 Open Access
 Total Downloads : 1556
 Authors : S. Senthilkumar, A. Velayudham, P. Maniarasan
 Paper ID : IJERTV2IS60606
 Volume & Issue : Volume 02, Issue 06 (June 2013)
 Published (First Online): 18062013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Dynamic Structural Response Of An Aircraft Wing Using Ansys
S. Senthilkumar1 , A. Velayudham2, P. Maniarasan3
Assistant professor1, PG scholar.2, Principal3
12Department of Aeronautical Engineering, NIET Coimbatore, 3Nehru institute of engineering and technology, Coimbatore.
Abstract
The objective of this project is to analyse the dynamic structural response of an aircraft wing and to simulate it for various boundary conditions. The analysis has been done for two different wing and material properties and the comparison between the results has been studied. This report briefly explains aircraft wing vibration, finite element method and its application using ANSYS. The analysis is carried out in ANSYS 13.0. The loading conditions are the selfweight of the wing. The output extracted is the mode shapes of the wing at different frequencies.
Keyword:Dynamics structural response, Vibration, FEM, Mode shapes

Introduction
The dynamic structural response of on aircraft wing is to ensure the behaviour of the structure in which the vibration tends to occur. This analysis is considered as the modal analysisthe goal of modal analysis in structural mechanics is to determine the natural mode shapes and frequencies of an object or structure during freevibration. It is common to use the finite element method (FEM) to perform this analysis because, like other calculations using the FEM, the object being analysed can havearbitrary shape and the results of the calculations are acceptable. The types of equations whicharise from modal analysisare those seen in Eigen systems. The physical interpretation of the eigenvalues and eigenvectorswhich come from solving the system are that they represent the frequencies and corresponding mode shapes.
This document will attempt to explain some concepts about how structures vibrate and the use of some of the tools to solve structural dynamic problems. The intent of this document is to simply identify how structures vibrate from a nonmathematical perspective.The analysis of the signals typically relies on Fourier analysis. The resulting transfer function will show one or moreresonances, whose frequency can be estimated from the nodal solution.

Vibration Theory
Mathematical techniques allow us to quantify total displacement caused by all vibrations, to convert the displacement measurements to velocity or acceleration, to separate these data into their components through the use of FFT analysis, and to determine the amplitudes and phases of these functions. Such quantification is necessary if we are to isolate and correct abnormal vibrations in machinery.

Periodic Motion
Vibration is a periodic motion, or one that repeats itself after a certain interval of time called the period, T.

Harmonic Motion
It is the simplest kind of periodic motion or vibration. Harmonic motions repeat each time the rotating element or machine component completes one complete cycle.
The maximum value of the displacement is X, which is also called the amplitude. The period, T, is usually measured in seconds; its reciprocal is the frequency of the vibration, measured in cyclespersecond (cps) or Hertz (Hz).
f = 1
Another measure of frequency is the circular frequency,
, measured in radians per second.
= 2
For rotating machinery, the frequency is often expressed in vibrations per minute (vpm) or
=
By definition, velocity is the first derivative of
displacement with respect to time. For a harmonic motion, the displacement equation is:
X = X0sin (t)
The first derivative of this equation gives us the equation for velocity:
v = dX = x0cos(t)
This relationship tells us that the velocity is also harmonic if the displacement is harmonic and has a maximum value or amplitude of X0.
By definition, acceleration is the second derivative of
displacement (i.e., the first derivative of velocity) with respect to time.
This function is also harmonic with amplitude of 2X0.

No harmonic Motion
In most machinery, there are numerous sources of vibrations; therefore, most time domain vibration profiles are No harmonic. While all harmonic motions are periodic, not every periodic motion is harmonic.

Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency.

Amplitude
Amplitude refers to the maximum value of a motion or vibration. This value can be represented in terms of displacement (mils), velocity (inches per second), or acceleration (inches per second squared), each of which is discussed in more detail in the following section on Maximum Vibration Measurement.
Amplitude can be measured as the sum of all the forces causing vibrations within a piece of machinery (broadband), as discrete measurements for the individual forces (component), or for individual userselected forces (narrowband). Broadband, component, and narrowband are discussed in a later section titled Measurement Classifications. Also discussed in this section are the common curve elements: peaktopeak, zerotopeak, and rootmeansquare.

Displacement
Displacement is the actual change in distance or position of an object relative to a reference point and is usually expressed in units of mils, 0.001 inch. For example, displacement is the actual radial or axial movement of the shaft in relation to the normal centreline usually using the machine housing as the stationary reference. Vibration data, such as shaft displacement measurements acquired using a proximity probe or displacement transducer should always be expressed in terms of mils, peak to peak.

Velocity
Velocity is defined as the time rate of change of displacement (i.e., the first derivative), and is usually expressed as inches per second (in/sec). In simple terms,
velocity is a description of how fast a vibration component is movingrather than how far, which is described by displacement.
Used in conjunction with zerotopeak (PK) terms, velocity is the best representation of the true energy generated by a machine when relative or bearing cap data are used. In most cases, peak velocity values are used with vibration data between 0 and 1000 Hz. These data are acquired withmicroprocessorbased, frequency domain systems.

Acceleration
Acceleration is defined as the time rate of change of velocity (i.e., second derivative of displacement),and is expressed in units of inches per second squared (in. / sec2). Vibration frequencies above 1000 Hz should always be expressed as acceleration. Acceleration is commonly expressed in terms of the gravitational constant, g, which is 32.17 ft/sec2. In vibration analysis applications, acceleration is typically expressed in terms of gRMS or gPK. These are the best measures of the force generated by a machine, a group of components, or one of its components.


MODEL 1
In this paper, taper wing model is taken as Model 1.

Specification of Taper wing model
Fig.1 Taper wing model dimensions

Airfoil profile chosen for
design :NACA65210

Zerolift angle of attack(0L) :1.2Â°

Semi span length of the wing :2.286 m

Root chord width :0.726 m

Tip chord width :0.90 m

Aspect Ratio :9.0

Taper Ratio :0.4



Solid model of Taper Wing
Fig.2 Taper Wing solid model in CATIA
3.2.1Boundary condition for model 1 analysis
S. No
Material
Young's Modulus N/m2
Density Kg/m3
Poisson's Ratio
1
Aluminum
7.20E+10
2810.00
0.33
2
Titanium
1.10E+11
4420.00
0.34

Analysis Taper Wing result showing deflection (aluminium)
Fig.3 Maximum deflection of Wing (aluminium)

Analysis of Taper Wing result showing deflection (titanium)
Fig.4 Maximum deflection of Wing(Titanium)

Analysis results for model 1
Natural frequency:
Taper wing (aluminium) :13.412Hz Taper wing (titanium) :13.232Hz
Max.Displacement for model
Taper wing (aluminium) :0.2979mm Taper wing (titanium) :7.4975mm


MODEL 2
In this paper, rectangular wing model is taken as Model 2.

Specification of Taper wing model
In this rectangular wing dimension is a semi span length of 2.286m and root chord and tip chord width is
.726m.The air foil is used same as model 1and model 2

Solid model of Rectangular Wing
Fig.5 Rectangular wing solid model in CATIA
4.2.1Boundary condition for model 1 analysis
S. No
Material
Young's Modulus N/m2
Density Kg/m3
Poisson's Ratio
1
Aluminum
7.20E+10
2810.00
0.33
2
Titanium
1.10E+11
4420.00
0.34
S. No
Material
Young's Modulus N/m2
Density Kg/m3
Poisson's Ratio
1
Aluminum
7.20E+10
2810.00
0.33
2
Titanium
1.10E+11
4420.00
0.34
The same boundary condition used for Model 1and Model 2

Analysis ofrectangular Wing result showing deflection (aluminium)
The below figure shows the deflection caused due to the natural frequency at the Mode 1 by Using aluminium material
Fig.7 Maximum deflection of wing (Aluminium)

Analysis rectangular Wing result showing deflection (titanium)
Fig.8 Maximum deflection of wing(Titanium)

Analysis results for model 2
Natural frequency:
Rectangular wing (aluminium) :9.5488Hz Rectangular wing (titanium) :9.4249Hz
Max.Displacement for model
Rectangular wing (aluminium) :4.3567mm Rectangular wing (titanium) :3.4751mm


Comparison of Model 1 and Model 2Results
The comparison of model 1natural frequency and model 2 natural frequency

Analysis results(Natural frequency)

Analysis results (max displacement)
s
.
n o
Taper wing (aluminiu
m) mm
Taper wing (titanium) Mm
Rectangul arwing (aluminiu m)mm
Rectangul ar wing (titanium) mm
1
9.4031
7.4975
4.3567
3.4751
s
.
n o
Taper wing (aluminiu
m) mm
Taper wing (titanium) Mm
Rectangul arwing (aluminiu m)mm
Rectangul ar wing (titanium) mm
1
9.4031
7.4975
4.3567
3.4751


Conclusion
This paper concludes that, from the above modal analysis, the result shows that the natural frequency calculated for taper wing is higher than the normal rectangular wing and also the displacement for taper wing is less than the rectangular wing

References

Static and Dynamic Structural Response of an Aircraft Wing with Damage Using Equivalent Plate Analysis. Krishnamurthy*
NASA Langley Research Centre, Hampton, VA 23681, U.S.A.

Optimization of light weight aircraft wing structure, prof. Dr. Muhsin j. Jweeg ,2008

Vibration And Aero Elasticity Of Advanced Aircraft Wings Modeled As Thin Walled Beams, Zhanming Qin, 2001

University Of Alberta Ansys Tutorials

Experimental modal analysis, Dr. Peter Avitabile, 2001

D. J. Ewins: Modal Testing: Theory, Practice and Application

Jimin He, ZhiFang Fu (2001). Modal Analysis, ButterworthHeinemann
s . n o 
Taper wing (aluminiu m) Hz 
Taper wing (titanium) Hz 
Rectangu larwing (aluminiu m)Hz 
Rectangul ar wing (titanium) Hz 
1 
13.412 
13.232 
9.5488 
9.4249 