Nonlinear Fluid-structure Interaction Research Articles

Nonlinear geometric fluid-structure interaction model of multilayered sandwich plates in contact with unbounded or bounded fluid flow

Based on the Kirchhoff-Love theory and von Kármán's geometric nonlinearity, the nonlinear vibration analysis of multilayered sandwich plates under ideal flow is presented. Rectangular plates are considered to be laminated of orthotropic composite layers as upper and lower face sheets as well as a central lightweight core made of functionally graded (FG), anisogrid lattice or metal foam materials. Three coupled equations of motion are reformulated into one decoupled governing equation in terms of transverse deflection (w) using the method of inverse differential operator. For the first time, an impermeability condition is developed that considers the moderately large deflection of the contact surface in order to correct the pressure distribution of fluid flow. Based on the potential flow theory, closed-form expressions of hydrodynamic pressure are obtained for different fluid boundary conditions including infinite depth of fluid, flow bounded by a rigid wall and flow between two identical elastic plates. Then, the Galerkin and multiple-scale perturbation methods are used to obtain closed-form solution of nonlinear natural frequency in terms of maximum vibration amplitude. Finally, case studies are presented to investigate the effects of geometric ratios, boundary condition, material distribution, layup, characteristics of flow and geometric nonlinearity on the response quantities. Findings indicate that the large deformation term in the developed impermeability condition has significant effect on the pressure distribution and its effect is more pronounced for thicker plates with larger mode number in the flow direction. Therefore, the novel nonlinear fluid-structure interaction model should be considered to study flow-induced dynamic behavior of sandwich plates with different boundary conditions. In addition, the snap-through behavior is seen in the nonlinear frequency-upstream speed curves and the incipient points of dynamic instability can vary remarkably with the fluid boundary conditions.

Computational evaluation of flight performance of flapping-wing nano air vehicles using hierarchical coupling of nonlinear dynamic and fluid-structure interaction analyses

This study endeavours to introduce an inventive hierarchical coupling methodology for evaluating the flight capabilities of polymer micromachined flapping-wing nano air vehicles (FWNAVs) using advanced computational tools. Furthermore, our objective is to provide a practical demonstration of FWNAVs in both tethered and airborne scenarios. These dual objectives represent the distinctive and pioneering aspects of this research. Such FWNAVs, which are insect-inspired robots, have a 2.5-dimensional structure. An FWNAV comprises a micro piezoelectric drive system and a pair of micro thin flexible wings. The drive system includes a micro transmission and a piezoelectric bimorph actuator. The flight performance of the designed FWNAV is evaluated using a hierarchical coupling approach, where the whole system is decomposed into a micro wing and a micro piezoelectric drive system. The coupling between these parts is modelled as one-way coupling and that between the micro wings and the surrounding air is modelled as strong coupling. In the one-way coupling analysis, nonlinear structural dynamic analysis is conducted for the micro piezoelectric drive system, where the dynamic response is transmitted to the micro wings via the Dirichlet boundary condition. In the strong coupling analysis, strongly coupled fluid-structure interaction analysis is conducted for the micro wings and the surrounding air to consider their strong coupling. The optimisation of flight performance is conducted using fluid-structure interaction analysis to achieve sufficient lift force to support the weight of an FWNAV. The design of a tethered and flyable FWNAV with a size of 10 mm or smaller is demonstrated. This FWNAV can be easily fabricated using polymer micromachining.

A particle refinement technique with dynamic splitting and coalescing pattern for fluid-structure interaction problem

With the increasing demand of large scale computation, multi-resolution particle methods have been paid much attention by many researchers. In multi-resolution method, high resolution is applied in local area to reduce the whole computational costs and maintain the local accuracy. However, there are still many challenges in the stability and accuracy of multi-resolution particle methods. In this research, an efficient variable particle size (VSP) multi-resolution method, using particle splitting and coalescing techniques, is developed in moving semi-implicit particle (MPS) method. Particles split or coalesce in dynamic five steps to avoid particle overlap and clustering. The mixed splitting mechanism by combining hexagonal splitting pattern and pair splitting pattern are proposed in the five-step splitting algorithm. Pair splitting and coalescing techniques with variable particle size are proposed to strictly ensure the conservation of mass and momentum and avoid particle clustering. To solve the non-linear fluid-structure interaction problem, the VSP algorithm is introduced in MPS-DEM method. The numerical results are compared with the analytical solutions and experimental results. It shows that the proposed VSP algorithm cannot only maintain the local accuracy, but also improve the computational efficiency by avoiding unnecessary chain operations between particle splitting and coalescing.

Control of acoustic scattering of trailing edge flow by distributed compliance

In this paper, an approach for the reduction of trailing edge noise due to flow scattering from a semi-infinite splitter plate is proposed. It utilizes the fluid–structure interactions of well-designed multiple compliant elastic panels to suppress the flow instabilities within the boundary layers over the splitter plate to reduce overall trailing edge noise scattering. The approach is studied numerically using high-fidelity direct aeroacoustic simulation at low Reynolds numbers based on a panel length of 5×104. The noise reduction efficacy of the approach is analyzed by studying two different cases, and their underlying physical mechanisms are explored. First, the boundary layer over one side of the plate is subjected to a weak monochromatic acoustic excitation to produce laminar instabilities. Second, the boundary layer is subjected to a weak broadband excitation within the boundary layer. For each case, the panel system is uniquely designed with thorough consideration of the flow characteristics of the boundary layer instabilities of the problem. Comprehensive aeroacoustic analyses reveal that a significant sound power level reduction of 4.2 and 7.4 dB can be achieved by designed configurations for both kinds of excitation without any drag penalty. Nonlinear fluid–structure interactions of carefully designed elastic panels result in a weak correlation between the near-field flow instabilities and far-field noise. The flow-induced panel structural resonance is proven to effectively absorb the energy of boundary layer instabilities and their scattering at the trailing edge. Key characteristics for the design of compliance systems under different flow conditions are discerned and discussed.

Biomechanics of abdominal aortic aneurysm in the framework of Windkessel effect and fully-developed inflow velocity via two-way non-linear FSI

Abdominal aortic aneurysm (AAA) is a pathological condition characterised by localised dilation of the infrarenal aorta, which can be fatal if rupture occurs. Current diagnostic criteria for repair are not patient-specific, but computational modelling may help to predict the potential growth and risk of AAA rupture accurately. This paper highlights how important using the Windkessel effect and fully-developed inflow velocity framework for the biomechanical analysis of AAA is; in other words, this research investigates how different boundary conditions in modelling methods affect the ability to correctly represent the biomechanics of AAA with complex non-linear parameters using a two-way fluid–structure interaction (FSI) technique. Time-averaged wall shear stress (TAWSS) is highly sensitive to boundary conditions, so unrealistic or simplified boundary conditions can lead to very different TAWSS results. This study also revealed that the use of outflow 3-element Windkessel boundary conditions on pulsatile pressure affects the flow pattern and increases the flow recirculation period. By accounting for the Windkessel effect and preventing backflow in numerical studies of AAA, the maximum displacement found in the distal branches can also be reduced. Models assuming plug velocity profiles overestimate peak wall stress by approximately 20% compared with models using fully developed parabolic inlet velocity profiles. This study incorporated a three-layer anisotropic material model and non-Newtonian fluid properties into the simulation, providing a more realistic representation of the effect of boundary condition selection on AAA mechanics. The results summarised from the parametric study could contribute to better prediction of AAA growth and rupture risk, and have important implications for the development of improved treatment strategies for AAA patients.

The loading on a vertical cylinder in steep and breaking waves on sheared currents using smoothed particle hydrodynamics

Waves and currents coexist in a wide range of natural locations for the deployment of offshore structures and devices. This combined wave–current environment largely determines the loading of vertical surface piercing cylinders, which are the foundations typically used for offshore wind turbines along with many other offshore structures. The smoothed particle hydrodynamics (SPH) code DualSPHysics is used to simulate focused waves on sheared currents and assess subsequent loading on a vertical cylinder. Outputs from another numerical model are used to define the SPH inlet–outlet boundary conditions to generate the wave–current combinations. A modified damping zone is used to damp the waves, but allow the currents to exit the domain. Numerical results are validated against experimental measurements for surface elevation and associated loading on the cylinder. Four phase repeats are used in the SPH model to understand the harmonic structure of the surface elevation at the front face of the cylinder and associated loading. It is shown that the SPH model provides agreement with experimental measurements of harmonic components for both force and elevations. Taking advantage of the SPH method, wave amplitudes were increased up to, and beyond, the breaking threshold highlighting a complex relationship between peak force and wave phase, requiring detailed investigation. The numerical modeling of interactions of steep and breaking waves on sheared currents with the cylinder demonstrates the SPH model's capability for modeling highly nonlinear fluid–structure interaction problems.

Water nanolayer facilitated solitary-wave-like blisters in MoS2 thin films

Solitary waves are unique in nonlinear systems, but their formation and propagation in the nonlinear fluid-structure interactions have yet to be further explored. As a typical nonlinear system, the buckling of solid thin films is fundamentally related to the film-substrate interface that is further vulnerable to environments, especially when fluids exist. In this work, we report an anomalous, solitary-wave-like blister (SWLB) mode of MoS2 thin films in a humid environment. Unlike the most common telephone-cord and web buckling deformation, the SWLB propagates forward like solitary waves that usually appear in fluids and exhibits three-dimensional expansions of the profiles during propagation. In situ mechanical, optical, and topology measurements verify the existence of an interfacial water nanolayer, which facilitates a delamination of films at the front side of the SWLB and a readhesion at the tail side owing to the water nanolayer-induced fluid-structure interaction. Furthermore, the expansion morphologies and process of the SWLB are predicted by our theoretical model based on the energy change of buckle propagation. Our work not only demonstrates the emerging SWLB mode in a solid material but also sheds light on the significance of interfacial water nanolayers to structural deformation and functional applications of thin films.

Numerical study of the splashing wave induced by a seaplane using mesh-based and particle-based methods

In recent years, forest fires and maritime accidents have occurred frequently, which have had a bad impact on human production and life. Thus, the development of seaplanes is an increasingly urgent demand. It is important to study the taxiing process of seaplanes for the development of seaplanes, which is a strong nonlinear fluid-structure interaction problem. In this paper, the smoothed particle hydrodynamics (SPH) method based on the Lagrangian framework is utilized to simulate the taxiing process of seaplanes, and the SPH results are compared with those of the finite volume method (FVM) based on the Eulerian method. The results show that the SPH method can not only give the same accuracy as the FVM but also have a strong ability to capture the splashing waves in the taxiing process, which is quite meaningful for the subsequent study of the effect of a splash on other parts of the seaplane.

Fluid-structure interaction analysis of nonlinear flapping dynamic behaviors of variable stiffness composite laminated plates in viscous flows

This paper is concerned with the development of a numerical model for the analysis of nonlinear fluid–structure interaction problems of large-deformable curvilinear fiber-reinforced composite laminated plates in viscous flows. A higher-order shear deformation zig-zag theory in conjunction with nonlinear von Kármán strains is employed to accommodate the large deformations of variable stiffness composite laminated plates. An implicit partitioned fluid–structure interaction method based on an arbitrary Lagrangian-Eulerian framework is adopted for dealing with the coupling of the large-deformable plate and the viscous flow. The validity of the proposed model and method is confirmed by comparing the computed results of a two-layered plate with those available solutions in the literature. Effects of material properties and fiber paths of composite plates on the periodic limit cycle oscillation and the wake-flow vortices are examined. It is found that symmetrical lay-ups of the constant stiffness composite laminated plates can produce asymmetrical flapping shapes, resulting in asymmetrical hairpin vortex structures in the wake flow. For a variable stiffness composite laminated plate, the flexibility of the leading or trailing sections can be adjusted by the curved fiber path, which in turn leads to changes in the plate flapping shapes.

Nonlinear vibration response of a rectangular sheet under harmonic forced excitation in three-dimensional uniform flow: Influence of excitation amplitudes on frequency response

Thin, flexible plates (sheets) are used in numerous industrial applications. As these sheets are subjected to fluid flow during the manufacturing process, violent vibrations may occur in the sheets owing to external disturbances, which may cause serious damage to the sheets. Thus, it is crucial to clarify the detailed vibration characteristics of the sheet in a fluid flow to avoid or suppress vibrations.In this study, the influence of excitation amplitudes on the frequency response of a sheet was investigated in detail for various flow velocities to gain a deeper understanding of the nonlinear aspect of this problem through both experiments and nonlinear analysis. In the experiments, harmonic displacement excitation was applied at the leading edge of the sheet in a vertical wind tunnel. The influence of the excitation amplitudes on the frequency response was investigated. For the nonlinear analysis, a nonlinear fluid–structure interaction model considering the influence of harmonic displacement excitation was developed to investigate the vibration response.The frequency response curves exhibit softening-type nonlinearity for relatively low flow velocities, whereas frequency response curves exhibit hardening-type nonlinearity for relatively high flow velocities in the experiments. In contrast, the frequency response curves exhibit the softening-type nonlinearity regardless of the flow velocity in the nonlinear calculations based on the potential flow.

Semi-analytical solution of the Reynolds equation considering cavitation

The numerical effort of rotordynamic simulations with hydrodynamic bearings is often dominated by the solution of the Reynolds equation. Because of the nonlinear fluid–structure interaction, this equation needs to be solved in every time step. Although computationally efficient analytical approximations and look-up table techniques exist, these approaches often do not provide the necessary modeling depth and accuracy. Thus, in many cases, numerical methods are preferred despite their computational cost.In recent studies, a semi-analytical solution of the Reynolds equation has been developed based on the scaled boundary finite element method (SBFEM) with the objective of improving the numerical efficiency. The developed approach assumed Gümbel conditions, which means that cavitation was handled in a highly simplified manner. In this work, the SBFEM solution is for the first time combined with a more complex, nonlinear cavitation model based on the Elrod algorithm. Because of the semi-analytical technique, this requires a simplification of the switch function that defines the locations of the pressure and cavitation zones. However, as demonstrated in this paper, the resulting bearing forces are still in good agreement with a standard numerical reference solution based on the finite volume method (FVM). Since the SBFEM model uses only a one-dimensional discretization, its high-order formulation is very straightforward, even in case of a non-equidistant grid with varying shape functions that take the smooth and non-smooth regions of the solution into account. As a result, the numerical effort is reduced significantly in comparison to the standard FVM.

Parametric model order reduction by machine learning for fluid–structure interaction analysis

An improved nonintrusive parametric model order reduction (pMOR) approach is proposed for the flow field interpolation regarding fluid–structure interaction (FSI) objects. Flow field computation using computational fluid dynamics (CFD) requires excessive computational time and memory. Nonintrusive and data-driven MOR schemes have been proposed to overcome such limitations. The present methodology is implemented by both proper orthogonal decomposition (POD) and a modified Nouveau variational autoencoder (mNVAE). POD attempts to reduce the number of degrees of freedom (DOFs) on the precomputed series of the full-order model parametric result. The reduced DOF yields parametrically independent reduced bases and dependent coefficients. Then, mNVAE is employed for the interpolation of POD coefficients, which will be combined with POD modes for parametrically interpolated flow field generation. The present approach is assessed on the benchmark problem of a two-dimensional plunging airfoil and the highly nonlinear FSI phenomenon of the limit cycle oscillation. The comparison was executed against other POD-based generative neural network approaches. The proposed methodology demonstrates applicability on highly nonlinear FSI objects with improved accuracy and efficiency.

The linear-time-invariance notion to the Koopman analysis: The architecture, pedagogical rendering, and fluid–structure association

This work augments a Linear-Time-Invariance (LTI) notion to the Koopman analysis, finding an invariant subspace on which consistent Koopman modes are expanded with fluid mechanics implications. The work also develops the Koopman-LTI architecture—a systematic procedure to associate fluid excitation and structure surface pressure by matching Koopman eigen tuples, establishing fluid–structure correspondences that examine fluid–structure interactions (FSIs) at new angles. The data-driven, modular architecture also exhibits the potential to evolve with advances in Koopman algorithms. A pedagogical prism wake example demonstrated that the Koopman-LTI generated a near-perfect linearization of nonlinear FSI dynamics involving inhomogeneous anisotropic turbulence, with mean and root-mean-squared errors of O−12 and O−9, respectively; the infinite-dimensional Koopman modes were also approximated with O−8 error. The subcritical wake during shear layer transition II was also reduced into only six dominant excitation-response Koopman duplets. The upstream and crosswind walls constitute a dynamically unified interface dominated by only two mechanisms. The downstream wall remains a distinct interface and is dominated by four other mechanisms. The complete revelation of the prism wake comes down to understanding the six mechanisms, which Part II [Li et al., “A parametric and feasibility study for data sampling of the dynamic mode decomposition: Range, resolution, and universal convergence states,” Nonlinear Dyn. 107(4), 3683–3707 (2022)] will address by investigating the physics implications of the duplets' in-synch phenomenological features. Finally, the analysis revealed z-velocity's marginal role in the convection-dominated free-shear flow, Reynolds stresses' spectral description of cascading eddies, wake vortices' sensitivity to dilation and indifference to distortion, and structure responses' origin in vortex activities.

A transfer learning-physics informed neural network (TL-PINN) for vortex-induced vibration

Vortex-induced vibration (VIV) is a typical nonlinear fluid-structure interaction (FSI) phenomenon, which widely exists in practical engineering (such as flexible risers, bridges and aircraft wings). Conventional numerical simulation and data-driven approaches for VIV analysis often suffer from the challenges of computational cost and dataset acquisition. This paper proposed a physics-informed neural network (PINN) enhanced by transfer learning (TL) to study a VIV system (2D). The TL-PINN only used 1/2, 1/4 and 1/8 of the training set (for PINN model) to reconstruct the information of flow field and structure, but with the same prediction accuracy as PINN model. In addition, a stepwise iterative training strategy was proposed to train PINN model. The strategy can effectively reduce the dependence of neural networks on data sets, so as to reduce the training cost of PINN model. The results show that PINN with the stepwise iterative training strategy and TL-PINN can enhance learning efficiency and keep predictability without requiring a huge quantity of datasets. Based on the proposed method, limited and scattered label data from monitoring, numerical and experimental can be fused to realize the reconstruction and prediction of flow field and structure information. It can break the limitation of monitoring equipment and methods in practical projects, and promote the in-depth study of VIV.

Seismic Performance Analysis of the Elevated RC Tanks under Strong Far- and Near-Fault Ground Motions Considering Fluid–Structure Interaction

The elevated reinforced concrete tanks assessed in the current work were the subject of a nonlinear sloshing analysis resulting from fluid–container interactions. The primary response quantity of interest was the height of free surface sloshing. To achieve this aim, the effect of the liquid contents on the seismic behavior of tanks subjected to various sets of far- and near-fault ground motions were measured. The variables considered in this study included bidirectional loading, the earthquake’s frequency content, water sloshing, and the three-dimensional geometry. The primary goal of this work was to analyze these crucial parameters through a parametric analysis using a finite element method considering the influence of nonlinear fluid–structure interactions under the influence of different ground motions. By contrasting the numerical results obtained by previous studies and those of the current investigation, the applicability of the current simulation in seismic analyses of the elevated reinforced concrete tanks was then examined, and significant conclusions were formed. The findings showed that the nonlinearity of sloshing may significantly affect the seismic performance of the liquid–container interactions and that failing to properly account for it may pose a severe threat to these structures’ ability to perform satisfactorily for a particular class of tanks, particularly under the influence of near-fault events.

Machine-learning prediction of aerodynamic damping for buildings and structures undergoing flow-induced vibrations

Aerodynamic damping, as the principal determinant of wind-induced vibrations, bears vast significance in building engineering. This study presents a new modular framework, called the Deep Neural Network-Genetic Algorithm (DNN-GA) architecture, to predict aerodynamic damping directly from surface pressure measurement while serving as one of the earliest references for GA applications in aerodynamic damping predictions. The accurate prediction can give building engineers better insights into potential designs' feasibility at substantially reduced costs, benefiting building design and engineering implementations. The DNN-GA is demonstrated on an aeroelastic tapered prism—a nonlinear bi-directional fluid-structure interaction (FSI) system with solid connections to building design—with synchronous, high-fidelity wind tunnel data for training and prediction. With pressure input, the DNN module predicts tip response as the intermediate product, based on which the GA module optimizes for aerodynamic damping in a fully automated workflow. Results showed that the DNN-GA outperformed six benchmark machine learning algorithms by at least 400%. A comparison between the GA module and the traditional Random Decrement Technique (RDT) showed an accuracy improvement of at least 700%. Finally, the DNN-GA predicted the aerodynamic damping for the Vortex-Induced Vibration (VIV), Galloping, and VIV-Galloping regimes with the maximum root-mean-squared and mean-absolute errors of only 3.874 × 10−3 and 3.053 × 10−3, attesting to the method's excellent accuracy and suitability to complex, nonlinear, and many types FSI vibrations. Given its data-driven nature, the DNN-GA is also applicable to experimental, numerical, and even field data, making it an attractive tool for building engineering applications.

Numerical investigation of the nonlinear interaction between the sinusoidal motion-induced and gust-induced forces acting on bridge decks

With the increasing spans and complex deck shapes, aerodynamic nonlinearity becomes a crucial concern in the design of long-span bridges. This paper investigates the nonlinear interaction between the gust-induced and motion-induced forces acting on bridge decks using the Vortex Particle Method (VPM) as a Computational Fluid Dynamics (CFD) method. This nonlinear interaction is complex and intractable by the conventional linear semi-analytical models that employ the superposition principle. To excite such interaction, a sinusoidally oscillating bridge deck is subjected to sinusoidal vertical gusts. Two distinct aspects are studied: The influence of large-scale sinusoidal vertical gusts on the shear layer of a moving body and the nonlinear dependence of the aerodynamic forces on the effective angle of attack. For the latter, the resultant aerodynamic forces based on a linear semi-analytical and a CFD model are compared for the same effective angle of attack due to sinusoidal gust and motion. The methodology is first employed to verify the linear behavior of a flat plate and then study the nonlinear behavior of two bridge decks. The results show that the linear superposition principle holds for streamlined bridge decks with minimal shear layer instability. However, this principle may not be valid for bluff bridge decks due to strong separation vortices that dictate the shear layer, which induces nonlinearity in the aerodynamic forces manifested through amplitude difference in the first harmonic and emergence of higher-order harmonics. The outcome of this study aims to provide a deeper understanding of the complex nonlinear fluid–structure interaction occurring for bluff bodies subjected to motion and free-stream gusts.

Probabilistic global well-posedness for a viscous nonlinear wave equation modeling fluid–structure interaction

We prove probabilistic well-posedness for a 2D viscous nonlinear wave equation modeling fluid–structure interaction between a 3D incompressible, viscous Stokes flow and nonlinear elastodynamics of a 2D stretched membrane. The focus is on (rough) data, often arising in real-life problems, for which it is known that the deterministic problem is ill-posed. We show that random perturbations of such data give rise almost surely to the existence of a unique solution. More specifically, we prove almost sure global well-posedness for a viscous nonlinear wave equation with the subcritical initial data in the Sobolev space , , which are randomly perturbed using Wiener randomization. This result shows ‘robustness’ of nonlinear fluid–structure interaction problems/models, and provides confidence that even for the ‘rough data’ (data in , ) random perturbations of such data (due to, e.g. randomness in real-life data, numerical discretization, etc.) will almost surely provide a unique solution which depends continuously on the data in the topology.

Development of a fully coupled numerical hydroelasto-plastic approach for offshore structure

Offshore structure encountering large waves could generate structural collapsed accident which is a problem of nonlinear fluid–structure interaction sometimes called hydroelasto-plasticity in which structural nonlinearities involving plasticity and buckling and wave load nonlinearities are generated. A viscous-flow numerical approach is put forward to study the hydroelasto-plastic problem in this paper. The viscous-flow hydroelasto-plastic approach combines CFD(Computational Fluid Dynamics) and nonlinear FEM(Finite Element Method) to realize one-way and two-way coupling. CFD platform uses VOF(Volume of Fluid) to models air-wave two-phase flow to make numerical waves which are compared to theory results, and uses DFBI(Dynamic Fluid–Body Interaction) and overlapping grid to calculate offshore structure motion and wave loads. Nonlinear FEM uses explicit nonlinear dynamic FEM to calculate offshore structural collapse responses considering plasticity and buckling. Radial basis function is used to interpolate wave pressures and structural motion and deformation on common surface of hydrodynamic model and FEM model. The viscous-flow hydroelasto-plastic approach is used to simulate an experiment model. Simulation results from both one-way and two-way coupling approaches are compared with experiments. Comparison shows that the two-way coupling provides a better numerical simulation of the experimental model. This paper proposes the viscous-flow hydroelasto-plastic approach coupling CFD and nonlinear FEM as new numerical means to study the offshore structural collapse problem caused by waves.

On nonlinear free vibration of externally compressible fluid-loaded sandwich cylindrical shells: Curvature nonlinearity in bending and impermeability condition

A nonlinear fluid–structure interaction (FSI) model is presented for nonlinear vibration analysis of sandwich cylindrical shells subjected to an external compressible flow by considering the curvature nonlinearity in impermeability condition and bending. The sandwich shells are made of two face sheets and a central core of advanced materials including functionally graded (FG), metal foam, and anisogrid lattice composite. Based on the Kirchhoff–love hypotheses with the geometric nonlinearities in the normal strain and curvature of mid-surface, one decoupled nonlinear integral–differential equation is obtained for axisymmetric bending vibration of sandwich cylindrical shells. For the first time, the nonlinear impermeability condition is developed in order to take into account the large deformation of thin structures in FSI modeling. In both subsonic and supersonic regimes of steady irrotational compressible flow, a closed-form expression for nonlinear pressure distribution is presented according to the conservation of mass and generalized Bernoulli equation of extended potential theory. Using the Galerkin’s method in conjunction with the multiple-scale perturbation technique, the decoupled equation is solved to obtain nonlinear frequency and time–history response. Finally, parametric studies are carried out to investigate the effects of geometric ratios, boundary conditions, fluid specifications, and material variation on the responses of sandwich shells with different layups such as [Al; FG core; ZrO2], [Al; foam core; ZrO2], [Al; lattice core; Al]. Significant differences in pressure variation due to curvature nonlinearity are observed for short shells with larger vibration amplitude and larger number of half-waves in the axial direction. Therefore, the linear vibration analysis is inadequate for analyzing short sandwich cylindrical shells surrounded by an external fluid flow especially in the case of movable ends.