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nonlinear structural DYNAMIC ANALYSIS USING A MODIFIED MODAL METHOD

AIAA JOURNAL 1985年第10期23卷 1594-1601页

作者： KNIGHT, NF NASA Langley Research Center Hampton Virginia

A procedure for predicting the nonlinear dynamic response of structural components subjected to a step loading is presented. The procedure is a modified modal method that involves a change of dependent variables from the unknown nodal degrees of freedom of the finite element model of the structure to a smaller set of generalized coordinates. This change of dependent variables uses a combination of the nonlinear static solution and some selected vibration mode shapes. The vibration mode shapes correspond to the eigenvectors obtained by solving a standard free vibration eigenvalue problem wherein the stiffness matrix is expanded about the nonlinear static solution. A strategy is also presented for determining which and how many vibration mode shapes to include in the transformation. The effect of inaccurate representation of the spatial distribution of the applied load on the nonlinear dynamic response is discussed for two classes of structural behavior. Application of the procedure to structures that exhibit a stiffening behavior and to those with a softening behavior is presented. © 1985 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： structural Dynamic Analysis Elastic Modulus Finite Element Modeling nonlinear structural dynamics Spherical Shell Transient Response Free Vibrations Integration Algorithm Numerical Integration nonlinear dynamics

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Parameterized Fictitious Mode of Morphing Wing with Bilinear Hinge Stiffness

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AIAA JOURNAL 2021年第7期59卷 2641-2656页

作者： Huang, Rui Zhou, Xinghua Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Mech Struct Inst Vibrat Engn Res Nanjing 210016 Peoples R China

As a typical morphing wing, a folding wing with structural nonlinearities may encounter complex nonlinear aeroelastic effects during the in-flight morphing process. This paper presents a novel parameterized modeling methodology for efficient modal and nonlinear aeroelastic analysis of a folding wing with bilinear hinge stiffness and the variation of the folding angle. The most attractive feature of the present modeling methodology is that the nonlinear structural dynamics of the folding wing at different folding angles can be efficiently represented via a parameterized fictitious mode. To demonstrate the accuracy of the present method in representing the nonlinear dynamics of the morphing wing, a folding wing with bilinear stiffness in both fuselage-inboard and inboard-outboard hinges was selected as a numerical example. The nonlinear dynamic model of the selected example can be divided into nine subsystems according to different combinations of fuselage-inboard and inboard-outboard hinge stiffness. This paper focuses on the efficient investigation of structural modes, flutter stability, and nonlinear aeroelastic behaviors of the folding wing at the complete morphing parameter space. Besides, the numerical results computed via the present parameterized fictitious mode method were also compared with the direct commercial software. The comparison shows that the nonlinear dynamics of the morphing wing with bilinear hinge stiffness can be investigated efficiently via the present parameterized modeling method.

关键词： Aircraft Wings structural Element Folding Wing nonlinear Aeroelastic Systems Fuselages nonlinear structural dynamics nonlinear dynamics structural nonlinearities structural Finite Elements Aerodynamic Configurations

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Improved nonlinear Analysis of a Propeller Blade Based on Hyper-Reduction

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AIAA JOURNAL 2022年第3期60卷 1909-1922页

作者： Kim, Yongse Kang, Seung-Hoon Cho, Haeseong Shin, SangJoon Seoul Natl Univ Active Aeroelastic & Rotorcraft Lab Sch Mech & Aerosp Engn Seoul 08826 South Korea Seoul Natl Univ Dept Aerosp Engn 1 Gwanak Ro Seoul 08826 South Korea Jeonbuk Natl Univ Dept Aerosp Engn Future Air Mobil Res Ctr 567 Baekje Daero Jeonju 54896 Jeollabuk Do South Korea Seoul Natl Univ Dept Mech & Aerosp Engn Inst Adv Aerosp Technol 1 Gwanak Ro Seoul 08826 South Korea

In this study, an improved nonlinear-analysis framework capable of predicting geometric nonlinearity and high-speed rotation in rotating structures was developed. A nonlinear time-transient simulation requires large computations owing to an iterative solution algorithm. To reduce the anticipated computational cost, a proper orthogonal decomposition (POD)-based reduced-order modeling (ROM) combined with hyper-reduction is applied. To efficiently perform computations during the online stage, three hyper-reduction techniques were employed to approximate the nonlinear finite-element matrices: discrete empirical interpolation method (DEIM), Gauss-Newton with approximated tensors (GNAT), and energy-conserving sampling and weighting (ECSW). The present frameworks are applied to the time-transient simulation of a propeller, including parametric variations. Compared with the DEIM method, the GNAT and ECSW methods exhibited better enhancement of the accuracy and robustness of the reduced-order representation. Additionally, the computational efficiency of the ECSW method was improved significantly compared with that of other POD-based ROM approaches.

关键词： Propeller Blades Numerical Stability Finite Element Formulation Resonant Frequencies Singular Value Decomposition nonlinear structural dynamics High Aspect Ratio ANSYS Fluid Structure Interaction Computational Fluid dynamics

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A coupled approach to model wear effect on shrouded bladed disk dynamics

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INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES 2023年 237卷

作者： Tamatam, Lakshminarayana Reddy Botto, Daniele Zucca, Stefano Politecn Torino Dept Mech & Aerosp Engn Corso Duca Abruzzi 24 I-10129 Turin Italy

This paper deals with modelling the effect of wear on the dynamics of the shrouded bladed disk with frictional contacts at the shrouds and the contact interface evolution. Prediction of fretting wear commonly occurring at the contacts of turbomachinery components, and its impact on the dynamics is increasingly researched due to the components subjected to their structural limits for performance and operating at high loading conditions. Over a lifetime, the fretting wear at these contacts could alter the global dynamic response of these bladed disks from the designed operating point and could lead to high vibration amplitudes. This study implements a coupled static/dynamic harmonic balance method (HBM) with wear energy approach and an adaptive wear logic to study the impact on the steady-state nonlinear dynamic response. Firstly, the methodology is applied to a cantilever beam with a contact patch and then to a shrouded bladed disk with shroud contacts using cyclic symmetry boundary conditions. The novelty of the paper is to show the effect of wear on the dynamics with the changing contact pre-load using a coupled approach. A wear acceleration parameter v(w,max) is defined, and the impact of the choice of this parameter is discussed in detail on the computation time and the accuracy of results. The test cases demonstrate the impact of wear on the dynamic nonlinear response curves and the contact interface evolution for various scenarios.

关键词： nonlinear structural dynamics Contact evolution Contact pre-load Fretting wear Harmonic balance method

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A Comparative Study of Two Families of Higher-Order Accurate Time Integration Algorithms

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INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS 2020年第8期17卷

作者： Kim, Wooram Lee, Jin Ho Korea Army Acad Yeongcheon Dept Mech Engn Yeongcheonsi 38900 Cyeongsangbukdo South Korea

Two families of higher-order accurate time integration algorithms are numerically tested by using various nonlinear problems of structural dynamics, and the numerical results obtained from them are compared. To be specific, the higher-order algorithms of Kim and Reddy and the higher-order algorithms of Fung are used for this study. In linear analyses, these two different families of higher-order algorithms do not present noticeable differences. However, performances of these algorithms are quite different when they are applied to various nonlinear dynamic problems. For the numerical tests, well-known nonlinear problems are selected from the past studies. For the completeness, the two families of algorithms are briefly reviewed, and their advantageous computational structures are also explained.

关键词： nonlinear structural dynamics implicit higher-order accurate time integration method weighted residual method differential quadrature method long term analysis Gauss-Lobbato quadrature

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A reduced order model for nonlinear time history seismic analyzes of elasto-plastic 3D frame structures

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EARTHQUAKE ENGINEERING & structural dynamics 2022年第9期51卷 2055-2076页

作者： Magisano, Domenico Corrado, Antonella Madeo, Antonio Garcea, Giovanni Univ Calabria Dipartimento Ingn Informat Modellist Elettron & S I-87036 Cosenza Italy

A reduced order model for the nonlinear dynamic seismic analysis of elasto-plastic 3D frame structures is presented. It is based on an approximated solution space for the displacement field that is assumed as the sum of two subspaces. The first subspace is generated by the relevant linear elastic modes of the generalized stiffness/mass linear eigenvalue problem in terms of participation factor. The second one is defined by collapse mechanisms associated to appropriate static load distributions. The time history analyzes are carried out within the reduced solution space, while the internal forces are evaluated on the full model to guarantee an accurate description of the constitutive laws. The proposed reduction method was tested for different structural geometries varying frequency content, direction and amplitude of the ground motion. Numerical results show accuracy and robustness also employing a few tens of modes, including elastic modes and plastic collapse mechanisms. In particular, the need for plastic modes in capturing the structural dynamics in case of seismic actions leading to significant plastic excursions is emphasized. This highlights the limits of simplified approaches based on the hypothesis of shape conservation in nonlinear problems, regardless of the building regularity.

关键词： 3D frame structures earthquake engineering nonlinear time history analysis nonlinear structural dynamics plasticity reduced order modeling

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Aeroelastic Analysis of a Composite Material Delta Wing in Low Subsonic Flow

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AIAA JOURNAL 2012年第1期50卷 162-175页

作者： Sapkal, Kedar S. Attar, Peter J. Univ Oklahoma Dept Aerosp & Mech Engn Norman OK 73019 USA

An experimental and computational study of the flutter and limit cycle oscillations of a three-layer carbon-fiber composite material 45 deg delta wing is presented. The computational aeroelastic model uses a set of nonlinear structural dynamics (modal) equations that are coupled to a vortex-lattice aerodynamic model. The nonlinear modal equations for the structure are formulated using a system identification methodology. To reduce the computational time needed in the computation of the strain energy needed to construct the reduced-order structural dynamics model, a new algorithm that uses a Smolyak sparse-grid technique is proposed to perform the sampling of strain energy data used for generation of the equations of motion. Experiments and computations are performed, and compared, for a number of layup configuration angles. The qualitative agreement between experimental flutter and limit cycle results is good, with both sets of results displaying similar trends with respect to variations in layup angle and a nondimensional parameter, which gives a measure of the bending torsion coupling in the laminate.

关键词： Laminated Composites Aeroelastic Stability Aircraft Wings Supersonic Flow nonlinear structural dynamics Vortex Rings System Identification Flow Velocity structural Finite Elements Low Speed Wind Tunnel

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EXPERIMENTAL OBSERVATION OF nonlinear VIBRATIONS USING A CLOSED-LOOP VIBRATION SYSTEM

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METROLOGY AND MEASUREMENT SYSTEMS 2015年第4期22卷 559-564页

作者： de Barros, Everaldo Souto, Carlos d'Andrade Mathias, Mauro Hugo Inst Aeronaut & Space BR-12228904 Sao Jose Dos Campos SP Brazil Univ Estadual Paulista BR-12516410 Guaratingueta SP Brazil

This paper presents experimental observation of nonlinear vibrations in the response of a flexible cantilever beam to transverse harmonic base excitations around its flexural mode frequencies. In the experimental setup, instead of manual control of the signal excitation frequency and amplitude, a closed-loop vibration system is used to keep the excitation amplitude constant during the frequency sweep and to increase confidence in the experimental results. The experimental results show the presence of the third mode in the response when varying the excitation frequency around the fourth mode. The frequency-response curves, response spectrum and Poincare plots were used for characterization of nonlinear dynamic behaviour of the beam.

关键词： nonlinear vibrations closed-loop vibration system nonlinear structural dynamics cantilever beam

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Experimental and Computational Study of a Rotating Bladed Disk with Under-Platform Dampers

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AIAA JOURNAL 2023年第10期61卷 4717-4727页

作者： Krizak, Troy Kurstak, Eric D'Souza, Kiran Ohio State Univ Dept Mech & Aerosp Engn Columbus OH 43210 USA

There has been an extensive amount of work developing reduced-order models (ROMs) for bladed disks using single-sector models and a cyclic analysis. Several ROMs currently exist to accurately model a bladed disk with under-platform dampers. To better predict the complex nonlinear response of a system with under-platform dampers, this work demonstrates how two linear models can determine bounds for the nonlinear response. The two cases explored are where the under-platform damper is completely stuck and also where the damper slides without friction. This work utilizes the component mode mistuning method to model small mistuning and a parametric ROM method to capture changes in properties due to rotational speed effects. Previously, these ROM methodologies have modeled freestanding bladed disk systems. To evaluate the ROM in predicting the bounds, blade tip amplitudes from the models are compared with high-speed rotating experiments conducted in a large, evacuated vacuum tank. The experimental data were collected during testing using strain gauges and laser blade tip timing probes. The blade amplitudes of the tip timing data, strain gauge data, and computational simulations are compared to determine the effectiveness of the simplified linear analysis in bounding the nonlinear response of the physical system.

关键词： Computational Simulation Strain Gauge Finite Element Modeling Mechanical and structural Vibrations Dynamic Analysis Critical Speed Turbomachinery Reduced Order Model Damped Vibrations nonlinear structural dynamics

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structural dynamics: Convergence properties in the presence of damage and applications to masonry structures

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structural ENGINEERING AND MECHANICS 1997年第5期5卷 587-598页

作者： Nappi, A Facchin, G Marcuzzi, C Department of Civil Engineering University of Trieste 34127 Trieste Piazzale Europa 1 Italy University of Trieste Italy

A numerical model for masonry is proposed by following an internal variable approach originally developed in the field of elastic-plastic analysis. The general features of the theoretical framework are discussed by focussing on finite element models applicable to incremental elastic-plastic problems. An extremum property is derived and its implications in terms of convergence for convenient algorithms are briefly discussed, by including the case of softening materials and damage effects. Next, a numerical model is presented, which is suitable for masonry, can be developed according to the same internal variable formulation and enjoys similar properties. Some numerical results are presented and compared with the response of a masonry shear wall subjected to pseudodynamic tests.

关键词： backward difference damage mechanics extremum properties internal variables masonry plasticity softening nonlinear structural dynamics

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