Kumar, Pramod (2020) Dynamic Response of Doubly-Tapered Laminated Composite Beams under Periodic and Non-Periodic Loadings. Masters thesis, Concordia University.
Preview |
Text (application/pdf)
6MBPramod_Kumar_MASc_S2021.pdf - Accepted Version Available under License Spectrum Terms of Access. |
Abstract
Doubly-tapered laminated composite beams provide a great opportunity to enhance capabilities such as high strength-to-weight ratio, high modulus-to-weight ratio, and design flexibility. Due to design tailoring capabilities, the use of doubly-tapered composite beams has increased in the automobile industry and aerospace industry. In the present thesis, the free and forced vibration analyses of the width-and-thickness-tapered, called herein as doubly-tapered, laminated composite beams are conducted considering different boundary conditions, taper configurations, and loadings. The exact and closed-form solutions for the mode shapes and natural frequencies of doubly-tapered composite beams could not be acquired because of the complexity of the corresponding partial differential equations. Therefore, the classical laminate theory and the one-dimensional laminated beam theory in combination with the Ritz method are used in evaluating the stiffness and mass matrices of the composite beam. The natural frequencies and the corresponding mode shapes are determined by solving the eigenvalue problem obtained using the Ritz method. The forced vibration analysis of the doubly-tapered composite beams subjected to the transverse periodic and non-periodic loadings is carried out by representing the periodic loading as the superposition of the harmonic components of various frequencies using the Fourier series expansion and by expressing the non-periodic pulse excitation as the superposition of two or more simpler functions for which solutions are easier to determine. The maximum deflection of the doubly-tapered composite beam in spatial and time coordinates is determined. Numerical and symbolic computations have been performed using MATLAB® software. The solutions to the free and forced vibration analyses of the composite beams are compared, with the solution available in the literature and with the solution based on the Finite Element Method obtained using ANSYS®, to demonstrate solution accuracy. The Rayleigh damping is considered to model the viscous damping of the composite beam. A detailed parametric study is carried out to investigate the influences of the loading components in the Fourier series expansion, loading type, period of the periodic loading, the rise and fall times of the non-periodic loadings, taper angle, width ratio, thickness ratio, laminate length, stacking sequence, and taper configuration on the forced response of the doubly-tapered composite beam considering different boundary conditions.
| Divisions: | Concordia University > Gina Cody School of Engineering and Computer Science > Mechanical, Industrial and Aerospace Engineering |
|---|---|
| Item Type: | Thesis (Masters) |
| Authors: | Kumar, Pramod |
| Institution: | Concordia University |
| Degree Name: | M.A. Sc. |
| Program: | Mechanical Engineering |
| Date: | 30 October 2020 |
| Thesis Supervisor(s): | Ganesan, Rajamohan |
| Keywords: | Free Vibration, Forced Vibration, General Periodic Loading, Harmonic Loading, Non-Periodic Loading, Tapered Composite Beam, Mode Superposition Method, Fourier Series Expansion |
| ID Code: | 987710 |
| Deposited By: | PRAMOD KUMAR |
| Deposited On: | 23 Jun 2021 16:35 |
| Last Modified: | 30 Sep 2024 00:00 |
References:
1. S. Seraj, “Free vibration and dynamic instability analyses of doubly-tapered rotating laminated composite beams”, M.A.Sc. Thesis, Concordia University, 2016.2. R. B. Abarcar and P. F. Cunniff, “The Vibration of Cantilever Beams of Fiber Reinforced Material”, Journal of Composite Materials, Vol. 6, pp. 504-516, 1972.
3. A. K. Miller and D. F. Adams, “An Analytic Means of Determining the Flexural and Torsional Resonant Frequencies of Generally Orthotropic Beams”, Journal of Sound and Vibration, Vol. 41 (4), pp. 433-449, 1975.
4. J. R. Vinson and R. L. Sierakowski, The Behavior of Structures Composed of Composite Materials, 2nd Edition, Kluwer Academic Publishers, 2002.
5. K. Chandrashekhara, K. Krishnamurthy and S. Roy, "Free Vibration of Composite Beams Including Rotary Inertia and Shear Deformation", Journal of Composite Structures, Vol. 14, pp. 269-279, 1990.
6. A. T. Chen and T. Y. Yang, "Static and Dynamic Formulation of a Symmetrically Laminated Beam Finite Element for a Microcomputer", Journal of Composite Materials, Vol. 19, pp. 459-475, 1985.
7. H. Abromivich and A. Livshits, “Free Vibration of Non-symmetric Cross-ply Laminated Composite Beams”, Journal of Sound and Vibration, Vol. 176 (5), pp. 596-612, 1994.
8. D. Hodges, A. R. Atilgan, M. V. Fulton and L. W. Rehfield, "Free-Vibration Analysis of Composite Beams", Journal of the American Helicopter Society, Vol. 36, pp. 36-47, 1991.
9. A. A. Khdeir and J. N. Reddy, “Free Vibration of Cross-Ply Laminated Beams with Arbitrary Boundary Conditions”, International Journal of Engineering Sciences, Vol. 32, pp. 1971-80, 1994.
10. S. R. Marur and T. Kant, "Free Vibration Analysis of Fiber Reinforced Composite Beams using Higher-Order Theories and Finite Element Modelling", Journal of Sound and Vibration, Vol. 194, pp. 337-351, 1996.
11. S. Krishnaswamy, K. Chandrashekhara and W. Z. B. Wu, “Analytical Solutions to Vibration of Generally Layered Composite Beams”, Journal of Sound and Vibration, Vol. 159, pp. 85-99, 1992.
12. M. Aydogdu, “Vibration Analysis of Cross-Ply Laminated Beams with General Boundary Conditions by Ritz Method”, International Journal of Mechanical Sciences, Vol. 47, pp. 1740-1755, 2005.
13. P. K. Roy and N. Ganesan., “A Technical Note on the Response of a Tapered Beam”, Computers and Structures, Vol. 45, pp. 185-195, 1992.
14. H. H. Yoo, S. H. Lee and S. H. Shin, "Flap Wise Bending Vibration Analysis of Rotating Multi-Layered Composite Beams", Journal of Sound and Vibration, Vol. 286, pp. 745-761, 2005.
15. S. Choi, J. Park, and J. Kim, "Vibration Control of Pre-Twisted Rotating Composite Thin-Walled Beams with Piezoelectric Fiber Composites", Journal of Sound and Vibration, Vol. 300, pp.176-196, 2006.
16. J. M. Bertholet, Composite Materials: Mechanical Behavior and Structural Analysis, New York: Springer, 1999.
17. J. M. Whitney, Structural Analysis of Laminated Anisotropic Plates, Lancaster: Technomic Publishing Company, 1987
18. M. W. Hyer, Stress Analysis of Fiber-Reinforced Composite Materials, Destech Publications Inc., 1998.
19. A. Zabihollah, “Vibration and Buckling Analysis of Tapered Composite Beams Using Conventional and Advanced Finite Element Formulations", M.A.Sc. Thesis, Concordia University, 2003.
20. M. S. Nabi and N. Ganesan, "A Generalized Element for the Free Vibration Analysis of Composite Beams", Computers and Structures, Vol. 51 (5), pp. 607-610, 1994.
21. H. E. U. Ahmed, “Free and Forced Vibrations of Tapered Composite Beams Including the Effects of Axial Force and Damping”, M.A.Sc. Thesis, Concordia University, 2008.
22. P. Salajegheh, "Vibrations of Thickness-and-width Tapered Laminated Composite Beams with Rigid and Elastic Supports", M.A.Sc. Thesis, Concordia University, 2013.
23. V. K. Badagi, "Dynamic Response of Width-and Thickness-tapered Composite Beams Using Rayleigh-Ritz Method and Modal Testing", M.A.Sc. Thesis, Concordia University, 2012.
24. M. A. Fazili, "Vibration Analysis of Thickness-and Width-Tapered Laminated Composite Beams using Hierarchical Finite Element Method", M.A.Sc. Thesis, Concordia University, 2013.
25. R. Ganesan and A. Zabihollah, "Vibration Analysis of Tapered Composite Beams Using a Higher-order Finite Element. Part I: Formulation", Composite Structures, Vol. 77, pp. 300-318, 2007.
26. R. Ganesan and A. Zabihollah, "Vibration Analysis of Tapered Composite Beams Using a Higher-order Finite Element. Part II: Parametric Study", Composite Structures, Vol. 77, pp. 319-330, 2007.
27. A. A. Babu, R. Vasudevan, N. Bandary, P. E. Sudhagar and S. Kumbhar, “Vibration Analysis of Carbon Nanotube Reinforced Uniform and Tapered Composite Beams”, Archives of Acoustics, Vol. 44 (2), pp. 309-320, 2019.
28. P. Krishnan and K. K. M. Kumar, “A Comparison of the Vibrational Responses of Four Different Uniform and Tapered Composite Beams”, International Journal of Surface Engineering and Interdisciplinary Materials Science, Vol. 6, pp. 44-58, 2018.
29. M. P. Singh and A. S. Abdelnassar, “Random Response of Symmetric Cross-Ply Composite Beams with Arbitrary Boundary Conditions”, AIAA Journal, Vol. 30, pp. 1081-1088, 1992.
30. N. Asghar, K. K. Rakesh and J. N. Reddy, "Forced Vibration of Low-Velocity Impact of Laminated Composite Plates", Journal of Computational Mechanics, Vol. 13, pp. 360-379, 1994.
31. M. H. Kadivar and S. R. Bohebpour, "Forced Vibration of Unsymmetrical Laminated Composite Beams Under the Action of Moving Loads", Journal of Composites Science and Technology, Vol. 58, pp. 1675-1684, 1998.
32. W. Hsu and A. Shabana, “Finite element analysis of impact-induced transverse waves in rotating beams”, Journal of Sound and Vibration, Vol. 168, pp. 355-369, 1992.
33. N. K. Chandiramania, C. D. Shetea and L. I. Librescu, “Vibration of higher-order-shearable pretwisted rotating composite blades”, International Journal of Mechanical Sciences, Vol. 45 (12), pp. 2017-2041, 2003.
34. S. S. Rao, Mechanical Vibrations, 5^th Edition, Pearson Education, Inc., 2004.
35. W. T. Thomson and M. D Dahleh, Theory of vibration with Application, 5th Edition, Prentice Hall, New Jersey, 1998.
36. S. S. Rao, Vibration of Continuous Systems, John Wiley & Sons, 2007.
37. A. K. Chopra, Dynamics of Structures: Theory and Applications to Earthquake Engineering, 4th Edition, Prentice Hall, New Jersey, 1998.
38. W. Zhen and C. Wanji, “Free and forced vibration of laminated composite beams”, AIAA Journal, Vol. 56, pp. 2877-2886, 2018.
39. Y. Qu, X. Long, H. Li and G. Meng, “A variational formulation for dynamic analysis of composite laminated beams based on a general higher-order shear deformation theory”, Journal of Composite Structures, Vol. 102, pp. 175-192, 2013.
40. M. Infantes, P. Vidal, R. Castro-Triguero, L. Gallimard, E. García-Macías and O. Polit, “Forced vibration analysis of composite beams based on the variable separation method”, Mechanics of Advanced Materials and Structures, pp. 1-17, 2019.
41. B. Arab, “Vibration Analysis of Thickness-Tapered Laminated Composite Square Plates Based on Ritz Method”, M.A.Sc. Thesis, Concordia University, 2019.
42. M. Paz, Structural dynamics – Theory and computation, New York, U.S.A, Chapman & Hall Inc., 1997.
43. A. Nigam, "Dynamic Analysis of Composite Beams Using Hierarchical Finite Element Formulations", M.A.Sc. Thesis, Concordia University, 2002.
44. J. C. Halpin, N. J. Pagano, J. M. Whitney and E. M. Wu, "Characterization of Anisotropic Composite Materials", Composite Materials: Testing and Design, ASTM STP 460, pp. 37-47, 1969.
45. S. M. Akhlaque-E-Rasul, “Buckling Analysis of Tapered Composite Plates Using Ritz Method Based on Classical and Higher-order Theories", M.A.Sc. Thesis, Concordia University, 2005.
46. A. C. Altunisik, "Dynamic response of masonry minarets strengthened with Fiber Reinforced Polymer (FRP) composites", Natural Hazards and Earth System Science, Vol. 11 (7), 2011.
47. J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd Edition., CRC Press, Inc., 2003.
48. O. O. Ochoa and J. N. Reddy, Finite Element Analysis of Composite Laminates, Kluwer Academic Publishers, 1992.
Repository Staff Only: item control page
Download Statistics
Download Statistics