Inverse Dynamic Analysis of an Inclined FGM Beam Due to Moving Load for Estimating the Mass of Moving Load Based on a CGM

Vahid Shokouhifard1, Saeedreza Mohebpour1,2, Parviz Malekzadeh1, Mohammadreza Golbaharhaghighi1
1Department of Mechanical Engineering, Persian Gulf University, Bushehr, Iran
2Department of Aerospace Engineering, Ryerson University, Toronto, Canada

Tóm tắt

In this paper, the use of the inverse solution method for estimating the mass of moving load on an inclined functionally graded material (FGM) Timoshenko beam is discussed based on the measured displacements. Fletcher–Reeves (FR) method is used to solve the inverse problem. Also, in the process of solving the inverse problem and in order to solve the direct problem, Newmark method is applied for discretization of the time domain and finite element method (FEM) is used for discretization of the space domain. According to many other similar types of research, instead of conducting an experiment and measuring displacements of the beam as inputs of the inverse solution, those inputs are obtained from the direct problem and then random errors are added. Furthermore, an inclined functionally graded (FG) beam with different boundary conditions and power-law exponents due to different speeds of the moving mass has been studied to evaluate the performance of the proposed method. The accuracy of results is very high in all cases.

Tài liệu tham khảo

Al-Baali M (1985) Descent property and global convergence of the Fletcher–Reeves method with inexact line search. IMA J Numer Anal 5(1):121–124 Altunışık AC, Okur FY, Kahya V (2017) Modal parameter identification and vibration based damage detection of a multiple cracked cantilever beam. Eng Fail Anal 79:154–170 Bathe KJ (1982) Finite element procedures in engineering analysis. Prentice Hall, New Jersey Carassale L, Marrè-Brunenghi M, Patrone S (2018) Wavelet-based identification of rotor blades in passage-through-resonance tests. Mech Syst Signal Process 98:124–138 Chen Z, Chan THT (2017) A truncated generalized singular value decomposition algorithm for moving force identification with ill-posed problems. J Sound Vib 401:297–310 Clough RW, Penzien J (1993) Dynamics of structures. McGraw Hill, New York Dai YH (1999) Further insight into the convergence of the Fletcher–Reeves method. Sci China 42(9):905–916 Dai YH, Yuan YX (1996) Convergence properties of the Fletcher–Reeves method. IMA J Numer Anal 16(2):155–164 Eroglu U, Tufekci E (2016) Exact solution based finite element formulation of cracked beams for crack detection. Int J Solids Struct 96:240–253 Esmailzadeh E, Ghorashi M (1995) Vibration analysis of beams traversed by uniform partially distributed moving masses. J Sound Vib 184(1):9–17 Esmailzadeh E, Ghorashi M (1997) Vibration analysis of a Timoshenko beam subjected to a travelling mass. J Sound Vib 199(4):615–628 Fernández-Sáez J, Morassi A, Rubio L (2017) Crack identification in elastically restrained vibrating rods. Int J Non Linear Mech 94:257–267 Fletcher R, Reeves CM (1964) Function minimization by conjugate gradient methods for optimization. SIAM J Optim 7:149–154 Foda MA, Abduljabbar ZA (1998) Dynamic green function formulation for the response of a beam structure to a moving mass. J Sound Vib 210(3):295–306 Giannopoulos GI (2017) Crack identification in graphene using eigenfrequencies. Int J Appl Mech 9(1):1750009 Gillich GR, Mituletu IC, Praisach ZI, Negru I, Tufoi M (2017) Method to enhance the frequency readability for detecting incipient structural damage. Iran J Sci Technol Trans Mech Eng 41(3):233–242 Golbahar Haghighi MR (2016) Estimation of heat flux in variable thickness functionally graded annular fin. Iran J Sci Technol Trans Mech Eng 40(3):203–214 Golbahar Haghighi MR, Eghtesad M, Malekzadeh P, Necsulescu DS (2008) Two-dimensional inverse heat transfer analysis of functionally graded materials in estimating time dependent surface heat flux. Numer Heat Transf 54:744–762 Golbahar Haghighi MR, Eghtesad M, Malekzadeh P, Necsulescu DS (2009) Three dimensional inverse transient heat transfer analysis of thick functionally graded plates. Energ Convers Manag 50:450–457 Golbahar Haghighi MR, Malekzadeh P, Rahideh H, Vaghefi M (2012) Inverse transient heat conduction problems of a multilayered functionally graded cylinder. Numer Heat Trans Part A Appl 61:717–733 Golbahar Haghighi MR, Malekzadeh P, Afshari M (2014) Inverse internal pressure estimation of functionally graded cylindrical shells under thermal environment. Acta Mech 225(12):3377–3393 Golbahar Haghighi MR, Malekzadeh P, Afshari M (2015) Inverse estimation of heat flux and pressure in functionally graded cylinders with finite length. Compos Struct 121:1–15 Gupta DK, Dhingra AK (2018) Dynamic programming approach to load estimation using optimal sensor placement and model reduction. Int J Comput Methods 15(3):1850071 Ichikawa M, Miyakawa Y, Matsuda A (2000) Vibration analysis of the continuous beam subjected to a moving mass. J Sound Vib 230(3):493–506 Lai T, Yi TH, Li HN (2016) Parametric study on sequential deconvolution for force identification. J Sound Vib 377:76–89 Lee HL, Chang WJ, Chen WL, Yang YC (2012a) Inverse heat transfer analysis of a functionally graded fin to estimate time-dependent base heat flux and temperature distributions. Energ Convers Manag 57:1–7 Lee HL, Chang WJ, Sun SH, Yang YC (2012b) Estimation of temperature distributions and thermal stresses in a functionally graded hollow cylinder simultaneously subjected to inner-and-outer boundary heat fluxes. Compos Part B Eng 43:786–792 Li XF (2008) A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams. J Sound Vib 318:1210–1229 Liu J, Han X, Jiang C, Ning HM, Bai YC (2011) Dynamic load identification for uncertain structures based on interval analysis and regularization method. Int J Comput Methods 8(4):667–683 Liu J, Sun X, Han X, Jiang C, Yu D (2014) A novel computational inverse technique for load identification using the shape function method of moving least square fitting. Comput Struct 144:127–137 Luong HTM, Zabel V, Lorenz W, Rohrmann RG (2017) Vibration-based model updating and identification of multiple axial forces in truss structures. Procedia Eng 188:385–392 Malekzadeh P, Monajjemzadeh SM (2013) Dynamic response of functionally graded plates in thermal environment under moving load. Compos B Eng 45(1):1521–1533 Malekzadeh P, Monajjemzadeh SM (2015) Nonlinear response of functionally graded plates under moving load. Thin Walled Struct 96:120–129 Malekzadeh P, Monajjemzadeh SM (2016) Dynamic response of functionally graded beams in a thermal environment under a moving load. Mech Adv Mater Struct 23(3):248–258 Malekzadeh P, Dehbozorgi M, Monajjemzadeh SM (2015) Vibration of functionally graded carbon nanotube-reinforced composite plates under a moving load. Sci Eng Compos Mater 22(1):37–55 Mamandi A, Kargarnovin MH, Younesian D (2010) Nonlinear dynamics of an inclined beam subjected to a moving load. Nonlinear Dyn 60(3):277–293 Matsuzaki R, Yamamoto K, Todoroki A (2017) Delamination detection in carbon fiber reinforced plastic cross-ply laminates using crack swarm inspection: Experimental verification. Compos Struct 173:127–135 Michaltsos G, Sophianopoulos D, Kounadis AN (1996) The effect of a moving mass and other parameters on the dynamic response of a simply-supported beam. J Sound Vib 191(3):357–362 Miyamoto Y, Kaysser WA, Rabin BH, Kawasaki A, Ford RG (1999) Functionally graded materials: design, processing and applications. Kluwer, Dordrecht Mofid M, Shadnam M (2000) On the response of beams with internal hinges under moving mass. Adv Eng Softw 31(5):323–328 Nami MR, Janghorban M (2015) Dynamic analysis of isotropic nanoplates subjected to moving load using state-space method based on nonlocal second order plate theory. J Mech Sci Technol 29(6):2423–2426 Nandakumar P, Shankar K (2015) Structural crack damage detection using transfer matrix and state vector. Measurement 68:310–327 Nikkhoo A, Farazandeh A, Ebrahimzadeh Hassanabadi M, Mariani S (2015) Simplified modeling of beam vibrations induced by a moving mass by regression analysis. Acta Mech 226(7):2147–2157 Nikkhoo A, Farazandeh A, Ebrahimzadeh Hassanabadi M (2016) On the computation of moving mass/beam interaction utilizing a semi-analytical method. J Braz Soc Mech Sci Eng 38(3):761–771 Nikkhoo A, Zolfaghari S, Kiani K (2017) A simplified-nonlocal model for transverse vibration of nanotubes acted upon by a moving nanoparticle. J Braz Soc Mech Sci Eng 39(12):4929–4941 Nord TS, Øiseth O, Lourens EM (2016) Ice force identification on the Nordströmsgrund lighthouse. Comput Struct 169:24–39 Pan CD, Yu L, Liu HL, Chen ZP, Luo WF (2018) Moving force identification based on redundant concatenated dictionary and weighted l1-norm regularization. Mech Syst Signal Process 98:32–49 Polak E, Ribire G (1969) Note sur la convergence de methods de directions conjugues. Rev. Fr. d’ Inform Recherche Oprationnelle 16:35–43 Polyak BT (1969) The conjugate gradient method in extremal problems. USSR Comput Math Math Phys 9(4):94–112 Powell MJD (1977) Restart procedure for the conjugate gradient method. Math Program 12(1):241–254 Powell MJD (2006) Non-convex minimization calculation and the conjugate gradient method. Lect Notes Math 1066:122–141 Przemieniecki JS (1985) Theory of matrix structural analysis. McGraw Hill, New York Qiao B, Zhang X, Wang C, Zhang H, Chen X (2016) Sparse regularization for force identification using dictionaries. J Sound Vib 368:71–86 Rao SS (2009) Engineering optimization theory and practice. Wiley, New Jersey Rao ARM, Lakshmi K, Krishna Kumar S (2015) Detection of delamination in laminated composites with limited measurements combining PCA and dynamic QPSO. Adv Eng Softw 86:85–106 Reddy JN (2000) Analysis of functionally graded plates. Int J Numer Meth Eng 47:663–684 Rezayat A, Nassiri V, De Pauw B, Ertveldt J, Vanlanduit S, Guillaume P (2016) Identification of dynamic forces using group-sparsity in frequency domain. Mech Syst Signal Process 70–71:756–768 Shahsavari D, Janghorban M (2017) Bending and shearing responses for dynamic analysis of single-layer graphene sheets under moving load. J Braz Soc Mech Sci Eng 39(10):3849–3861 Shahsavari D, Karami B, Janghorban M, Li L (2017) Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment. Mater Res Express 4(8):085013 Stanis̆ić MM, Hardin JC (1969) On the response of beams to an arbitrary number of concentrated moving masses. J Frankl Inst 287(2):115–123 Suresh S, Mortensen A (1998) Fundamentals of functionally graded materials. IOM Communications, London Teidj S, Khamlichi A, Driouach A (2016) Identification of beam cracks by solution of an inverse problem. Procedia Technol 22:86–93 Torabi K, Sharifi D, Ghassabi M, Mohebbi A (2018) Semi-analytical solution for nonlinear transverse vibration analysis of an Euler–Bernoulli beam with multiple concentrated masses using variational iteration method. Iran J Sci Technol Trans Mech Eng. https://doi.org/10.1007/s40997-018-0168-7 Touati-Ahmed D, Storey C (1990) Globally convergent hybrid conjugate gradient methods. J Optim Theory Appl 64(2):379–397 Vincent H, Gentiane V, Nasser R, Philippe G (2017) Improving the upper-limb force feasible set evaluation by muscles maximal isometric force identification and cocontraction factors. J Biomech 57:131–135 Wang C, Lian S (2006) Global convergence properties of the two new dependent Fletcher–Reeves conjugate gradient methods. Appl Math Comput 181(2):920–931 Wu JJ (2004) Dynamic responses of a three-dimensional framework due to a moving carriage hoisting a swinging object. Int J Numer Meth Eng 59(13):1679–1702 Wu JJ (2005) Dynamic analysis of an inclined beam due to moving loads. J Sound Vib 288:107–131 Xu X, Xu W, Genin J (1997) A non-linear moving mass problem. J Sound Vib 204(3):495–504 Yang TY (1986) Finite element structural analysis. Prentice Hall, New Jersey Yang C, Oyadiji SO (2017) Identification of beam cracks by solution of an inverse problem. Comput Struct 179:109–126 Yang YC, Chen WL, Chou HM, Salazar JLL (2013) Inverse hyperbolic thermoelastic analysis of a functionally graded hollow circular cylinder in estimating surface heat flux and thermal stresses. Int J Heat Mass Transf 60:125–133 Zhang L, Yang G, Hu D (2018) Identification of voids in structures based on level set method and FEM. Int J Comput Methods 15(3):1850015 Zhao J, Gao R, Yang Y, Wang B (2017) An optimized rail crack detection algorithm based on population status. Int J Comput Mater Sci Eng 6(2):1750022