Nonlinear Aeroelastic Behavior of Slender Wings Considering a Static Stall Model Based on Wagner Function

2012 ◽  
Vol 186 ◽  
pp. 297-304 ◽  
Author(s):  
Davood Badiei ◽  
Mohammad Homayoon Sadr ◽  
Shahrokh Shams
Keyword(s):  
Equations Of Motion ◽  
Linear Part ◽  
Beam Theory ◽  
Structural Equations ◽  
Aeroelastic Response ◽  
Linear Elastic ◽  
Model Based ◽  
Aerodynamic Model ◽  
Lift Curve ◽  
Nonlinear Aerodynamic

The aeroelastic behavior of high aspect ratio wings in an incompressible flow is investigated. The nonlinear nonplanar bending-bending-twisting motions of beam theory is used for the structural equations assuming large deformations with small strains, small Poisson effects, inextensional beam theory, and linear elastic material characteristics by neglecting warping and shear deformation. An Unsteady nonlinear aerodynamic static stall model based on the Wagner function is introduced and then is used for determination of aerodynamic loading of the wing. In this aerodynamic model, the static lift curve vs. angle of attack is approximated by a piece-wise curve and for each linear part of this curve a corrected Wagner theory is used. Combining these two types of formulation yields fully nonlinear integro-differentials aeroelastic equations of motion. The governing equations will be solved to predict the nonlinear aeroelastic response of a wing in the stall and post stall regions using Galerkin's method and a numerical method without the need of adding any aerodynamic state-space variables and their corresponding equations. The obtained equations are solved for some test cases and the obtained results are compared with the results given in the literature. Also a study is done to show effects of nonlinear aerodynamic static stall model on the limit cycle oscillations.

Nonlinear Aeroelastic Behavior of Slender Wings Considering a Static Stall Model Based on Wagner Function

2013 ◽  
Vol 325-326 ◽  
pp. 172-179
Author(s):  
D. Badiei ◽  
M.H. Sadr ◽  
Sh. Shams
Keyword(s):  
Equations Of Motion ◽  
Linear Part ◽  
Beam Theory ◽  
Structural Equations ◽  
Aeroelastic Response ◽  
Linear Elastic ◽  
Model Based ◽  
Aerodynamic Model ◽  
Lift Curve ◽  
Nonlinear Aerodynamic

The aeroelastic behavior of high aspect ratio wings in an incompressible flow is investigated. The nonlinear nonplanar bending-bending-twisting motions of beam theory is used for the structural equations assuming large deformations with small strains, small Poisson effects, inextensional beam theory, and linear elastic material characteristics by neglecting warping and shear deformation. An Unsteady nonlinear aerodynamic static stall model based on the Wagner function is introduced and then is used for determination of aerodynamic loading of the wing. In this aerodynamic model, the static lift curve vs. angle of attack is approximated by a piece-wise curve and for each linear part of this curve a corrected Wagner theory is used. Combining these two types of formulation yields fully nonlinear integro-differentials aeroelastic equations of motion. The governing equations will be solved to predict the nonlinear aeroelastic response of a wing in the stall and post stall regions using Galerkin's method and a numerical method without the need of adding any aerodynamic state-space variables and their corresponding equations. The obtained equations are solved for some test cases and the obtained results are compared with the results given in the literature. Also a study is done to show effects of nonlinear aerodynamic static stall model on the limit cycle oscillations.

Unilateral Impact and Contact of Elastic Structures Using Lagrangian Multipliers

2011 ◽  
Author(s):  
Sebastian Tatzko
Keyword(s):  
Equations Of Motion ◽  
Structural Equations ◽  
Contact Forces ◽  
Integration Scheme ◽  
Lagrangian Multiplier ◽  
Elastic Structures ◽  
Lagrangian Multipliers ◽  
Linear Elastic ◽  
Time Stepping ◽  
Numerical Effort

This paper deals with linear elastic structures exposed to impact and contact phenomena. Within a time stepping integration scheme contact forces are computed with a Lagrangian multiplier approach. The main focus is turned on a simplified solving method of the linear complementarity problem for the frictionless contact. Numerical effort is reduced by applying a Craig-Bampton transformation to the structural equations of motion.

Limit-Cycle Oscillation of High-Aspect-Ratio Wings

2014 ◽  
Vol 556-562 ◽  
pp. 4329-4332
Author(s):  
Yan Ping Xiao ◽  
Yi Ren Yang ◽  
Peng Li
Keyword(s):  
Aspect Ratio ◽  
Limit Cycle ◽  
High Aspect Ratio ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Structural Equations ◽  
Limit Cycle Oscillation ◽  
Nonlinear Beam ◽  
Structural Nonlinearity ◽  
Cycle Oscillation

In this paper structural equations of motion based on nonlinear beam theory and the unsteady aerodynamic forces are gained to study the effects of geometric nonlinearity on the aerodynamic response of high-aspect-ratio wings. Then the Galerkin’s method is used to discretize the equations of motion. The results of HALE wing show good agreement with references. And other results investigate the effects of geometric structural nonlinearity on the response of a wing. Also the complex changes of the limit-cycle oscillation with speed increasing is carefully studied.

Flutter/LCO suppression for high-aspect ratio wings

2009 ◽  
Vol 113 (1144) ◽  
pp. 409-416 ◽  
Author(s):  
D. Tang ◽  
E. H. Dowell
Keyword(s):  
Aspect Ratio ◽  
Limit Cycle ◽  
High Aspect Ratio ◽  
Equations Of Motion ◽  
Wind Tunnel Test ◽  
Beam Theory ◽  
Control Device ◽  
Structural Equations ◽  
Limit Cycle Oscillations ◽  
Tip Mass

Abstract An experimental high-aspect ratio wing aeroelastic model with a device to provide a controllable slender body tip mass distribution has been constructed and the model response due to flutter and limit cycle oscillations has been measured in a wind tunnel test. A theoretical model has also been developed and calculations made to correlate with the experimental data. Structural equations of motion based on nonlinear beam theory are combined with the ONERA aerodynamic stall model (an empirical extension of Theodorsen aerodynamic theory that accounts for flow separation). A dynamic perturbation analysis about a nonlinear static equilibrium is used to determine the small perturbation flutter boundary which is compared to the experimentally determined flutter velocity and flutter frequency. Time simulation is used to compute the limit cycle oscillations response when the flutter/LCO control system is ON or OFF. Theory and experiment are in good agreement for predicting the flutter/LCO suppression that can be achieved with the control device.

Disk Position Nonlinearity Effects on the Chaotic Behavior of Rotating Flexible Shaft-Disk Systems

2012 ◽  
Vol 28 (3) ◽  
pp. 513-522 ◽  
Author(s):  
H. M. Khanlo ◽  
M. Ghayour ◽  
S. Ziaei-Rad
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamic Behavior ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Disk System ◽  
Partial Differential ◽  
Rayleigh Beam ◽  
Flexible Shaft

AbstractThis study investigates the effects of disk position nonlinearities on the nonlinear dynamic behavior of a rotating flexible shaft-disk system. Displacement of the disk on the shaft causes certain nonlinear terms which appears in the equations of motion, which can in turn affect the dynamic behavior of the system. The system is modeled as a continuous shaft with a rigid disk in different locations. Also, the disk gyroscopic moment is considered. The partial differential equations of motion are extracted under the Rayleigh beam theory. The assumed modes method is used to discretize partial differential equations and the resulting equations are solved via numerical methods. The analytical methods used in this work are inclusive of time series, phase plane portrait, power spectrum, Poincaré map, bifurcation diagrams, and Lyapunov exponents. The effect of disk nonlinearities is studied for some disk positions. The results confirm that when the disk is located at mid-span of the shaft, only the regular motion (period one) is observed. However, periodic, sub-harmonic, quasi-periodic, and chaotic states can be observed for situations in which the disk is located at places other than the middle of the shaft. The results show nonlinear effects are negligible in some cases.

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks

2004 ◽  
Vol 126 (1) ◽  
pp. 175-183 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Disk Model ◽  
Sector Model ◽  
Bladed Disk ◽  
Symmetry Properties

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disk using a periodic sector model without any loss of accuracy in calculations and modeling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disk forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disk model: (i) using sector finite element matrices and (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disk with shrouds have demonstrated the high efficiency of the method.

Free vibration analysis and post-critical free vibrations of nanocomposite rotating beams reinforced with graphene platelet

2021 ◽  
pp. 107754632110511
Author(s):  
Arameh Eyvazian ◽  
Chunwei Zhang ◽  
Farayi Musharavati ◽  
Afrasyab Khan ◽  
Mohammad Alkhedher
Keyword(s):  
Natural Frequency ◽  
Thermal Environment ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Weight Fraction ◽  
Free Vibrations ◽  
Graphene Platelet ◽  
The Impact

Treatment of the first natural frequency of a rotating nanocomposite beam reinforced with graphene platelet is discussed here. In regard of the Timoshenko beam theory hypothesis, the motion equations are acquired. The effective elasticity modulus of the rotating nanocomposite beam is specified resorting to the Halpin–Tsai micro mechanical model. The Ritz technique is utilized for the sake of discretization of the nonlinear equations of motion. The first natural frequency of the rotating nanocomposite beam prior to the buckling instability and the associated post-critical natural frequency is computed by means of a powerful iteration scheme in reliance on the Newton–Raphson method alongside the iteration strategy. The impact of adding the graphene platelet to a rotating isotropic beam in thermal ambient is discussed in detail. The impression of support conditions, and the weight fraction and the dispersion type of the graphene platelet on the acquired outcomes are studied. It is elucidated that when a beam has not undergone a temperature increment, by reinforcing the beam with graphene platelet, the natural frequency is enhanced. However, when the beam is in a thermal environment, at low-to-medium range of rotational velocity, adding the graphene platelet diminishes the first natural frequency of a rotating O-GPL nanocomposite beam. Depending on the temperature, the post-critical natural frequency of a rotating X-GPL nanocomposite beam may be enhanced or reduced by the growth of the graphene platelet weight fraction.

Motion planning of a fish-like piezoelectric actuated robot using model-based predictive control

2021 ◽  
pp. 107754632110482
Author(s):  
Arthur S Barbosa ◽  
Lucas Z Tahara ◽  
Maíra M da Silva
Keyword(s):  
Motion Planning ◽  
Predictive Control ◽  
Fiber Composite ◽  
Beam Theory ◽  
Mode Shapes ◽  
Design Strategies ◽  
Mechanical Coupling ◽  
Model Based ◽  
Input Signals ◽  
Bounded Input

This work proposes a novel methodology for planning the motion of fish-like soft robots actuated by macro-fiber composite (MFC) pairs. These structures should mimic oscillatory and undulation movements, which can be accomplished if the amplitude of the tail motion is larger than that of the head motion. Design strategies, such as the use of concentrated and distributed masses, are addressed to mimic fish-like motion since they guarantee suitable mode shapes for the structure. The motion planning proposal explores a model-based predictive control (MPC) strategy for deriving the input signals for the MFC actuators. This model-based control strategy requires the use of reasonably small-sized models. This is accomplished by extracting modal state-space models based on the free–free Euler–Bernoulli beam theory considering the electro-mechanical coupling of the MFC actuator pairs. Numerical results demonstrate the capability of the proposal for deriving bounded input signals that generate oscillatory and undulation movements even in the presence of disturbances. This general approach can be further extended for other applications.

Effect of Segmented Electrodes on Piezo-Elastic and Piezo-Aero-Elastic Responses of Generator Plates

2009 ◽  
Author(s):  
Carlos De Marqui ◽  
Alper Erturk ◽  
Daniel J. Inman
Keyword(s):  
Electrical Power ◽  
Elastic Behavior ◽  
Elastic Model ◽  
Fe Model ◽  
Aeroelastic Response ◽  
Aerodynamic Model ◽  
Frequency Excitation ◽  
Elastic Responses ◽  
Electrical Power Output ◽  
Tip Mass

In this paper, the use of segmented electrodes is investigated to avoid cancellation of the electrical outputs of the torsional modes in energy harvesting from piezo-elastic and piezo-aero-elastic systems. The piezo-elastic behavior of a cantilevered plate with an asymmetric tip mass under base excitation is investigated using an electromechanically coupled finite element (FE) model. Electromechanical frequency response functions (FRFs) are obtained using the coupled FE model both for the continuous and segmented electrodes configurations. When segmented electrodes are considered torsional modes also become significant in the resulting electrical FRFs, improving broadband (or varying-frequency excitation) performance of the generator plate. The FE model is also combined with an unsteady aerodynamic model to obtain the piezo-aero-elastic model. The use of segmented electrodes to improve the electrical power generation from aeroelastic vibrations of plate-like wings is investigated. Although the main goal here is to obtain the maximum electrical power output for each airflow speed (both for the continuous and segmented electrode cases), piezoelectric shunt damping effect on the aeroelastic response of the generator wing is also investigated.

scholarly journals Vibration and Instability of Rotating Composite Thin-Walled Shafts with Internal Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ren Yongsheng ◽  
Zhang Xingqi ◽  
Liu Yanghang ◽  
Chen Xiulong
Keyword(s):  
Virtual Work ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Dynamical Analysis ◽  
Design Parameters ◽  
Internal Damping ◽  
Analysis Method ◽  
Governing Equations ◽  
Thin Walled

The dynamical analysis of a rotating thin-walled composite shaft with internal damping is carried out analytically. The equations of motion are derived using the thin-walled composite beam theory and the principle of virtual work. The internal damping of shafts is introduced by adopting the multiscale damping analysis method. Galerkin’s method is used to discretize and solve the governing equations. Numerical study shows the effect of design parameters on the natural frequencies, critical rotating speeds, and instability thresholds of shafts.

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