Identification of Stiffness and Damping Coefficients of Beams Supports

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Abstract

Supports and joints play a basic and important role in the engineering structures. It is necessary to identify the various parameters of supports. The stiffness and damping parameters are the most important parameters of a support. In this paper, an inverse method based on dynamic acceleration measurement data is used to identify and study the stiffness and damping coefficients of the supports of cantilever and doubly clamped beams. To this end, an optimization problem using the least squares method is defined, and solved subsequently. In the cantilever beam, the effect of various parameters such as the magnitude of measurement errors, number of measured data, number of sensors, time duration of the applied load, magnitudes of the stiffness and damping parameters, and time interval of data collection, on the inverse solutions are studied. For the doubly clamped beam, the effects of the magnitude of measurement errors, number of measured data, data type and number of sensors on the results are studied. The results show that the doubly clamped beam problem is much more difficult than the cantilever beam problem. It is very appropriate to use two sensors for problems with the doubly clamped beam. By careful investigation of obtained numerical results, an attempt has been made to answer the questions and difficulties that may occur during practical tests.

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References

[1] Yoshimura M, Okushima K (1977) Measurement of dynamic rigidity and damping property for simplified joint models and simulation by computer. Annals of the CIRP 25: 193-198.
[2] Yoshimure M (1980) Computer design improvement of machine tool structure incorporation joint dynamics data. Annals CIRP, Vol. 28(1): 241-246.
[3] Good MR, Marioce D (1989) Using experimental modal analysis to characterize automobile body joints and improve finite element analysis. Proceedings of the Seventh International Modal Analysis Conference, Las Vegas, NV 106-110.
[4] Inamura T (1979) Stiffness and damping properties of the elements of a machine tool structure. Annals of the CIRP 28: 235-239.
[5] Yuan J, Wu X (1985) Identification of the joint structural parameters of machine tool by DDS and FEM. J Manuf Sci Eng 107(1): 64-69.
[6] Tsai JS, Chou YF (1988) The identification of dynamic characteristics of a single bolt joint. J Sound Vib 125(3): 487-502.
[7] Mottershead J, Stanway R (1986) Identification of structural vibration parameters by using a frequency domain filter. J Sound Vib 109(3): 495-506.
[8] Ibrahim R, Pettit C (2005) Uncertainties and dynamic problems of bolted joints and other fasteners. J sound and Vib 279(3): 857-936.
[9] Bickford J (1995) An introduction to the design and behavior of bolted joints. Revised and expanded: CRC press.
[10] Jones S, Kirby P, Nethercort D (1983) The analysis of frames with semi-rigid connections—a state-of-the-art report. J Constr Steel Res 3(2): 2-13.
[11] Kim T, Wu S, Eman K (1989) Identification of joint parameters for a taper joint. J Manuf Sci Eng 111(3): 282-287.
[12] Ito Y, Masuko M (1971) Study on the Horizontal Bending Stiffness of Bulletin of the Bolted Joint. Bulletin of JSME 14(74): 876-889.
[13] Ikegami R, Church S, Keinholz D, Fowler B (1987) Experimental characterization of deployable trusses and joints.  Workshop on Structure Control and Interaction Flexible Structures, Marshall Space Flight Center, Huntsville, AL. 1271-1288.
[14] Crawley EF, O'Donnell KJ (1987) Force-state mapping identification of nonlinear joints. AIAA journal 25(7): 1003-1010.
[15] Adams R, Cawley P, Pye C, Stone B (1978) A vibration technique for non-destructively assessing the integrity of structures. J Mech Eng Sci 20(2): 93-100.
[16] Haisty B, Springer W (1988) A general beam element for use in damage assessment of complex structures. J Vib Acous 110(3): 389-394.
[17] Loya JA, Rubio L, Fernández-Sáez J (2006) Natural frequencies for bending vibrations of Timoshenko cracked beams. J Sound Vib 290(3): 640-653.
[18] Silva T, Maia N, Roque A, Travassos J (2009) Identification of Elastic Support Properties on a Bernoulli-Euler Beam. Society for Experimental Mechanics (SEM), editor, Proceedings of the 27th International Modal Analysis Conference, Orlando, USA.
[19] De Rosa M, Franciosi C, Maurizi M (1996) On the dynamic behaviour of slender beams with elastic ends carrying a concentrated mass. Comp Struct 58(6): 1145-1159.
[20] Goel R (1976) Transverse vibrations of tapered beams. J Sound Vib 47(1): 1-7.
[21] Sato K (1980) Transverse vibrations of linearly tapered beams with ends restrained elastically against rotation subjected to axial force. Int J Mech Sci 22(2): 109-115.
[22] Abbas B (1984) Vibrations of Timoshenko beams with elastically restrained ends. J. Sound Vib. 97(4): 541-548.
[23] Hadamard J (2014) Lectures on Cauchy's problem in linear partial differential equations: Courier Corporation.
[24] Hollandsworth P, Busby H (1989) Impact force identification using the general inverse technique. Int J Imp Eng 8(4): 315-322.
[25] Kazemi M, Hematiyan MR (2009) An efficient inverse method for identification of the location and time history of an elastic impact load. J Test Eval 37(6): 545-555.
[26] Soares CM, De Freitas MM, Araújo A, Pedersen P (1993) Identification of material properties of composite plate specimens. Compos Struct 25(1): 277-285.
[27] Hematiyan MR, Khosravifard A, Shiah Y, Tan C (2012) Identification of Material Parameters of Two-Dimensional Anisotropic Bodies Using an Inverse Multi-Loading Boundary Element Technique. Comput. Model Eng Sci (CMES) 87(1): 55-76.
[28] Shokrieh MM, Madoliat R, Bostani B, Ghasemi GA, Mahmoodian V (2015) A new inverse method for determination of unidirectional ply mechanical properties of a laminated composite. Modares Mec Eng 15(1): 352-360. (In Persian)
[29] Khodadad M (2015) Identifying two regular interfacial boundary configurations and simultaneously estimation of mechanical properties using Imperialist competitive Algorithm and Simplex method. Modares Mec Eng 14(10): 71-79. (In Persian)
[30] Talebi A (2014) Vibration analysis of a variable cross-section cracked Timoshenko beam and their crack detection using genetic algorithm. Modares Mech Eng 13(13): 78-89. (In Persian)
[31] Law S, Lu Z (2005) Crack identification in beam from dynamic responses. J. Sound Vib. 285(4): 967-987.
[32] Lele S, Maiti S (2002) Modelling of transverse vibration of short beams for crack detection and measurement of crack extension. J Sound Vib 257(3): 559-583.
[33] Rao SS, Yap FF (1995) Mechanical vibrations: Addison-Wesley New York.
[34] Ohkami T, Ichikawa Y, Kawamoto T (1991) A boundary element method for identifying orthotropic material parameters. Int J Num Anal Methods Geomech. 15(9): 609-625.
[35] Huang L, Sun X, Liu Y, Chen Z (2004) Parameter identification for two-dimensional orthotropic material bodies by the boundary element method. Eng Anal Bound Elem 28(2): 109-121.
[36] Gallego R, Comino L, Ruiz‐Cabello A (2006) Material constant sensitivity boundary integral equation for anisotropic solids. Int J Num Methods Eng 66(12): 1913-1933.
[37] Hematiyan MR, Khosravifard A, Shiah YC (2015) A novel inverse method for identification of 3D thermal conductivity coefficients of anisotropic media by the boundary element analysis. Int J Heat Mass Transfer 89: 685-693.
[38] Muniz WB, Velho HFC, Ramos FM (1999) A comparison of some inverse methods for estimating the initial condition of the heat equation. Appl & Comput Top Part Diff Eq 103(1): 145-163.
[39] Bitterlich S, Knabner P (2002) An efficient method for solving an inverse problem for the Richards equation. J Comput Appl Math 147(1): 153-173.
[40] Dennis BH, Jin W, Dulikravich GS, Jaric J (2011) Application of the Finite Element Method to Inverse Problems in Solid Mechanics. Int J Struc Changes Sol Mech & Appl 3(2): 11-21.
[41] Golsorkhi NA, Tehrani HA (2014) Levenberg-Marquardt Method for Solving the Inverse Heat Transfer Problems. J Math & Comp Sci 13: 300-310.
 [42] Beck JV (1985) Inverse Heat Conduction: Ill-Posed Problems, James Beck, 1985.
[43] Möller PW (1999) Load identification through structural modification. J Appl Mech 66(1): 236-241.
[44] Najafi H, Woodbury KA, Beck JV (2015) A filter based solution for inverse heat conduction problems in multi-layer mediums. Int J Heat Mass Transfer 83: 710–720.
Journal of Solid and Fluid Mechanics
Volume 6, Issue 1
March and April 2016
Pages 43-60

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