Volume 19, Issue 8 (August 2019)
Modares Mechanical Engineering 2019, 19(8): 1837-1844 |
Back to browse issues page
1- Aerospace Engineering Faculty, Malek-Ashtar University of Technology, Tehran, Iran
2- Aerospace Engineering Faculty, Malek-Ashtar University of Technology, Tehran, Iran , s_shokrollahi@mut.ac.ir
2- Aerospace Engineering Faculty, Malek-Ashtar University of Technology, Tehran, Iran , s_shokrollahi@mut.ac.ir
Abstract: (7074 Views)
In this paper, a new method for determining the Young's modulus of structural elements, using the finite element model updating approach, is presented. The model updating is the correction of the numerical model of a structure based on measured data from the real structure. Therefore, after introducing a case study of an aluminum alloy (7075-T651) beam, the frequency of bending vibrations of the case study was measured, using frequency response functions derived from the modal test. Then, Young's modulus for the case study was calculated, using the relationships in the ASTM E 1876-01standard and also the analytical relations governing Euler–Bernoulli beam behavior. The results of the model updating method indicate that there is a very good adaptation with the results of the two recent approaches, the Standard and Euler–Bernoulli beam relations. As a result, this method can be developed with good precision to identify the Young’s modulus in structural elements with more complex shapes, where the relations derived from the aforementioned standard and analytical relations are not efficient due to geometric constraints.
Article Type: Original Research |
Subject:
Aerospace Structures
Received: 2018/05/13 | Accepted: 2019/01/19 | Published: 2019/08/12
Received: 2018/05/13 | Accepted: 2019/01/19 | Published: 2019/08/12
References
1. Shabani R, Honarvar F. Young modulus measurement by ultrasonic method. Journal of Vibration and Sound. 2016;5(10):59-66. [Persian] [Link]
2. Wilson F, Lord Jr AE. Young's modulus determination via simple, inexpensive static and dynamic measurements. American Journal of Physics. 1973;41(5):653. [Link] [DOI:10.1119/1.1987325]
3. Lord JD, Morrell R. Comparison of static and dynamic methods for measuring stiffness of high modulus steels and metal composites. Canadian Metallurgical Quarterly. 2014;53(3):292-299. [Link] [DOI:10.1179/1879139514Y.0000000139]
4. Turvey K. An undergraduate experiment on the vibration of a cantilever and its application to the determination of Young's modulus. American Journal of Physics. 1990;58(5):483. [Link] [DOI:10.1119/1.16480]
5. Massaq A, Rusinek A, Klósak M. Method for determination of the dynamic elastic modulus for composite materials. Engineering Transactions. 2013;61(4):301-315. [Link]
6. Cheng CH, Johnston DH. Dynamic and Static Moduli. Geophysical Research Letters. 1981;8(1):39-42. [Link] [DOI:10.1029/GL008i001p00039]
7. Olsen GT, Wolfenden A, Hebsur MG. Experimental investigation of the dynamic elastic modulus and vibration damping in MoSi2-30%Si3N4 as a function of temperature. Journal of Materials Engineering and Performance. 2000;9(1):116-119. [Link] [DOI:10.1361/105994900770346376]
8. Srikanth N, Lim CV, Gupta M. The modelling and determination of dynamic elastic modulus of magnesium based metal matrix composites. Journal of Materials Science. 2000;35(18):4661-4666. [Link] [DOI:10.1023/A:1004886503104]
9. Hu E, Wang W. The elastic constants measurement of metal alloy by using ultrasonic nondestructive method at different temperature. Mathematical Problems in Engineering. 2016;2016:6762076. [Link] [DOI:10.1155/2016/6762076]
10. Pradhan R, Dhara AK, Panchadhyayee P, Syam D. Determination of Young's modulus by studying the flexural vibrations of a bar: Experimental and theoretical approaches. European Journal of Physics. 2016;37(1):015001. [Link] [DOI:10.1088/0143-0807/37/1/015001]
11. Mottershead JE, Friswell MI. Model Updating In Structural Dynamics: A Survey. Journal of Sound and Vibration. 1993;167(2):347-375. [Link] [DOI:10.1006/jsvi.1993.1340]
12. Adel F, Shokrollahi S, Jamal-Omidi M, Ahmadian H. A model updating method for hybrid composite/aluminum bolted joints using modal test data. Journal of Sound and Vibration. 2017;396:172-185. [Link] [DOI:10.1016/j.jsv.2017.02.035]
13. Choi KK, Kim NH. Structural sensitivity analysis and optimization 1: Linear systems. New York: Springer Science & Business Media; 2005. [Link]
14. Tortorelli DA, Michaleris P. Design sensitivity analysis: Overview and review. Inverse Problems in Engineering. 1994;1(1):71-105. [Link] [DOI:10.1080/174159794088027573]
15. Haug AJ, Choi KK, Komkov V. Design sensitivity analysis of structural systems. Orlando FL: Academic Press; 1986. [Link]
16. Mottershead JE, Link M, Friswell MI. The sensitivity method in finite element model updating: A tutorial. Mechanical Systems and Signal Processing. 2011;25(7):2275-2296. [Link] [DOI:10.1016/j.ymssp.2010.10.012]
17. Demmel JW. Applied numerical linear algebra. Philadelphia: SIAM; 1997. [Link] [DOI:10.1137/1.9781611971446]
18. ASM Aerospace Specification Metals Inc. Aluminum 7075-T6, 7075-T651 [Internet]. Pompano Beach FL: ASM Aerospace Specification Metals Inc; 2018 [cited 2018 Dec 30]. Available from: asm.matweb.com/search/GetReference.asp?bassnum=MA7075T6 [Link]
19. Ewins DJ. Modal testing: Theory, practice and application. 2nd Edition. Baldock: Research Studies Press; 2000. [Link]
20. International Organization for Standardization. ISO 2954: 2012: Mechanical vibration of rotating and reciprocating machinery -- requirements for instruments for measuring vibration severity [Internet]. Geneva: ISO; 2012 [cited 2018 Feb 21]. Available from: https://www.iso.org/standard/21835.html [Link]
21. ASTM. ASTM E1876-01: Standard test method for dynamic Young's modulus, shear modulus, and Poisson's ratio by impulse excitation of vibration [Internet]. West Conshohocken PA: ASTM International; 2001 [cited 2018 Feb 21]. Available from: https://www.astm.org/DATABASE.CART/HISTORICAL/E1876-01.htm [Link]
22. Han SM, Benaroya H, Wei T. Dynamics of transversely vibrating beams using four engineering theories. Journal of Sound and Vibration. 1999;225(5):935-988. [Link] [DOI:10.1006/jsvi.1999.2257]
| Rights and permissions | |
 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |