arterial wall and the corresponding von Mises (VM) stress were found significantly increased in aneurysm cases, in comparison to that of no aneurysm cases, which strongly correlated with the hemodynamic characteristics of the blood flow and the geometric features of the aneurysms. This escalation would intensify the risk of aneurysm wall rupture. These findings have critical implications for enhancing treatment strategies for patients with extracranial aneurysms.

Wind-Induced Response Assessment of CAARC Building Based on LBM and FSI Simulation

It is very important for the wind-resistant design of high-rise buildings to assess wind-induced vibrations efficiently. The Lattice Boltzmann Method-based Large Eddy Simulation and Fluid–Structure Interaction techniques are used to identify the surface wind pressure and wind-induced dynamic response of a CAARC standard high-rise building. Compared with wind tunnel tests, a detailed analysis of the accuracy of simulated wind pressures and base moments of the CAARC model are discussed under multiple wind direction angles. The differences between one-way and two-way Fluid–Structure Interaction simulations are compared under two different reduced wind velocities. The research results show that the simulated mean surface wind pressures of building under seven wind direction conditions have an error within 15% compared to probe measurements, and the average and root mean square base bending moments agree well with the wind tunnel tests. The top transverse wind-induced vibrations of the buildings are significantly larger when the reduced wind velocity reaches 4.6, indicating that aerodynamic damping effects on structural responses should not be overlooked. The research findings of this article provide valuable technical references for the application of LBM methods in the wind load effect assessments of high-rise buildings.

Advances in biomedical fluid–structure interaction: Methodologies and applications from an interfacing perspective

Fluid–structure interaction (FSI) is a nonlinear multiphysics phenomenon that describes the interactions between incompressible fluid flows and immersed structures, making it invaluable to biomedical research. In this work, the common FSI methodologies in biomedical research were systematically summarized and classified into three groups based on FSI interfaces: fluid–channel interfaces, fluid–particle interfaces, and multi-interface interactions. A discussion of the role of the numerical FSI methods was also made, outlining its indispensable advantage in handling complex geometries, boundary conditions, and thus FSI interfaces. The applications of these methods are discussed in terms of blood vessel-related applications, drug-delivering micropumps, particle dynamics/cell sorting, and particle deformation and rapture. The development progress, current advances, and prospects of FSI's future application in biomedical research were illustrated. It was concluded that with the advances in computation technologies, the rapidly developing FSI methods can achieve state-of-the-art level details, helping to improve our understanding of various biomedical-related problems and the use of FSI techniques in biomedical research is likely to continue to grow.

A general FSI framework for an effective stress analysis on composite wind turbine blades

The fluid-structure interaction (FSI) technique has been extensively used and developed in the past decades. Commonly, the reduced-order models are used in FSI analyses to assure the numerical robustness and efficiency. However, due to the increasing demand for higher numerical resolutions in modern wind turbine composite blade applications, intrinsic limitations of reduced-order models, such as their inability to account for complex aerodynamic flow interactions, multi-motion couplings, and sophisticated composite properties, have become the weaknesses in existing reduced-order FSI approaches. In this study, we propose a general FSI framework, which combines the advantages of high-fidelity Computational Fluid Dynamics (CFD) and robust Multi-Body Dynamics (MBD) methods, and detailed Finite Element Analysis (FEA) for analysing the detailed stress distributions on the composite structures. The results of predicted dynamics and the Von Mises stress on the composite blade structures under given operation condition are compared and reasonably agreed with the literature results, with a significant computational cost reduction by nearly 25% is achieved. The proposed FSI framework can be a general approach to investigate the multi-physical interactions where the composite structure specifications are involved, coupling with complex dynamic motions in three-dimensional space.

Dynamic crushing and energy absorption of bio-inspired shear thickening fluid-filled origami metastructure

In this study, a novel approach is proposed to enhance the crushing efficiency and energy-absorbing performance of origami metastructure by incorporating the shear thickening fluid (STF), which mimics the existence of the viscoelastic material found inside the protective mechanism in nature. The dynamic crushing and energy-absorbing performances of the proposed STF-filled origami metastructure are numerically investigated using the commercial software LS-DYNA. A fluid-structure interaction (FSI) technique is employed to simulate the coupling between the structure parts and the infilled fluid. The crushing performances of the proposed STF-filled origami metastructure (STF-OM) are investigated and compared with the non-filled and viscous fluid-filled counterparts under various crushing velocities. The effects of the filled height of STF, the viscosity of STF, and the origami folding angle on the crushing performances of STF-OM are also investigated. It is found that the proposed STF-OM can generate a higher and more steady crushing force without inducing a significantly high initial peak force. Its crushing resistance and energy-absorbing capability increase with the increase in crushing velocity, demonstrating its adaptive crushing performance for various impact scenarios. The filled height and viscosity of STF, as well as the origami folding angle, significantly affect the energy-absorbing efficiency and crushing performance of the proposed structure.

A Review of the CFD Method in the Modeling of Flow Forces

Hydraulic valves are key components of fluid power systems. They control the flow rate and pressure in hydraulic lines, actuator motion, and direction. Valves that control flow rate or pressure can be divided into two main categories: spool-type valves, where control components are similar to the piston inside a sleeve with control orifices; and seat-type valves, in which a poppet inside a seat opens and closes the flow. Forces induced on valve components during oil flow are crucial to the valve’s operational capabilities. They can be calculated using a formula originating from the momentum conservation equation for a two-dimensional control volume. Increasing demands for flow rate and pressure control accuracy cause flow forces to be calculated much more accurately than when using the analytical formula. Therefore, computational fluid dynamics (CFD) simulations are the only effective tool for their calculation. This paper reviews the CFD approaches used for calculating flow forces inside hydraulic valves. It presents typical approaches used for evaluating flow forces inside hydraulic valves. The oldest and most common are conducted for a fixed position of valve components for defined flow conditions, which do not cover all components of flow forces. The dynamic flow forces can be calculated using more complex CFD models using fluid–structure interaction (FSI) techniques. This paper presents available FSI techniques for the simulation of transient flow forces, mainly for valves whose component position is determined by the forces occurring during oil flow.

A 2D elastic wall model to analyze the hyper‐viscous effects on blood flow across abdominal aortic aneurysm in COVID patients by fluid–structure interaction technique with ALE formulation

The worldwide dissemination of the coronavirus, as well as its dependencies, is being aided by detrimental urbanization. The impact of the viral infection upon an infected person is also thought to be influenced by any pre‐existing medical issues. Recent investigations have demonstrated that COVID‐19 patients have a higher degree of blood viscosity as a result of alterations in morphology in blood cells. Examining the importance of hyper‐viscosity in patients with COVID is crucial in determining the diseases of the arteries since viscosity is a key flow characteristic that affects the flow across a stenosis as well as an aneurysm. In the current study, a patient‐specific instance with an aneurysm across the abdominal aortal walls was taken into consideration. Given that abdominal aneurysms occur frequently in people, the high viscosity values are taken into account while examining the hyper‐viscous impact of fluid on its passage through the affected aorta. The current study is the initial endeavor to use the Arbitrary Lagrangian–Eulerian (ALE) Technique to study the impact of fluid–structure interaction (FSI) on the movement of fluid across an aneurysmal aortal section in conjunction with hyper‐viscous anomalous blood characteristics. The investigation backs up the different medical results that described the negative consequences of blood hyper‐viscosity. The computational findings from employing a finite element method (FEM) solver to resolve the fluid mechanical computations complemented alongside the solid mechanical principles indicate a possibility that the increased stress imposed by the hyper‐viscous propagates on the interior walls of the aneurysmal aorta may prompt the aneurysmal pouch to grow or breakdown. Also, the hyper‐viscous blood in COVID patients destroys the smooth muscle cells of the media layer endangering its normal structure and functions and leading to the development of new aneurysms.

Analize učinaka oštećenja na rešetkasto postolje izvanobalne platforme

In this paper, an offshore platform subjected to dynamic loading for different damage cases was modelled via fluid-structure interaction (FSI) analysis. Different damage models were considered in the case where one leg was broken, and the Young’s modulus of the damaged member was reduced with four different severity ratios. In addition to the five damaged structures, the undamaged structure was modelled according to two different leg spacing conditions. Thus, the damaged models were compared among themselves as well as with undamaged models. In this study, models were investigated using a numerical FSI technique. The numerical technique was verified using semi-analytical modelling. At this stage, the equation of motion of one of the structural models was solved using a semi-analytical method based on a multi-degree-of-freedom system. In addition, the numerical environment model was verified using a semi-analytical solution of the free-surface motion equation and the wave velocity-wave force curve. An Abaqus finite-element analysis program was used to model the structures and their surroundings. While the structures were modelled using the Lagrangian technique, the fluid surroundings were modelled using the Eulerian technique. Both the conditions of leg spacing and different severity ratios were modelled, and the most negative damage type was revealed.

Blade Structure Analysis of 2 MW V-Shaped Vertical Axis Wind Turbine Using Numerical Simulation

The intensive research on large-scale Vertical Axis Wind Turbine (VAWT) couldprovide an alternative to Horizontal Axis Wind Turbine (HAWT) in offshore deployment for the future. Regarding this fact, this article develops a conceptual design of the VAWT blade structure and analyzes its feasibility using numerical simulation. The blade structure is designed for 2 MW Darrieus type V- shaped VAWT. The blade is tapered, 90m long, and inclined at 35° to the vertical axis. Initially, the blade design is tested for ultimate strength test according to IEC 61400-01 standard using aluminum alloy and homogenized composite material. In doing so, maximum aerodynamic loading on the blade is calculated after steady state 3-D RANS CFD simulation of the blade in ANSYS Fluent. The Finite Element Method (FEM) model of the blade is created using shell element in ANSYS Static Structural with structured meshing strategy, and tested with the aerodynamic load using the one-way Fluid-Structure Interaction (FSI) technique, to obtain mesh independent solution. The impact of the using 2, 3, and 4 number of shear webs is then analyzed on the selected mesh model of the blade. Finally, a four-shear web model of the blade is tested under extreme conditions. The thickness of the blade surface and shear web are varied to test maximum deflection at the tip, and maximum allowable strain of the blade. After obtaining the required blade structure, the deformation, maximum equivalent stress, and maximum equivalent strain for the blade are studied at rotation Tip Speed Ratio (TSR) of 5 under aerodynamic and gravitational loading, using both materials. The study showed significant deflection at the tip of the blade for the tower-less V-VAWT blade, suggesting an alternative support mechanism for the blade. Also, the study concluded that better structural robustness is achieved while using a composite material instead of an aluminum alloy. This article provides basis to study structural behavior of the novel V-VAWT blades and contribute to continuing research on obtaining optimized blade structure for such turbine.

Application of CFD–FEA coupling to predict hydroelastic responses of a single module VLFS in extreme wave conditions

Freak waves, as a kind of strong nonlinear waves, have a great threat to the safety of Very Large Floating Structures (VLFS). Freak wave produces enormous wave height, which caused the hydroelastic responses on the VLFS to increase significantly. Nevertheless, due to the complexity of the highly nonlinear interactions between waves and VLFS, studies of wave-induced loads and the hydroelastic responses of VFLS in freak waves are rare. In this paper, a fluid-structure interaction technique that strongly connects the CFD and FEA solvers is proposed to evaluate the wave-induced loads and hydroelastic responses of a single module VLFS under freak wave circumstances. The accuracy and reliability of the CFD–FEA coupling approach is validated through the comparisons of the results of hydroelastic responses of VLFS in regular waves with those from other numerical methods. Finally, the global motion and vertical bending moment (VBM) of VLFS in freak wave conditions are investigated. The result shows that the freak wave will lead to the global motion of VLFS being multiplied several times and largely increasing the instantaneous maximum VBM. The novel findings in this study will provide a reference for the structural design of VLFS under survival conditions.

Impact of sleep posture and breathing pattern on soft palate flutter and pharynx vibration in a pediatric airway using fluid–structure interaction

Snoring is a common condition in the general population, and the management of snoring requires a better understanding of its mechanism through a fluid–structure interaction (FSI) perspective. Despite the recent popularity of numerical FSI techniques, outstanding challenges are accurately predicting airway deformation and its vibration during snoring due to complex airway morphology. In addition, there still needs to be more understanding of snoring inhibition when lying on the side, and the possible effect of airflow rates, as well as nose or mouth-nose breathing, on snoring remains to be investigated. In this study, an FSI method verified against in vitro models was introduced to predict upper airway deformation and vibration. The technique was applied to predict airway aerodynamics, soft palate flutter, and airway vibration in four sleep postures (supine, left/right lying, and sitting positions) and four breathing patterns (mouth-nose, nose, mouth, and unilateral nose breathing). It was found that, at given elastic properties of soft tissues, the evaluated flutter frequency of 19.8 Hz in inspiration was in good agreement with the reported frequency of snoring sound in literature. Reduction in flutter and vibrations due to the mouth-nose airflow proportion changes were also noticed when having side-lying and sitting positions. Breathing through the mouth results in larger airway deformation than breathing through the nose or mouth-nose. These results collectively demonstrate the potential of FSI for studying the physics of airway vibration and clarify to some degree the reason for snoring inhibition during sleep postures and breathing patterns.

Study on transient performance of tilting-pad thrust bearings in nuclear pump considering fluid-structure interaction

To study the lubrication performance of tilting-pad thrust bearing (TPTBs) during start-up in nuclear pump, a hydrodynamic lubrication model of TPTBs was established based on the computational fluid dynamics (CFD) method and the fluid-structure interaction (FSI) technique. Further, a mesh motion algorithm for the transient calculation of thrust bearings was developed based on the user defined function (UDF).The result demonstrated that minimum film thickness increases first and then decreases with the rotational speed under start-up condition. The influence of pad tilt on minimum film thickness is greater than that of collar movement at low speed, and the establishment of dynamic pressure mainly depends on pad tilt and minimum film thickness increases. As the increase of rotational speed, the influence of pad tilt was abated, where the influence of the moving of the collar dominated gradually, and minimum film thickness decreases. For TPTBs, the circumferential angle of the pad is always greater than the radial angle. When the rotational speed is constant, the change rate of radial angle is greater than that of circumferential angle with the increase of loading forces. This study can provide reference for improving bearing wear resistance.

Dynamic crushing performance of bio-inspired sandwich structures with beetle forewing cores

A novel design of Sandwich Structure inspired by Beetle Forewing (SSBF) is proposed in this study by mimicking the internal structure of beetle forewing. The viscoelastic material and the arch shape of hollow cavity structures found inside the forewing structure of the beetle are imitated by utilising the shear thickening fluid (STF) and semi-arch cores, respectively. The coupling interaction between fluid and structural components is analysed using a fluid-structure interaction (FSI) technique in LS-DYNA. It is found that the proposed SSBF by partially filling the core with STF generates a higher mean crushing force and stabilises the crushing force-displacement profile without a noticeably high initial peak crushing force as compared with the empty, polyurethane (PU) foam-filled, or Newtonian viscous fluid-filled counterparts. Furthermore, this stable crushing force of SSBF enhances with the increase of crushing speed, showing ideal behaviour for energy absorption and crushing resistance for the adaptation to the design of structures to resist impact loads.

Abstract 12899: A Patient-Specific Fluid-Structure Interaction-Based Approach to Improve Surgical Predictability in Bicuspid Aortic Valve Patients

Introduction: BAV is the most common congenital heart defect affecting ~1.4% of the population. It also brings with it an increased risk of aortopathy, including coarctation, aneurysm, dissection, and accelerated calcification with either stenosis or aortic insufficiency. Quantifying BAV function, altered blood flow, and corresponding hemodynamic forces and their impact on accelerated BAV deterioration improves BAV diagnosis. Predicting how these parameters improve post-interventions may improve surgical predictability and long-term outcome. Methods: A patient-specific modeling protocol based on MRI-based patient data and strongly coupled fluid-structure interaction (FSI) technique was developed to evaluate BAV. Flow via left ventricle, BAV, ascending and descending aorta (Fig A-B) was simulated to obtain biomechanical insights near valve vicinity and study its effects downstream. Diseased anatomy was simulated, and biomechanics compared with virtual interventions that included 1) surgical aortic valve replacement (SAVR), 2) valve sparing root replacement (VSRR) with a sinus graft, and 3) VSRR without sinus graft (Fig C). Results: Our model predictions showed that viscous dissipation (or energy loss) was the greatest in the diseased BAV indicating a high energy loss that substantially reduced post-virtual interventions. Specifically, energy loss reduced by 2.55-, 1.65-, 2.52- folds for SAVR, VSRR-sinus, and VSRR+sinus respectively at peak-systole (Fig. E-H). Interestingly, while SAVR produced the largest orifice area (OA), OA of BAV marginally reduced post VSRR during peak-systole (Fig. I) Conclusions: These studies provide insights into BAV dynamics and may help determine the optimal interventions for a patient. These insights may help improve diagnosis and surgical predictability, optimize treatment, and help with clinical decision making for BAV patients at risk.

Validation of the Reduced Unified Continuum Formulation Against In Vitro 4D-Flow MRI.

We previously introduced and verified the reduced unified continuum formulation for vascular fluid-structure interaction (FSI) against Womersley's deformable wall theory. Our present work seeks to investigate its performance in a patient-specific aortic setting in which assumptions of idealized geometries and velocity profiles are invalid. Specifically, we leveraged 2D magnetic resonance imaging (MRI) and 4D-flow MRI to extract high-resolution anatomical and hemodynamic information from an in vitro flow circuit embedding a compliant 3D-printed aortic phantom. To accurately reflect experimental conditions, we numerically implemented viscoelastic external tissue support, vascular tissue prestressing, and skew boundary conditions enabling in-plane vascular motion at each inlet and outlet. Validation of our formulation is achieved through close quantitative agreement in pressures, lumen area changes, pulse wave velocity, and early systolic velocities, as well as qualitative agreement in late systolic flow structures. Our validated suite of FSI techniques offers a computationally efficient approach for numerical simulation of vascular hemodynamics. This study is among the first to validate a cardiovascular FSI formulation against an in vitro flow circuit involving a compliant vascular phantom of complex patient-specific anatomy.

Fluid–structure interaction approach with smoothed particle hydrodynamics and particle–spring systems

This paper presents a novel three-dimensional fluid–structure interaction (FSI) approach, where the meshless smoothed particle hydrodynamics (SPH) method is used to simulate the motion of incompressible fluid flows, whilst structures are represented by a simplified approach based on particle–spring systems. The proposed FSI technique allows to use independent spatial–temporal resolutions for the fluid and structural computational domains. The particle–spring elastic constants are calibrated and relationships with the mechanical material properties, Young’s modulus and Poisson’s ratio, are determined. Fluid and structure computational domains are separated by interfaces made of triangular elements whose position is updated during the simulation following the structural deformation. The coupling of the two media at the fluid–structure interfaces is handled by the introduction of solid and fluid boundary particles. This approach, automatically and without introducing further complexity, avoids the penetration of fluid particles into the solid domain. The efficiency and accuracy and the present method are validated with analytical/benchmark solutions from the literature.

The Effect of Flow-Induced Vibration on Heat and Mass Transfer Performance of Hollow Fiber Membranes in the Humidification/Dehumidification Process.

Cross-flow hollow fiber membranes are commonly applied in humidification/dehumidification. Hollow fiber membranes vibrate and deform under the impinging force of incoming air and the gravity of liquid in the inner tube. In this study, fiber deformation was caused by the pulsating flow of air. With varied pulsating amplitudes and frequencies, single-fiber deformation was investigated numerically using the fluid–structure interaction technique and verified with experimental data testing with a laser vibrometer. Then, the effect of pulsating amplitude and frequency on heat and mass transfer performance of the hollow fiber membrane was analyzed. The maximum fiber deformation along the airflow direction was far larger than that perpendicular to the flow direction. Compared with the case where the fiber did not vibrate, increasing the pulsation amplitude could strengthen Nu by 14–87%. Flow-induced fiber vibration could raise the heat transfer enhancement index from 13.8% to 80%. The pulsating frequency could also enhance the heat transfer of hollow fiber membranes due to the continuously weakened thermal boundary layer. With the increase in pulsating amplitude or frequency, the Sh number or Em under vibrating conditions can reach about twice its value under non-vibrating conditions.

A novel MRI-based data fusion methodology for efficient, personalised, compliant simulations of aortic haemodynamics

We present a novel, cost-efficient methodology to simulate aortic haemodynamics in a patient-specific, compliant aorta using an MRI data fusion process. Based on a previously-developed Moving Boundary Method, this technique circumvents the high computational cost and numerous structural modelling assumptions required by traditional Fluid-Structure Interaction techniques. Without the need for Computed Tomography (CT) data, the MRI images required to construct the simulation can be obtained during a single imaging session. Black Blood MR Angiography and 2D Cine-MRI data were used to reconstruct the luminal geometry and calibrate wall movement specifically to each region of the aorta. 4D-Flow MRI and non-invasive pressure measurements informed patient-specific inlet and outlet boundary conditions. Luminal area closely matched 2D Cine-MRI measurements with a mean error of less than 4.6% across the cardiac cycle, while physiological pressure and flow distributions were simulated to within 3.3% of patient-specific targets. Moderate agreement with 4D-Flow MRI velocity data was observed. Despite lower peak velocity, an equivalent rigid-wall simulation predicted a mean Time-Averaged Wall Shear Stress (TAWSS) 13% higher than the compliant simulation. The agreement observed between compliant simulation results and MRI data is testament to the accuracy and efficiency of this MRI-based simulation technique.

Innovative computational modal analysis of a marine propeller

It is a fact that specifying numerically the natural frequencies of a marine propeller rotating in a water environment is quite difficult due to the problem that arises from the inability to consider the effect of rotation and pressure distribution in the modal acoustic module of the software. In the present study, an alternative approach to the experimental studies is proposed to come through this problem that enables researchers to predict numerically the change in natural frequency of a three-bladed marine propeller. The method based on the fluid-structure interaction (FSI) technique uses the modal stiffness and the modal mass that is calculated from the numerical analysis of a rotating marine propeller in air and then considers the effects of the added mass by utilizing the frequency reduction ratio (FRR) and finally defines the natural frequencies of the rotating propeller in the water. The simulations revealed that the natural frequencies of the propeller decrease substantially in water due to the added mass and the reduction in the natural frequencies with respect to frequencies in the air is 28% for the first, 34% for the second, and the third. Since natural frequencies of a rotating propeller in water cannot be simulated the equivalent stiffness and masses were defined for each frequency from the analyses of propeller rotating in the air. It was concluded that the natural frequency of the propeller decreases when the propeller is placed in water for the same boundary conditions.