scholarly journals Dynamic Gust Load Analysis for Rotors

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Yuting Dai ◽  
Linpeng Wang ◽  
Chao Yang ◽  
Xintan Zhang
Keyword(s):  
Structural Model ◽  
Beam Theory ◽  
Bending Moment ◽  
Iteration Algorithm ◽  
Beam Model ◽  
Euler Beam ◽  
Helicopter Rotors ◽  
Aeroelastic Model ◽  
Flap Deflection ◽  
The Time Domain

Dynamic load of helicopter rotors due to gust directly affects the structural stress and flight performance for helicopters. Based on a large deflection beam theory, an aeroelastic model for isolated helicopter rotors in the time domain is constructed. The dynamic response and structural load for a rotor under the impulse gust and slope-shape gust are calculated, respectively. First, a nonlinear Euler beam model with 36 degrees-of-freedoms per element is applied to depict the structural dynamics for an isolated rotor. The generalized dynamic wake model and Leishman-Beddoes dynamic stall model are applied to calculate the nonlinear unsteady aerodynamic forces on rotors. Then, we transformed the differential aeroelastic governing equation to an algebraic one. Hence, the widely used Newton-Raphson iteration algorithm is employed to simulate the dynamic gust load. An isolated helicopter rotor with four blades is studied to validate the structural model and the aeroelastic model. The modal frequencies based on the Euler beam model agree well with published ones by CAMRAD. The flap deflection due to impulse gust with the speed of 2m/s increases twice to the one without gust. In this numerical example, results indicate that the bending moment at the blade root is alleviated due to elastic effect.

scholarly journals Gust Response Analysis for Helicopter Rotors in the Hover and Forward Flights

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Linpeng Wang ◽  
Yuting Dai ◽  
Chao Yang
Keyword(s):  
Shear Force ◽  
Thrust Force ◽  
Vertical Direction ◽  
Beam Theory ◽  
Response Analysis ◽  
Forward Flight ◽  
Helicopter Rotors ◽  
Aerodynamic Model ◽  
Aeroelastic Model ◽  
The Time Domain

Dynamic load due to gust for helicopter rotors directly affects the structural stress and flight performance. In case of gust, it may cause the loss of trust force or the increase of deflection for rotors. In current work, an effective coupled aeroelastic model based on a medium-deflection beam theory and a nonlinear unsteady aerodynamic model in the time domain were constructed. Three types of gust in vertical direction were added in the model. The dynamic response and structural load for helicopter rotors under three types of gust were calculated, respectively. Results indicated that when rotors suffer a gust in hover at downward direction, the thrust force on rotor disk would decrease significantly when the gust amplitude increases, which should be paid attention in the design. Among the three gust types with the same gust strength, the maximum instantaneous shear force due to impulse shape gust is the largest. When the rotors suffer a gust in a forward flight, the shear force at the root of rotors would increase with the gust strength first but then it decreases. More attention should be paid to the decrease of thrust force and the increase of structural load in a forward flight.

scholarly journals Beam Theory of Thermal–Electro-Mechanical Coupling for Single-Wall Carbon Nanotubes

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 923
Author(s):  
Kun Huang ◽  
Ji Yao
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Beam Theory ◽  
Bending Stiffness ◽  
Single Wall Carbon Nanotubes ◽  
Beam Model ◽  
Euler Beam ◽  
New Model ◽  
Mechanical Coupling ◽  
Electrostatic Fields

The potential application field of single-walled carbon nanotubes (SWCNTs) is immense, due to their remarkable mechanical and electrical properties. However, their mechanical properties under combined physical fields have not attracted researchers’ attention. For the first time, the present paper proposes beam theory to model SWCNTs’ mechanical properties under combined temperature and electrostatic fields. Unlike the classical Bernoulli–Euler beam model, this new model has independent extensional stiffness and bending stiffness. Static bending, buckling, and nonlinear vibrations are investigated through the classical beam model and the new model. The results show that the classical beam model significantly underestimates the influence of temperature and electrostatic fields on the mechanical properties of SWCNTs because the model overestimates the bending stiffness. The results also suggest that it may be necessary to re-examine the accuracy of the classical beam model of SWCNTs.

Elastic Analysis of Beam-Support Impact

1985 ◽  
Vol 107 (1) ◽  
pp. 64-67 ◽  
Author(s):  
M. A. Salmon ◽  
V. K. Verma ◽  
T. G. Youtsos
Keyword(s):  
Analytical Solutions ◽  
Beam Theory ◽  
Bending Moment ◽  
General Purpose ◽  
Euler Beam ◽  
Piping Systems ◽  
Euler Beam Theory ◽  
Impact Problems ◽  
Fixed End ◽  
Spring Support

The effect of gaps present in the seismic supports of nuclear piping systems has been studied with the use of such large general-purpose analysis codes as ANSYS. Exact analytical solutions to two simple beam-impact problems are obtained to serve as benchmarks for the evaluation of the ability of such codes to model impact between beam elements and their supports. Bernoulli-Euler beam theory and modal analysis are used to obtain analytical solutions for the motion of simply supported and fixed-end beams after impact with a spring support at midspan. The solutions are valid up to the time the beam loses contact with the spring support. Numerical results are obtained which show that convergence for both contact force and bending moment at the point of impact is slower as spring stiffness is increased. Finite element solutions obtained with ANSYS are compared to analytical results and good agreement is obtained.

Aerolelastic Analysis of a Thin-Walled Composite Aircraft Wing With an External Store Subjected to a Follower Force

2014 ◽  
Author(s):  
Alev Kacar Aksongur ◽  
Seher Eken ◽  
Metin O. Kaya
Keyword(s):  
Transverse Shear ◽  
Structural Model ◽  
Follower Force ◽  
Beam Model ◽  
Aircraft Wing ◽  
Sweep Angle ◽  
Aerodynamic Loads ◽  
Unsteady Aerodynamic ◽  
Thin Walled ◽  
The Time Domain

This study reports dynamic aeroelastic analyses of an aircraft wing with an attached mass subjected a lateral follower force in an incompressible flow. A swept thin-walled composite beam with a biconvex cross-section is used as the structural model that incorporates a number of non-classical effects such as material anisotropy, transverse shear deformation and warping restraint. A symmetric lay-up configuration i.e. circumferentially asymmetric stiffness (CAS) is further adapted to this model to generate the coupled motion of flapwise bending-torsion-transverse shear. For this beam model, the unsteady aerodynamic loads are expressed using Wagners function in the time-domain as well as using Theodorsen function in the frequency-domain. The flutter speeds are evaluated for several ply angles and the effects of follower force, transverse shear, fiber-orientation and sweep angle on the aeroelastic instabilities are further discussed.

Vibration of Steel–Concrete Composite Beams Using the Timoshenko Beam Model

2005 ◽  
Vol 11 (6) ◽  
pp. 829-848 ◽  
Author(s):  
Stefan Berczyński ◽  
Tomasz Wróblewski
Keyword(s):  
Dynamic Behavior ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Composite Beams ◽  
Free Vibrations ◽  
Timoshenko Beam Theory ◽  
Analytical Models ◽  
Beam Model ◽  
Euler Beam ◽  
Flexural Vibrations

In this paper we present a solution of the problem of free vibrations of steel–concrete composite beams. Three analytical models describing the dynamic behavior of this type of constructions have been formulated: two of these are based on Euler beam theory, and one on Timoshenko beam theory. All three models have been used to analyze the steel–concrete composite beam researched by others. We also give a comparison of the results obtained from the models with the results determined experimentally. The model based on Timoshenko beam theory describes in the best way the dynamic behavior of this type of construction. The results obtained on the basis of the Timoshenko beam theory model achieve the highest conformity with the experimental results, both for higher and lower modes of flexural vibrations of the beam. Because the frequencies of higher modes of flexural vibrations prove to be highly sensitive to damage occurring in the constructions, this model may be used to detect any damage taking place in such constructions.

Aeroelastic Response of an Aircraft Wing Modeled as a Thin-Walled Composite Beam

2013 ◽  
Author(s):  
Seher Durmaz ◽  
Metin O. Kaya
Keyword(s):  
Transverse Shear ◽  
Composite Beam ◽  
Structural Model ◽  
Beam Model ◽  
Aircraft Wing ◽  
Sweep Angle ◽  
Aeroelastic Response ◽  
Aerodynamic Loads ◽  
Thin Walled ◽  
The Time Domain

This study reports static and dynamic aeroelastic analyses of an aircraft wing in an incompressible flow. A swept thin-walled composite beam with a biconvex cross-section is used as the structural model that incorporates a number of non-classical effects such as material anisotropy, transverse shear deformation and warping restraint. A symmetric lay-up configuration i.e. circumferentially asymmetric stiffness (CAS) is further adapted to this model to generate the coupled motion of flap-wise bending-torsion-transverse shear. For this beam model, the unsteady aerodynamic loads are expressed using Wagners function in the time-domain as well as using Theodorsen function in the frequency-domain. The divergence and the flutter speeds are evaluated for several ply angles and the aeroelastic response of an aircraft wing exposed to gust load is examined. The effects of transverse shear, fiber-orientation and sweep angle on the aeroelastic instabilities and the aeroelastic response of the beam are further discussed.

A Laminated Beam Theory With Interlayer Slip

1984 ◽  
Vol 51 (3) ◽  
pp. 551-559 ◽  
Author(s):  
H. Murakami
Keyword(s):  
Virtual Work ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Transverse Shear Strain ◽  
Beam Model ◽  
Euler Beam ◽  
Concentrated Load ◽  
Laminated Beam ◽  
Wide Range ◽  
Interlayer Slip

A Timoshenko beam theory with built-in interlayer slip is developed to facilitate analytical means of simulating the effect of interlayer slip on the stiffness degradation of laminated beam structures. The proposed theory is unique in the sense that any well-structures interlay slip law can be adopted in the beam model. Based on the principle of virtual work, well-posed boundary value problems of the proposed beam theory are defined. It is shown that the proposed theory reduces to the existing Bernoulli-Euler beam theory with interlayer slip by introducing the kinematic constraint of zero transverse shear strain. As a demonstration of the theory the load-deflection curves of a simply supported sandwich beam subjected to a concentrated load at the center are computed for several characteristic interlayer slip laws. It is found that the proposed model has the capability of simulating the deformation of beams with wide range of interlayer bond qualities, from interface with perfect bond to interface without connectors.

scholarly journals Stress Analysis of Suspended Pipe Partially Buried in Linear Elastic Soil

2016 ◽  
Vol 10 (1) ◽  
pp. 161-169
Author(s):  
Kun Huang ◽  
Xia Li ◽  
Yiheng Zhang
Keyword(s):  
Beam Theory ◽  
Bending Moment ◽  
Critical Length ◽  
Beam Model ◽  
Linear Elastic ◽  
Limit Value ◽  
Axial Tension ◽  
Calculation Results ◽  
Stress And Deformation ◽  
Elastic Soil

Based on the small deflection beam theory, bending equation with axial tension of suspended pipe partially buried in the linear elastic soil is established. And the corresponding boundary conditions are given according to the stress and deformation characteristics of suspended section and buried section. Then deflection equation for the suspended section is deduced. Afterwards, the stress and critical length of a suspended pipeline are calculated and analyzed. The results show that the tensile stress and bending stress on the endpoint of the suspended section meet the requirement of first strength theory and the critical suspended length is greater than the real suspended length, which is consistent with the actual situation. When the stiffness of soil tends to approach infinity, both the limit value of axial tension and endpoint bending moment agree well with the calculation results of fixed-fixed supported beam model.

scholarly journals Dynamic Response Analysis of Cable of Submerged Floating Tunnel under Hydrodynamic Force and Earthquake

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Zhiwen Wu ◽  
Guoxiong Mei
Keyword(s):  
Dynamic Response ◽  
Hydrodynamic Force ◽  
Structural Parameters ◽  
Beam Theory ◽  
Response Analysis ◽  
Analysis Model ◽  
Euler Beam ◽  
Earthquake Excitation ◽  
Submerged Floating Tunnel ◽  
The Time Domain

A simplified analysis model of cable for submerged floating tunnel subjected to parametrically excited vibrations in the ocean environment is proposed in this investigation. The equation of motion of the cable is obtained by a mathematical method utilizing the Euler beam theory and the Galerkin method. The hydrodynamic force induced by earthquake excitations is formulated to simulate real seaquake conditions. The random earthquake excitation in the time domain is formulated by the stochastic phase spectrum method. An analytical model for analyzing the cable for submerged floating tunnel subjected to combined hydrodynamic forces and earthquake excitations is then developed. The sensitivity of key parameters including the hydrodynamic, earthquake, and structural parameters on the dynamic response of the cable is investigated and discussed. The present model enables a preliminary examination of the hydrodynamic and seismic behavior of cable for submerged floating tunnel and can provide valuable recommendations for use in design and operation of anchor systems for submerged floating tunnel.

Aeroelastic Modelling of Three-Dimensional Lifting Bodies With an Accelerated Boundary Element Method

2020 ◽  
Author(s):  
Ludwig Könnecke ◽  
Joseph Saverin
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Analytical Model ◽  
Lift Force ◽  
Structural Model ◽  
Three Dimensional ◽  
Beam Theory ◽  
Beam Model ◽  
Set Up ◽  
Element Method

Abstract Investigated was the aeroelastic treatment of a three-dimensional NACA0006 wing by coupling the boundary element method (panel method) for the aerodynamic solution with a beam model (Chrono) for the structural-elastic solution to obtain an aeroelastic solution. Aerodynamic information is interpolated to the structural model by using radial basis functions. As a validation case an analytical model was set up by calculating the lift force from the lifting-line theory and the resulting deflection and torsion predicted with a linear beam theory. This analytical model considers a purely torsional aeroelastic case which is comparable with the simulation results. The distribution of the lift force over the span position of the simulation and the analytical model agrees well, particularly in comparison to the purely torsional case.

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