Structural dynamics of Aeroplane

1. Abstract

The modern aviation industry, particularly remotely piloted aircraft, is changing from fixed – wing aircraft vehicles to molded wings.  Evolving wing may produce cleaner airfoils surface, rendering the aircraft quite flexible and effective than those of the airplane that travels with several other discreet static charges.   The comparison of Rayleigh Method and Ansys results for dynamics structural analysis are done. The structural analysis of the cantilever model is done using finiteelementanalysis with the help of Ansys

2. Introduction

For any airplane wind type of structure, the main load taking components are spars. In the case of UAV, wind span is of less length. In our case it is of 2m span. For reducing the mass typical method used is to use tapered spars. The spar used in this case has section of 0.5*0.04m at root and 0.25*0.04 at tip. Thus taper only in one dimension is used. The material used is Al, whose density is 2700 Kg/m3 and E of 70*109Pa. The poison ration is 0.3. The wind is shown in Figure 1. WE need to perform following four tasks.

3. Methodology

Rayleigh Method

Use the Rayleigh method to obtain approximate values for first bending frequency and first torsion frequency. Refer to the useful information below and choose appropriate polynomial functions given in the lecture notes for “Structural Dynamics” as the assumed modes for the calculation.

Solution:

Given data to solve the problem by using Rayleigh method:

E=70 G Pa

Poisson’s ratio ν=0.3 Depth (h) =0.15 m Length (L) =2 m ρ=2700kg/m³.

To find the first bending frequency we need take a node shape which must satisfy the boundary condition

At x=0, dv(x)/dx=0 v(x) = 12x^2-x^3

dv(x)/dx=24x-2x^2 at x= 0, dv(x)/dx=0

The First Bending frequency found from mat-lab: 10.85 Hz.

Torsional Frequency:

Given data to solve the problem by using Rayleigh method:

E=70 GPa

Poisson’s ratio ν=0.3

Depth (h) =0.15 m

Length (L) =2 m

ρ=2700kg/m³

Mode shape Used: v(x) = (3*L*x^2)-(x^3)

G= E/2(1+ ν)

K=ab³ (16/3-3.36b/a) where and b are taken from the cross section of the wing a=0.25, b=0.04

The Torsional frequency found from Mat-lab: 243.65 Hz.

In order to map the shapes such as the first bending and torsion mode corresponding to the normal frequency,  list function from the ANSYS is used.

Figure 1: List Results for Bending

Figure 2: List Results for Torsional

4. ANSYS Modal Analysis

4.1 Geometry:

The element type of the beam is defined as 2 node / 188 and then modeling of the beam is done by creating key points in active CS. Then real sections of the beam are defined. The beam is considered as three sections (root, tip, taper).

Figure 3: Geometry of the beam

Figure 4 Geometry details of rectangular section

4.2Defining material properties:

The material used in the problem is aluminum alloy which obeys Hooke’s law and is known as linear elastic material. To describe the linear elastic material three main properties are used which is

Young’s modulus is: 70Gpa

Density of Cantilever beam: 2700kg/m^3

Poisson ratio: 0.3

And also aluminum alloy is isotropic since in all directions it has same value of properties.

Figure 5: Defining material Properties

4.3Meshing:

Meshing is done for the line and the number of division in meshing is taken as 20.

Figure 6: Meshing

4.4Boundary Conditions:

The structural displacement load is defined for the nodes. The left end of the node is defined by all degrees of freedom and all other nodes are defined by Ux, Uy, and ROTZ.

4.5Solution:

The new analysis is defined as modal solution and the block lanczos method is used .From current LS the solution is solved.

Figure 7: Solution

4.6 Results:

The results of first five natural frequencies are displayed. The first frequency is a bending frequency and the beam bends at the minimum moment of inertia. The fifth frequency is a torsion frequency as it twisted by rotational moment of inertia.

Figure 8: First Natural Frequency

Figure 9: Second Natural Frequency

Figure 10: Third Natural Frequency

Figure 11: Fourth Natural Frequency

Figure 12: Fifth Natural Frequency

Figure 13: Summarized Result

Compare and comment on the results you obtain. Can you suggest any quick ‘hand calculation’ checks you could carry out to confirm your results are reasonable?

Solution:

Table 1 Comparison between Rayleigh and Ansys Result

From comparison of results from Rayleigh method and Ansys , we find that Rayleigh method predicts little higher values as expected, since the Rayleigh method used assumed deflection shape thus makes the structure little more stiff, so frequency predicted are higher.

To find Bending frequency:

To find Torsion Frequency:

The values are mentioned in the Task 1, using that the bending and torsion frequency is calculated.

5. Structural dynamics of Aeroplane

For aeroplane structure, the structural dynamics is linked to the vibratory behavior excited due application of external forces. The forcing is done due to aerodynamic loading, and inertia loading. The basic material provides the stiffness and damping. Mostly all the aircraft wing requires the structural dynamic analysis. Here analysis of flapping wing is done which is similar to the wing of humming birds. Here the thrust production is also function of  wing deformation so  flexibility is important. AS wind deforms amplitude and phase of twist and bending interacts with the loading due to aerodynamic and improves the wing performance.

Flapping wings of MAV is has advantages as they have higher maneuverability. The transition, from hovering to forward flight occurs smoothly. Produces less noise (PWu1, 2011). Though advantages are more, the design complexity are also more. This is due aero elastic coupling of the wing structure. Hence we need to for dynamic and structural response of the wing. The dynamic response depends on wing inertia and stiffness.  Technology known as OpticalImage Correlation (DIC) is seen to produce better dynamic analysis of the flapping wings. Here high resolution measurements are used for total fluttering motion, catching bothfinite element method and deformity.  (Wu P, 2008). Thus we get spatial resolution with superior deformation measurement.

And also flutter test are must for elimination of the error in the structural design of the flapping wing. This test will show at which speed the flutter or unstable movement will occur in the wing. Finite element modal analysis are used to find frequency of the bending and torsional vibration. To study the structural dynamics, the wing is tested by taking the reinforcement layer (Refer Figure: 15), for every reinforcement layer the wing has different bending stiffness.

6. References

1. PWu1, B. K. (2011). Structural dynamics and aerodynamics. IOP PUBLISHING,
2. Wu P, S. B. (2008). Digital Image correlation technique for full fielddisplacement measurement of micro air vehicle flapping wing. Tech, 33-53.
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5. Chati, , Rand,  R.  and  Mukherjee,  S. “Modal analysis of a cracked beam”, Journal of sound and vibration, 207(2), pp. 249-270. (1997).
6. Chondros T. G., Dimarogonas A. D. and Yao J ” Longitudinal  vibration  of  a  bar  with  a breathing  crack”,  Engineering  fracture mechanics, pp.503-518,1998.