Aim:

This assignment is to carry out a structural vibration analysis of an airplane wing model and

investigate structural integrity assessment through vibration tests.

Why are we asking you to do this?

Structural vibration is the fundamental cause of many structural failures. This can be due to the high

level of stress/strain in the material when a structure is subject to extreme loading conditions or

experiences a resonant condition. More commonly a structure fails unexpectedly due to fatigue after

the material undergoes cyclic stress/strain over a long period of time when the system vibrates within

its normal operating environment. The apparent ‘sudden fracture’ is the result of fatigue damage

being accumulated to a critical level and hence by logic monitoring the fatigue damage accumulation

will allow predictive maintenance of the structure and avoid the eventual fatigue failure of the

structure. In industry, various methods of predictive maintenance have been researched and

developed continuously and in the era of Industry 4.0, this is becoming an integral part of PLM

(product lifecycle management). One important group of techniques uses vibration and this is mainly

due to that vibration characteristics relate directly to the structural integrity status, and also because

vibration responses can be measured easily and reliably in general.

To develop the analytics to establish the relationship between the vibration responses and the

structural integrity condition, an understanding of the input/output relationship of the vibrating

structure through vibration analysis is important. For simple systems, theoretical analysis can be

utilised to solve the governing equation of motion. For real-world engineering structures, vibration

analysis is carried out typically by numerical simulations. Furthermore, the knowledge and skills of

digital signal processing are of great importance for developing methods that can be used together

with other PLM tools in the digital era.

An airplane wing is a representative example of structures that works in a dynamic loading

environment over a long period of time and therefore its structural integrity status needs to be

assessed periodically, especially due to its safety critical nature. In this assignment, an airplane wing

will be modelled as a multi-DOF system. Through doing this assignment, you gain the experience of

carrying out a representative structural vibration analysis of a multi-DOF system involving theoretical

analysis, numerical simulation and digital signal processing. An emphasis has been placed on the

verification of the results obtained by different solution methods. This is a good practice for increasing

your confidence in your results as well as developing the critical thinking ability and professional

attitude that will greatly benefit your future careers whatever they will be.

Task description

A twin-engined airplane is shown in Figure 1(a). The wings have a cantilevered structural configuration

and experience dynamic stress/strain due to dynamic loading during flight. In order to develop

analytics for assessing the structural integrity of the wing, the relationship between the equivalent

stiffness and the vibratory behaviour of the wing needs to be established. In this coursework, a

mathematical model of a two-DOF mass-spring-damper system is considered that will allow

investigations to be carried out in the low frequency range covering the the first two resonant

frequencies. A corresponding computer model using Matlab will be constructed to simulate a

vibration test scenario as shown in Figure 1(b). The Matlab program will first be verified by theoretical

solutions. Then the Matlab program will be used to simulate vibration responses to more realistic and

complex types of excitation. The simulated input (excitation) and output (response) will be used to

represent the measured signals of the vibration tests and British Standards regarding digital signal

processing of vibration measurements will be used.

Figure 1 (a) A twin-engine airplane DA42-VI

Figure 1 (b) Idealised 2-DOF models of one wing in the vertical plane (without

damping) and a vibration testing scenario

Table 2 Task descriptions with details

Task DETAILS

1 Setting up equations of motion

1.1 State the assumptions that are required to idealise the system in Figure 1(a) to

obtain the 2-DOF model in Figure 1(b).

1.2 Apply the following methods to set up equations of motion:

(a) Newton’s 2nd law method

(b) Lagrange’sequations

2 Carrying out modal analysis

2.1 Determine the natural frequencies and the normal modes using the following

method:

• Manual solution by the matrix iteration method

3 Calculating the vibration response under sinusoidal excitation by

the modal superposition method

3.1 Obtain the time histories of vibration responses by

(a) Manual solution by modal superposition method

4 Investigating the sensitivities of the resonant frequencies to the change of the

effective stiffness

4.1 Determine and record the changes in the two resonant frequencies corresponding

to the changes of k1 and k2

Table 1: Tasks

Initial variables:

m1 (kg) m2 (kg) k1 (N/m) k2 (N/m) F0 (N) 𝜁” 𝜁#

280.2618 70.42342 1.07E+08 3.23E+06 5.28E+03 0.05 0.03

Table 2: Initial variables

Default duration of simulation: T = 40 s (This can be changed with justification)

Range of values of k1 and k2 for sensitivity study:

from 0.5 to 1.5 (i.e., from 50% to 120%) times the initial value

Further notes:

1. w1 and w2 are the two natural frequencies of the 2-DOF model.

2. For Task 3.1, the excitation force f(t) is a sinusoidal signal.

𝑓(𝑡) = 𝐹*sin (𝜔𝑡)

### Quick Links

### Use Our Writing Service

Our team has experienced writers that follow all the codes used in professionalism when writing academic essays. We focus our services on satisfied clients. Through critical attention to detail, our writers abide by all the instructions given by clients. Additionally, the paper format is done according to the dictates of the client in respect to the set academic style. We are proud of completing outstanding top-quality papers.