Analytical nonlinear flutter and sensitivity analysis of aircraft wings subjected to a transverse follower force

2018 ◽  
Vol 233 (4) ◽  
pp. 1503-1515 ◽  
Author(s):  
E Zafari ◽  
MM Jalili ◽  
A Mazidi
Keyword(s):  
Sensitivity Analysis ◽  
Analytical Solution ◽  
Structural Model ◽  
Multiple Scales ◽  
Unit Length ◽  
Time History ◽  
Follower Force ◽  
Design Parameters ◽  
Wing Chord ◽  
Flutter Margin

In the present study, the nonlinear aeroelastic and sensitivity analysis of high aspect ratio wings subjected to a transverse follower force are discussed. A nonlinear structural model of wings is extracted and coupled with an incompressible unsteady aerodynamic model. The governing equations of motions are obtained via Hamilton’s principle and Galerkin method. Utilizing the method of multiple-scales, analytical approximate flutter response of the system is obtained. For validation, the analytical solution is compared with numerical solution and good agreement is observed. The time history of the tip displacement and tip twist solution are plotted for different airspeeds. Effects of follower force and its spanwise location and also the wing geometric characteristics on the flutter margin are discussed. Moreover, flutter margin sensitivity to different design parameters is analyzed. Results indicate that increasing the wing chord makes the system unstable. Furthermore, according to the analytical solution, effects of the wing chord and mass per unit length on the flutter margins are more important than the other system parameters.

scholarly journals CONCEPTUAL DESIGN FOR ASSEMBLY IN AEROSPACE INDUSTRY: SENSITIVITY ANALYSIS OF MATHEMATICAL FRAMEWORK AND DESIGN PARAMETERS

2021 ◽  
Vol 1 ◽  
pp. 731-740
Author(s):  
Giovanni Formentini ◽  
Claudio Favi ◽  
Claude Cuiller ◽  
Pierre-Eric Dereux ◽  
Francois Bouissiere ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Conceptual Design ◽  
Design Parameters ◽  
Design For Assembly ◽  
Mathematical Framework ◽  
Commercial Aircraft ◽  
System Architectures ◽  
Complex Engineering ◽  
Aircraft System ◽  
Definition Of

AbstractOne of the most challenging activity in the engineering design process is the definition of a framework (model and parameters) for the characterization of specific processes such as installation and assembly. Aircraft system architectures are complex structures used to understand relation among elements (modules) inside an aircraft and its evaluation is one of the first activity since the conceptual design. The assessment of aircraft architectures, from the assembly perspective, requires parameter identification as well as the definition of the overall analysis framework (i.e., mathematical models, equations).The paper aims at the analysis of a mathematical framework (structure, equations and parameters) developed to assess the fit for assembly performances of aircraft system architectures by the mean of sensitivity analysis (One-Factor-At-Time method). The sensitivity analysis was performed on a complex engineering framework, i.e. the Conceptual Design for Assembly (CDfA) methodology, which is characterized by level, domains and attributes (parameters). A commercial aircraft cabin system was used as a case study to understand the use of different mathematical operators as well as the way to cluster attributes.

Vulnerability-Based Design of Sliding Concave Bearings for the Seismic Isolation of Steel Storage Tanks

2016 ◽  
Author(s):  
Hoang Nam Phan ◽  
Fabrizio Paolacci ◽  
Silvia Alessandri ◽  
Phuong Hoa Hoang
Keyword(s):  
Liquid Steel ◽  
Seismic Isolation ◽  
Failure Modes ◽  
Fragility Curves ◽  
Time History ◽  
Probability Of Failure ◽  
Design Parameters ◽  
Economic Losses ◽  
Storage Tanks ◽  
Isolation System

Liquid steel storage tanks are strategic structures for industrial facilities and have been widely used both in nuclear and non-nuclear power plants. Typical damage to tanks occurred during past earthquakes such as cracking at the bottom plate, elastic or elastoplastic buckling of the tank wall, failure of the ground anchorage system, and sloshing damage around the roof, etc. Due to their potential and substantial economic losses as well as environmental hazards, implementations of seismic isolation and energy dissipation systems have been recently extended to liquid storage tanks. Although the benefits of seismic isolation systems have been well known in reducing seismic demands of tanks; however, these benefits have been rarely investigated in literature in terms of reduction in the probability of failure. In this paper, A vulnerability-based design approach of a sliding concave bearing system for an existing elevated liquid steel storage tank is presented by evaluating the probability of exceeding specific limit states. Firstly, nonlinear time history analyses of a three-dimensional stick model for the examined case study are performed using a set of ground motion records. Fragility curves of different failure modes of the tank are then obtained by the well-known cloud method. In the following, a seismic isolation system based on concave sliding bearings is proposed. The effectiveness of the isolation system in mitigating the seismic response of the tank is investigated by means of fragility curves. Finally, an optimization of design parameters for sliding concave bearings is determined based on the reduction of the tank vulnerability or the probability of failure.

Damage-Involved Structural Pounding in Bridges under Seismic Excitation

2017 ◽  
Vol 754 ◽  
pp. 309-312 ◽  
Author(s):  
Robert Jankowski
Keyword(s):  
Structural Damage ◽  
Structural Model ◽  
Viscoelastic Model ◽  
Time History ◽  
Seismic Wave Propagation ◽  
Seismic Excitation ◽  
Lumped Mass ◽  
Positive Role ◽  
Contact Points ◽  
Elevated Bridge

During severe earthquakes, pounding between adjacent superstructure segments of highway elevated bridges was often observed. It is usually caused by the seismic wave propagation effect and may lead to significant damage. The aim of the present paper is to show the results of the numerical analysis focused on damage-involved pounding between neighbouring decks of an elevated bridge under seismic excitation. The analysis was carried out using a lumped mass structural model with every deck element discretized as a SDOF system. Pounding was simulated by the use of impact elements which become active when contact is detected. The linear viscoelastic model of collision was applied allowing for dissipation of energy due to damage at the contact points of colliding deck elements. The results show that pounding may substantially modify the behaviour of the analysed elevated bridge. It may increase the structural response or play a positive role, and the response depends on pattern of collisions between deck elements. The results also indicate that a number of impacts for a small in-between gap size is large, whereas the value of peak pounding force is low. On the other hand, the pounding force time history for large gap values shows only a few collisions, but the value of peak pounding force is substantially large, what may intensify structural damage.

A Development of the Visco-Elastic Damper for Timber Structure and a Suggestion of the Technological Design Assistance System

2013 ◽  
Vol 778 ◽  
pp. 714-721
Author(s):  
Katsuhiko Kohara ◽  
Takeshi Nomura ◽  
Kazuyoshi Koumoto
Keyword(s):  
Seismic Response ◽  
Elastic Body ◽  
Structural Model ◽  
Time History ◽  
Timber Structure ◽  
Response Analysis ◽  
Frame Design ◽  
Timber Frame ◽  
Loading Tests ◽  
Controlled Structure

Our research team developed a brace type and an angle brace type of the visco-elastic damper on seismic-response controlled structure for timber structure. We performed various dependence evaluations by the materials examination of the styrene olefin-based visco-elastic body which we developed newly. We made a structural model using the performance that loading tests in timber frame. We inspected the validity of the structural model. In addition, we built a technical support system for damper setting by the time history response analysis so that a general design architect was easy to use the damper. We could express dynamics properties of visco-elastic body properties by Voigt model, and the structural model almost accorded with an examination property value. We made a structural model of the whole frame system by Kb of installation rigidity obtained from loading tests in timber frame. Because a design level almost accorded with experimental value, the validity of the frame design on seismic-response controlled structure in consideration of the dependence (distortion, frequency, temperature) of the visco-elastic body was confirmed. This visco-elastic damper on seismic-response controlled structure acquired minister authorization of Ministry of Land, Infrastructure and Transport. In addition, this damper acquired the certification of the Japan Building Disaster Prevention Association.

scholarly journals Parametric and Internal Resonances of an Axially Moving Beam with Time-Dependent Velocity

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Bamadev Sahoo ◽  
L. N. Panda ◽  
G. Pohit
Keyword(s):  
Internal Resonance ◽  
Multiple Scales ◽  
Time History ◽  
Mean Value ◽  
Phase Portraits ◽  
Axially Moving Beam ◽  
Internal Resonances ◽  
Moving Beam ◽  
Axially Moving ◽  
The Stability

The nonlinear vibration of a travelling beam subjected to principal parametric resonance in presence of internal resonance is investigated. The beam velocity is assumed to be comprised of a constant mean value along with a harmonically varying component. The stretching of neutral axis introduces geometric cubic nonlinearity in the equation of motion of the beam. The natural frequency of second mode is approximately three times that of first mode; a three-to-one internal resonance is possible. The method of multiple scales (MMS) is directly applied to the governing nonlinear equations and the associated boundary conditions. The nonlinear steady state response along with the stability and bifurcation of the beam is investigated. The system exhibits pitchfork, Hopf, and saddle node bifurcations under different control parameters. The dynamic solutions in the periodic, quasiperiodic, and chaotic forms are captured with the help of time history, phase portraits, and Poincare maps showing the influence of internal resonance.

Direct Sensitivity Analysis of Spatial Multibody Systems With Joint Friction Using Index-1 Formulation

2021 ◽  
Author(s):  
Adwait Verulkar ◽  
Corina Sandu ◽  
Daniel Dopico ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Multibody Systems ◽  
Friction Model ◽  
Design Parameters ◽  
Adjoint Sensitivity ◽  
Joint Friction ◽  
Multibody Dynamic ◽  
Model Dynamics ◽  
Direct Sensitivity

Abstract Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.

Direct Sensitivity Analysis of Multibody Systems: A Vehicle Dynamics Benchmark

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Alfonso Callejo ◽  
Daniel Dopico
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Automatic Differentiation ◽  
Time Integration ◽  
General Purpose ◽  
Contact Forces ◽  
Design Parameters ◽  
Computational Techniques ◽  
Computationally Efficient ◽  
Integration Algorithm

Algorithms for the sensitivity analysis of multibody systems are quickly maturing as computational and software resources grow. Indeed, the area has made substantial progress since the first academic methods and examples were developed. Today, sensitivity analysis tools aimed at gradient-based design optimization are required to be as computationally efficient and scalable as possible. This paper presents extensive verification of one of the most popular sensitivity analysis techniques, namely the direct differentiation method (DDM). Usage of such method is recommended when the number of design parameters relative to the number of outputs is small and when the time integration algorithm is sensitive to accumulation errors. Verification is hereby accomplished through two radically different computational techniques, namely manual differentiation and automatic differentiation, which are used to compute the necessary partial derivatives. Experiments are conducted on an 18-degree-of-freedom, 366-dependent-coordinate bus model with realistic geometry and tire contact forces, which constitutes an unusually large system within general-purpose sensitivity analysis of multibody systems. The results are in good agreement; the manual technique provides shorter runtimes, whereas the automatic differentiation technique is easier to implement. The presented results highlight the potential of manual and automatic differentiation approaches within general-purpose simulation packages, and the importance of formulation benchmarking.

Design Sensitivity Analysis of Nonlinear Multidisciplinary Multibody Systems in the MIXEDMODELS Platform

2007 ◽  
Author(s):  
Shilpa A. Vaze ◽  
Prakash Krishnaswami ◽  
James DeVault
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
The State ◽  
Design Sensitivity Analysis ◽  
Design Parameters ◽  
State Variables ◽  
Sensitivity Coefficients ◽  
Design Variables

Most state-of-the-art multibody systems are multidisciplinary and encompass a wide range of components from various domains such as electrical, mechanical, hydraulic, pneumatic, etc. The design considerations and design parameters of the system can come from any of these domains or from a combination of these domains. In order to perform analytical design sensitivity analysis on a multidisciplinary system (MDS), we first need a uniform modeling approach for this class of systems to obtain a unified mathematical model of the system. Based on this model, we can derive a unified formulation for design sensitivity analysis. In this paper, we present a modeling and design sensitivity formulation for MDS that has been successfully implemented in the MIXEDMODELS (Multidisciplinary Integrated eXtensible Engine for Driving Metamodeling, Optimization and DEsign of Large-scale Systems) platform. MIXEDMODELS is a unified analysis and design tool for MDS that is based on a procedural, symbolic-numeric architecture. This architecture allows any engineer to add components in his/her domain of expertise to the platform in a modular fashion. The symbolic engine in the MIXEDMODELS platform synthesizes the system governing equations as a unified set of non-linear differential-algebraic equations (DAE’s). These equations can then be differentiated with respect to design to obtain an additional set of DAE’s in the sensitivity coefficients of the system state variables with respect to the system’s design variables. This combined set of DAE’s can be solved numerically to obtain the solution for the state variables and state sensitivity coefficients of the system. Finally, knowing the system performance functions, we can calculate the design sensitivity coefficients of these performance functions by using the values of the state variables and state sensitivity coefficients obtained from the DAE’s. In this work we use the direct differentiation approach for sensitivity analysis, as opposed to the adjoint variable approach, for ease in error control and software implementation. The capabilities and performance of the proposed design sensitivity analysis formulation are demonstrated through a numerical example consisting of an AC rectified DC power supply driving a slider crank mechanism. In this case, the performance functions and design variables come from both electrical and mechanical domains. The results obtained were verified by perturbation analysis, and the method was shown to be very accurate and computationally viable.

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