Computational Study of Excitation Controlling Parameters Effect on Uniform Beam Deformation under Vibration

Document Type : Original Article

Authors

Material Manufacturing and Surface Engineering Research Center (MaSE),The Sirindhron International Thai-German Graduate School of Engineering (TGGS), King Mongkut’s University of Technology North Bangkok (KMUTNB), Bangkok, Thailand

Abstract

Understanding a structure’s behavior is necessary for most applications, especially excitation in ultrasonic applications. Currently, ultrasonic devices are used in various fields and have an essential role in nondestructive testing (NDT). The structure’s behavior must be concerned with achieving the best practice. The structural vibrational behavior depends on natural frequency and mode shape. This study attempted to determine the effect of influence parameters on shape deformation for designing the adequate excitation condition. In this study, the influence parameters of a uniform beam, including geometry, support condition, and material, were included to investigate their effect on the frequency, mode shape, and structural response. The result showed the significant influence of a structure’s length and support condition on the mode frequency, dramatically decreasing mode frequency for extended installation and cantilever support. This study investigated the three common mode shapes revealed that the longitudinal bending shape dominated due to the loading direction. Therefore, the shape deformation of the structure is mainly governed by the external excitation source, and the high structural response is received by applying the excitation near the antinode position of the vibration. Nevertheless, the computational result showed a good agreement with the analytical validation with less than 1 % error. The study leads to understanding the vibration, which can be further used for either the effective sensor attachment or designing the vibration control of ultrasonic applications.

Keywords

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References

  1. Hibeller, R., Deflections, structural analysis. 2012, Pearson Prentice Hall, Pearson Education Inc.: Upper Saddle River, NJ, USA.
  2. Hosseini, O., Malekinejad, M. and Rahgozar, R., "A closed form solution for free vibration analysis of tube-in-tube systems in tall buildings", International Journal of Engineering, Transactions A: Basics, Vol. 25, No. 2, (2012), 107-114. doi: 10.5829/idosi.ije.2012.25.02a.01.
  3. Serway, R.A. and Vuille, C., "College physics, Cengage Learning, (2014).
  4. Liu, Y. and Chu, F., "Nonlinear vibrations of rotating thin circular cylindrical shell", Nonlinear Dynamics, Vol. 67, No. 2, (2012), 1467-1479. https://doi.org/10.1007/s11071-011-0082-7
  5. Baker, C., "Measurements of the natural frequencies of trees", Journal of Experimental Botany, Vol. 48, No. 5, (1997), 1125-1132. https://doi.org/10.1093/jxb/48.5.1125
  6. Lashin, M.M., Saleh, W.S. and Alrowais, F., "Determination of different structures’ materials natural frequencies using fuzzy logic system", International Journal of Engineering and Advanced Technology, Vol. 9, No. 3, (2020), 723-727. doi: 10.35940/ijeat.B3641.029320.
  7. Halliday, D., Resnick, R. and Walker, J., "Fundamentals of physics, John Wiley & Sons, (2013).
  8. Billah, K.Y. and Scanlan, R.H., "Resonance, tacoma narrows bridge failure, and undergraduate physics textbooks", American Journal of Physics, Vol. 59, No. 2, (1991), 118-124. https://doi.org/10.1119/1.16590
  9. Griggs Jr, F., "Tacoma narrows bridge failure 1940, galloping gertie part 2", Structure, (2022), 60. https://www.structuremag.org/?p=19995
  10. de Macêdo Wahrhaftig, A. and da Fonseca, R.M.L.R., "Representative experimental and computational analysis of the initial resonant frequency of largely deformed cantilevered beams", International Journal of Solids and Structures, Vol. 102, (2016), 44-55. https://doi.org/10.1016/j.ijsolstr.2016.10.018
  11. Mondal, S., Ghuku, S. and Saha, K.N., "Effect of clamping torque on large deflection static and dynamic response of a cantilever beam: An experimental study", International Journal of Engineering and Technologies, Vol. 15, (2018), 1-16. https://doi.org/10.18052/www.scipress.com/IJET.15.1
  12. Wahrhaftig, A., Brasil, R., Groba, T., Rocha, L., Balthazar, J. and Nascimento, L., "Resonance of a rotary machine support beam considering geometric stiffness", Journal of Theoretical and Applied Mechanics, Vol. 58, (2020). doi: 10.15632/jtam-pl/126681.
  13. Wahrhaftig, A.d.M., Magalhães, K.M., Silva, M.A., da Fonseca Brasil, R.M. and Banerjee, J.R., "Buckling and free vibration analysis of non-prismatic columns using optimized shape functions and rayleigh method", European Journal of Mechanics-A/Solids, Vol. 94, (2022), 104543. https://doi.org/10.1016/j.euromechsol.2022.104543
  14. de Macêdo Wahrhaftig, A., Dantas, J.G.L., da Fonseca Brasil, R.M.L.R. and Kloda, L., "Control of the vibration of simply supported beams using springs with proportional stiffness to the axially applied force", Journal of Vibration Engineering & Technologies, (2022), 1-15. https://doi.org/10.1007/s42417-022-00502-2
  15. Wahrhaftig, A.d.M., Silva, M.A.d. and Brasil, R.M., "Analytical determination of the vibration frequencies and buckling loads of slender reinforced concrete towers", Latin American Journal of Solids and Structures, Vol. 16, (2019). https://doi.org/10.1590/1679-78255374
  16. Wahrhaftig, A.d.M., Magalhães, K.M., Brasil, R.M. and Murawski, K., "Evaluation of mathematical solutions for the determination of buckling of columns under self-weight", Journal of Vibration Engineering & Technologies, Vol. 9, No. 5, (2021), 733-749. https://doi.org/10.1007/s42417-020-00258-7
  17. Ahmed, O.H., Hazem, A.-R. and Shawky, A.A., "Seismic performance of staircases in the 3d analysis of rc building", Civil Engineering Journal, Vol. 7, (2022), 114-123. doi: 10.28991/CEJ-SP2021-07-08.
  18. Ruiter, A.G., Veerman, J.A., Van Der Werf, K.O. and Van Hulst, N.F., "Dynamic behavior of tuning fork shear-force feedback", Applied Physics Letters, Vol. 71, No. 1, (1997), 28-30. https://doi.org/10.1063/1.119482
  19. Hansen, H.H., "Optimal design of an ultrasonic transducer", Structural Optimization, Vol. 14, No. 2, (1997), 150-157. https://doi.org/10.1007/BF01812517
  20. Gururaja, T., Schulze, W.A., Cross, L.E. and Newnham, R.E., "Piezoelectric composite materials for ultrasonic transducer applications. Part ii: Evaluation of ultrasonic medical applications", IEEE Transactions on Sonics and Ultrasonics, Vol. 32, No. 4, (1985), 499-513. doi.
  21. Krautkrämer, J. and Krautkrämer, H., "Ultrasonic testing of materials, Springer Science & Business Media, (2013).
  22. Foorginejad, A., Taheri, M. and Mollayi, N., "A non-destructive ultrasonic testing approach for measurement and modelling of tensile strength in rubbers", International Journal of Engineering, Transactions C: Aspects, Vol. 33, No. 12, (2020), 2549-2555. doi: 10.5829/IJE.2020.33.12C.16.
  23. Xu, C., Xie, J., Zhang, W., Kong, Q., Chen, G. and Song, G., "Experimental investigation on the detection of multiple surface cracks using vibrothermography with a low-power piezoceramic actuator", Sensors, Vol. 17, No. 12, (2017), 2705. https://doi.org/10.3390/s17122705
  24. Lindgren, E., Forsyth, D., Aldrin, J. and Spencer, F., "Asm handbook, volume 17, nondestructive evaluation of materials", ASM International, (2018).
  25. Young, W.C., Budynas, R.G. and Sadegh, A.M., "Roark's formulas for stress and strain, McGraw-Hill Education, (2012).
  26. Hassanpour, P.A., Alghemlas, K. and Betancourt, A., "Experimental modal analysis of a fixed-fixed beam under axial force", in ASME International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers. Vol. 58370, (2017), V04AT05A053.
  27. Cafeo, J.A., Trethewey, M.W. and Sommer III, H.J., "Beam element structural dynamics modification using experimental modal rotational data", (1995). doi: 10.1115/1.2874446.
  28. Zhang, Z. and Zhang, C., "Mechanical properties analysis of bilayer euler-bernoulli beams based on elasticity theory", International Journal of Engineering, Transactions B: Applications, Vol. 33, No. 8, (2020), 1662-1667. doi: 10.5829/ije.2020.33.08b.25.
  29. Rao, S.S., "Vibration of continuous systems: John wiely & sons", New Jersy, (2007).
  30. Ghazwani, M.H., "Development of an analytical model for beams with two dimples in opposing directions", (2016).
  31. Mehdianfar, P., Shabani, Y. and Khorshidi, K., "Natural frequency of sandwich beam structures with two dimensional functionally graded porous layers based on novel formulations", International Journal of Engineering, Transactions B: Applications, Vol. 35, No. 11, (2022), 2092-2101. doi: 10.5829/IJE.2022.35.11B.04.
International Journal of Engineering
Volume 36, Issue 1
TRANSACTIONS A: Basics
January 2023
Pages 60-70

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