Continuum Aeroelastic Model for Inviscid Subsonic Bending-Torsion Wing Flutter

A full continuum aeroelastic model for bending-torsion dynamics of a slender high-aspect-ratio wing in inviscid subsonic airflow is developed avoiding finite element or Padé approximations. The structure model is the classical cantilever model of Goland. The aerodynamics is simplified to the two-dimensional typical section theory. Stability is discussed in the Laplace domain leading to the calculation of the aeroelastic modes, the stability curve, and a precise definition of flutter speed, as well as an explicit formula for divergence speed. The flutter speed is shown to be monotonic decreasing as M increases for small k (normalized complex frequency); if a mode flutters at M = 0 then it flutters for every M>0 excepting M = 1. A time-domain state space model is developed requiring the language of abstract functional analysis in the form of a “convolution-evolution” equation in a Hilbert space. The time domain model for M = 0 differs radically from 0相似文献   

Flutter Phenomenon in Aeroelasticity and Its Mathematical Analysis

The present paper is the last part of a three-part survey paper, in which I give a review of several research directions in the area of mathematical analysis of flutter phenomenon. Flutter is known as a structural dynamical instability, which occurs in a solid elastic structure interacting with a flow of gas or fluid and consists of violent vibrations of the structure with rapidly increasing amplitudes. The focus of this paper is a collection of models of fluid-structure interaction, for which precise mathematical formulations are available. My main interest is in the analytical results on such models: the results that can be used to explain flutter and its qualitative and even quantitative treatments. This study does not pretend to be a comprehensive review of an enormous engineering literature on analytical, computational, and experimental aspects of the flutter problem. I present a brief exposition of the results obtained in several selected papers or groups of papers. In this paper, I concentrate on the most well-known cases of flutter, i.e., flutter in aeroelasticity. Namely, I discuss aircraft flutter in historical retrospective and outline some future directions of flutter analysis. The last two sections of the paper are devoted to the precise analytical results obtained in my several recent works on a specific aircraft wing model in a subsonic, inviscid, incompressible airflow. I also mention that in the previous papers (Parts I and II of the survey), I discuss such topics as: (1) bending–torsion vibrations of coupled beams; (2) flutter in transmission lines; (3) flutter in rotating blades; (4) flutter in hard disk drives; (5) flutter in suspension bridges; and (6) flutter of blood vessel walls.     

Flutter of an Arch Bridge via a Fully Nonlinear Continuum Formulation

A fully nonlinear parametric model for wind-excited arch bridges is proposed to carry out the flutter analysis of Ponte della Musica under construction in Rome. Within the context of an exact kinematic formulation, all of the deformation modes are considered (extensional, shear, torsional, in-plane, and out-of-plane bending modes) both in the deck and supporting arches. The nonlinear equations of motion are obtained via a total Lagrangian formulation while linearly elastic constitutive equations are adopted for all structural members. The parametric nonlinear model is employed to investigate the bridge limit states appearing either as a divergence bifurcation (limit point obtained by path following the response under an increasing multiplier of the vertical accidental loads) or as a Hopf bifurcation of a suitable eigenvalue problem (where the bifurcation parameter is the wind speed). The eigenvalue problem ensues from the governing equations of motion linearized about the in-service prestressed bridge configuration under the dead loads and wind-induced forces. The latter are expressed in terms of the aeroelastic derivatives evaluated through wind-tunnel tests conducted on a sectional model of the bridge. The results of the aeroelastic analysis—flutter speed and critical flutter mode shape—show a high sensitivity of the flutter condition with respect to the level of prestress and the bridge structural damping.     

Adaptive Control of Aircraft Wing Flutter by Stress-Induced Stiffness Modification

Lightweight unoccupied air vehicles (UAVs) with wide wingspans are especially vulnerable to dynamic instability. Such instability can be contained by using mass and stiffness balancing and the shape and attitude of the aircraft in flight. Passive methods and pilot-operated devices such as dampers, ailerons, flaps, and other actuators, are currently used. Also, ongoing attempts exist to develop self-adaptive controls by using piezoelectric and other devices. The present work is concerned with controlling aerodynamic flutter by using stress-induced elements in selected structural components of the aircraft wing. A scheme has been developed to determine the “optimal” locations for such elements to be activated, in real time, to contain the dynamic instability or flutter condition. Various stress-induced stiffening schemes have been developed to modify the frequency response of aircraft wings by shifting the critical flutter speed to safe levels. Results and conclusions include the identification of the optimal location and type of the stress-induced elements and the magnitude and distribution of induced stress for best results with the least expense of energy during actuation.     

Possio Integral Equation of Aeroelasticity Theory

This paper presents a new abstract function space formulation of the subsonic small disturbance potential field equations of aeroelasticity and an operator theoretic treatment of the Possio integral equation in the generality of the Laplace transform variable λ. A key result is the new form of the kernel—which is shown to be analytic in the whole plane, excepting the negative real axis—using an existence and uniqueness theorem is proved valid for small ∣λ∣. The main new feature is the use of spatial Lp-Lq Fourier transforms for 1相似文献   

Mathematical Modeling and Analysis of Flutter in Bending-Torsion Coupled Beams, Rotating Blades, and Hard Disk Drives

In this study I present a review of several research directions in the area of mathematical analysis of flutter phenomenon. Flutter is known as a structural dynamical instability that occurs in a solid elastic structure interacting with a flow of gas or fluid, and consists of violent vibrations of the structure with rapidly increasing amplitudes. The focus of this review is a collection of models of fluid-structure interaction, for which precise mathematical formulations are available. The main objects of interest are analytical results on such models, which can be used for flutter explanation, its qualitative and even quantitative treatments. This paper does not pretend to be a comprehensive review of the enormous amount of engineering literature on analytical, computational, and experimental aspects of the flutter problem. I present a brief exposition of the results obtained in several selected papers or groups of papers on the following topics: (1) bending-torsion vibrations of coupled beams; (2) flutter in transmission lines; (3) flutter in rotating blades; (4) flutter in hard disk drives; (5) flutter in suspension bridges; and (6) flutter of blood vessel walls. Finally, I concentrate on the most well-known case of flutter, i.e., flutter in aeroelasticity. The last two sections of this review are devoted to the precise analytical results obtained in my several recent papers on a specific aircraft wing model in a subsonic, inviscid, incompressible airflow.     

Study of Passive Deck-Flaps Flutter Control System on Full Bridge Model. I: Theory

A passive aerodynamic control method for suppression of the wind-induced instabilities of a very long span bridge is presented in this paper. The control system consists of additional control flaps attached to the edges of the bridge deck. Control flap rotations are governed by prestressed springs and additional cables spanned between the control flaps and an auxiliary transverse beam supported by the main cables of the bridge. The rotational movement of the flaps is used to modify the aerodynamic forces acting on the deck and provides aerodynamic forces on the flaps used to stabilize the bridge. A time-domain formulation of self-excited forces for the whole three-dimensional suspension bridge model is obtained through a rational function approximation of the generalized Theodorsen function and implemented in the FEM formulation. This paper lays the theoretical groundwork for the one that follows.     

Modified Kostiakov Infiltration Function: Accounting for Initial and Boundary Conditions

The effect of specific initial and boundary conditions is generally not considered when applying the Kostiakov infiltration functions. A methodology is developed to account for changes in water levels and initial soil moisture. First, Richards’ equation is solved numerically to generate a database of one-dimensional infiltration values, with varying initial (water content or pressure head) and boundary (ponding depth) conditions for three contrasting soils. These are then used to calibrate corresponding coefficients for modified Kostiakov models and, by considering linear regressions, to obtain simple correction factors. Results show that the correction factors are not universally valid, and only the correction to the Kostiakov k parameter shows statistically consistent applicability. However, examples demonstrate potentially significant improvement in the accuracy of irrigation models by correcting the Kostiakov equation to account for initial and boundary conditions.     

Three-Dimensional Electromechanical Impedance Model. II: Damage Analysis and PZT Characterization

Piezoceramic transducers (PZTs) are extensively used in the nondestructive evaluation of damages in various engineering structures. This paper, the second of a two-part paper, focuses on the application of a PZT using three-dimensional (3D) directional sum impedance (DSI). The semianalytical 3D admittance has been formulated and experimentally validated in the first paper. This part deals with the application of the 3D DSI model in damage analysis where by damages were numerically simulated for various types of specimens and the DSI admittance signatures were predicted and compared. The deviations of the signature from that of the undamaged state provide an indicator for the health of the structure. This technique is nondestructive in nature, and the damages were quantified using root-mean-square deviation in signatures with respect to the undamaged state signature. In Part I, the properties of the PZT and their influences on admittance signatures were briefly presented. In this part, a thorough investigation was made and the importance of all the PZT properties in damage analysis was presented.     

Exact Discontinuous Solutions of Exner’s Bed Evolution Model: Simple Theory for Sediment Bores

Determining the evolution of the bed of a river or channel due to the transport of sediment was first examined in a theoretical context by Exner in 1925. In his work, Exner presents a simplified bed evolution model derived from the conservation of fluid mass and an “erosion” equation that is commonly referred to as the sediment continuity or Exner equation. Given that Exner’s model takes the form of a nonlinear hyperbolic equation, one expects, depending on the given initial condition of the bed, the formation of discontinuities in the solution in finite time. The analytical solution provided by Exner for his model is the so-called classical or genuine solution of the initial-value problem, which is valid while the solution is continuous. In this paper, using the general theory of nonlinear hyperbolic equations, we consider generalized solutions of Exner’s classic bed evolution model thereby developing a simple theory for the formation and propagation of discontinuities in the bed or so-called sediment bores.     

Multiple Linear Regression Model Approach for Aerosol Dispersion in Ventilated Spaces Using Computational Fluid Dynamics and Dimensional Analysis

Aerosol dispersion in living spaces especially bioaerosols, due to accidents or deliberate acts, is of significant current interest. Computational fluid dynamics (CFD) provides an accurate and detailed platform to study the influence of different parameters on aerosol distribution in indoor spaces. The simulations however are time consuming and site-specific. The work here introduces an approach toward addressing this challenge. During emergencies, an accurate, quicker, and more general model is required to give rapid answers to first responders. Significant parameters influencing aerosol behavior in an office room were identified and through dimensional analysis, nine dimensionless groups were developed. Fractional factorial design was used to build sixteen scenarios to explore the design space. These scenarios were then simulated using a comprehensive CFD model. Large eddy simulation with the Smagorinsky subgrid scale model was applied to compute the airflow. Aerosols were modeled as a dispersed solid phase using the Lagrangian treatment. The influence of the dimensionless groups on the temporal variation of the number of aerosols in the room and the spatial distribution of the particles in the room was analyzed. The results showed that all the identified dimensionless groups were significant. Multiple linear regression models were developed for the prediction of the number of aerosols in the room and their spatial distribution as a function of the significant parameters influencing aerosol transport. The linear models accurately predicted the data on which they were based but did not predict the results of the independent tests as well. The limited predictive ability of the model showed that the relationships between the dimensionless groups are nonlinear and a higher level of experimental design will have to be applied to better explore the design space.     

Version and Configuration Model for Structural Design Objects: Design and Implementation

This paper presents the design and implementation of a version and configuration model (VCM) for structural design objects. The VCM is developed to capture the incremental, evolutionary, multipath and iterative nature of the structural design process. Specifically, this model: (1) defines representational frameworks for representing the versions and configurations of design objects; (2) suggests sets of manipulation operations for creating and tracking the versions and configurations of design objects across the different representational frameworks; and (3) presents a prototype implementation scheme of a version manager, that is based on the representational frameworks and the manipulation operations of the proposed VCM. A case study of reinforced concrete T-beam is presented together with its prototype implementation using Object Pascal as a proof of concept. This is to describe the elements of the model, validate its effectiveness and demonstrate its viability. It is concluded that the VCM and its implementation is a valuable and necessary ingredient for developing a truly integrated structural engineering design system.     

Global and Local Nonlinear System Responses under Narrowband Random Excitations. II: Prediction, Simulation, and Comparison

The response behavior of the single-degree-of-freedom (SDOF) nonlinear structural system subjected to narrowband stochastic excitations studied in Part I is investigated via simulations to verify the stochastic system characteristics assumed in the development of the semianalytical method. In addition, to demonstrate the accuracy of the method, predicted response–amplitude probability distributions are presented and compared to simulation results. Numerical simulations are conducted by directly integrating the SDOF system with the narrowband excitation modeled by the 1971 Shinozuka formulation. It is observed that the proposed semianalytical method is capable of accurately characterizing the stochastic response behavior of the nonlinear system by predicting the response–amplitude probability distribution and capturing the trends of variations in the response–amplitude statistical properties. In both the primary and the subharmonic resonance regions, good agreements between the response–amplitude probability distributions predicted by the semianalytical method and obtained from simulation results are observed both qualitatively and quantitatively. In addition, trends of the variations in the probability masses associated with the modes with variations in excitation parameters (bandwidth and variance) are captured.     

Applying MODFLOW Model for Drainage Problem Solution: A Case Study from Jahir Irrigated Fields, Israel

High water table and soil salinization processes are common in irrigated fields in Israel. Subsurface drainage systems are a common technique to solve soil salinity problems. Subsurface drainage models can contribute to the efficiency of the drainage system as it can assist in the selection of the proper drainage system and its proper placement in the field. In this study we used the MODFLOW groundwater flow model to simulate groundwater levels in Jahir irrigated fields, the Jordan Valley, Israel. Using a three-layer groundwater flow model, the most efficient drainage system was found to be a combination of deep drains with relief wells and a pump placed in the area with soil salinity problem and upward hydraulic pressure. It was found that simulated drainage system can yield nearly 200,000?m3 of water per year. Given certain information, a spatially distributed groundwater flow model such as MODFLOW can provide more reliable information than different analytical solutions for planning of an effective subsurface drainage system.     

3D Unsteady RANS Modeling of Complex Hydraulic Engineering Flows. II: Model Validation and Flow Physics

A chimera overset grid flow solver is developed for solving the unsteady Reynolds-averaged Navier-Stokes (RANS) equations in arbitrarily complex, multiconnected domains. The details of the numerical method were presented in Part I of this paper. In this work, the method is validated and applied to investigate the physics of flow past a real-life bridge foundation mounted on a fixed flat bed. It is shown that the numerical model can reproduce large-scale unsteady vortices that contain a significant portion of the total turbulence kinetic energy. These coherent motions cannot be captured in previous steady three-dimensional (3D) models. To validate the importance of the unsteady motions, experiments are conducted in the Georgia Institute of Technology scour flume facility. The measured mean velocity and turbulence kinetic energy profiles are compared with the numerical simulation results and are shown to be in good agreement with the numerical simulations. A series of numerical tests is carried out to examine the sensitivity of the solutions to grid refinement and investigate the effect of inflow and far-field boundary conditions. As further validation of the numerical results, the sensitivity of the turbulence kinetic energy profiles on either side of the complex pier bent to a slight asymmetry of the approach flow observed in the experiments is reproduced by the numerical model. In addition, the computed flat-bed flow characteristics are analyzed in comparison with the scour patterns observed in the laboratory to identify key flow features responsible for the initiation of scour. Regions of maximum shear velocity are shown to correspond to maximum scour depths in the shear zone to either side of the upstream pier, but numerical values of vertical velocity are found to be very important in explaining scour and deposition patterns immediately upstream and downstream of the pier bent.     

Fluid-Induced Seismicity: Theory, Modeling, and Applications

Operations including borehole fluid injections are typical for exploration and development of hydrocarbon or geothermic reservoirs. Microseismicity occurring during such operations has a large potential for understanding physics of the seismogenic process as well as in obtaining detailed information about reservoirs at locations as far as several kilometers from boreholes. We propose that the phenomenon of microseismicity triggering by borehole fluid injections is related to the process of the Frenkel–Biot slow wave propagation. In the low-frequency range (hours or days of fluid injection durations) this process reduces to the pore-pressure diffusion. We search for diffusion-related features of induced microseismicity. Two types of such signatures are considered. The first one is related to the geometry of microseismic clouds. Another type of signature is related to the probability of microearthquakes. On this basis we introduce a concept for interpretation of microseismic data which provides a possibility to infer information about hydraulic properties of rocks. Such information can be of significant importance for industrial applications and for understanding physical properties of geological structures.     

Setting Up a Numerical Model of a DAF Tank: Turbulence, Geometry, and Bubble Size

This paper discusses the modeling framework and identifies a number of parameters relevant when setting up a computational fluid dynamics simulation of a dissolved air flotation (DAF) tank. The selection of a turbulence model, the choice between performing two-dimensional (2D) or three-dimensional (3D) simulations, the effects of the design of the flow geometry and the influence of the size of the air bubbles are addressed in the paper. The two-phase flow of air and water is solved in the Eulerian-Lagrangian frame of reference. The realizable k-ε model with nonequilibrium wall functions is suggested as a compromise between a need to effectively resolve the flow and the cost of the simulations. There is a discussion on the conditions for which the steady-state simulations are appropriate. We demonstrate that a steady 2D model can simulate a stratified flow pattern. Our results show that 2D models require adjustments in geometry (e.g., substitution of the outlet pipes to an outlet distributed over the total width of the tank) and in the parameters governing the flow in order to account for the true 3D nature of some of the flow patterns. In addition, we show that the bubble size has a larger influence on the flow in the separation zone than in the contact zone.     

Two-Dimensional Simulation Model for Contour Basin Layouts in Southeast Australia. II: Irregular Shape and Multiple Basins

The development of a two-dimensional simulation model for single regular shape (rectangular) contour basin irrigation layout in southeast Australia is reported in a companion paper. Contour basin layouts as used in Southeast Australia are often irregular in shape and laid out as multiple basin systems. Irrigation of these basins is carried out sequentially involving back flow to the supply channel and inter-basin flow. This paper presents the extension of the earlier model to incorporate irregular shape basins and multiple basin operation. The governing equation is solved by adopting a “split-operator approach” using the method of characteristics coupled with two-dimensional Taylor series expansion for interpolation and calculation of diffusion terms. The numerical solution scheme is based on a grid of quadrilaterals for spatial discretization, to provide geometric flexibility. Infiltration is computed using either the empirical Kostiakov–Lewis equation or the quasianalytical Parlange equation. The model was validated against field data collected from irrigation events monitored on a commercial laser leveled contour layout consisting of five basins.     

Simulation Model for Level Furrows. II: Description, Validation, and Application

In a companion paper, experimental evidence was elaborated to confirm that in particular circumstances the performance of level-furrow irrigation can exceed that of level-basin irrigation. The application of a single furrow simulation model to an irrigation event in a level-furrow field resulted in large estimation errors. To overcome them, the development and validation of a numerical model of level-furrow irrigation is reported in this work. The model is based on the interconnection of a number of one-dimensional channels. The individual channels are connected using confluence or bifurcation points. Furrow infiltration is modelled through a Kostiakov infiltration equation including the furrow discharge as an independent variable. The proposed model is validated using the experimental level furrow evaluation presented in the companion paper. Finally, the model is applied to explore the conditions in which level furrow irrigation can outperform level basin irrigation. The proposed model stands as a valuable tool in the design and management of level furrow irrigation systems.     

Microplane Model M5 with Kinematic and Static Constraints for Concrete Fracture and Anelasticity. I: Theory

Presented is a new microplane model for concrete, labeled M5, which improves the representation of tensile cohesive fracture by eliminating spurious excessive lateral strains and stress locking for far postpeak tensile strains. To achieve improvement, a kinematically constrained microplane system simulating hardening nonlinear behavior (nearly identical to previous Model M4 stripped of tensile softening) is coupled in series with a statically constrained microplane system simulating solely the cohesive tensile fracture. This coupling is made possible by developing a new iterative algorithm and by proving the conditions of its convergence. The special aspect of this algorithm (contrasting with the classical return mapping algorithm for hardening plasticity) is that the cohesive softening stiffness matrix (which is not positive definite) is used as the predictor and the hardening stiffness matrix as the corrector. The softening cohesive stiffness for fracturing is related to the fracture energy of concrete and the effective crack spacing. The postpeak softening slopes on the microplanes can be adjusted according to the element size in the sense of the crack band model. Finally, an incremental thermodynamic potential for the coupling of statically and kinematically constrained microplane systems is formulated. The data fitting and experimental calibration for tensile strain softening are relegated to a subsequent paper in this issue, while all the nonlinear triaxial response in compression remains the same as for Model M4.