Boundary condition modelling and identification for cantilever-like structures using natural frequencies
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摘要
The actual boundary conditions of cantilever-like structures might be non-ideally clamped in engineering practice, and they can also vary with time due to damage or aging. Precise modelling of boundary conditions, in which both the boundary stiffness and the boundary mass should be modelled correctly, might be one of the most significant aspects in dynamic analysis and testing for such structures. However, only the boundary stiffness was considered in the most existing methods. In this paper, a boundary condition modelling and identification method for cantilever-like structures is proposed to precisely model both the boundary stiffness and the boundary mass using sensitivity analysis of natural frequencies. The boundary conditions of a cantilever-like structure can be parameterized by constant mass, constant rotational inertia,constant translational stiffness, and constant rotational stiffness. The relationship between natural frequencies and boundary parameters is deduced according to the vibration equation for the lateral vibration of a non-uniform beam. Then, an iterative identification formulation is established using the sensitivity analysis of natural frequencies with respect to the boundary parameters. The regularization technique is also used to solve the potential ill-posed problem in the identification procedure.Numerical simulations and experiments are performed to validate the feasibility and accuracy of the proposed method. Results show that the proposed method can be utilized to precisely model the boundary parameters of a cantilever-like structure.
The actual boundary conditions of cantilever-like structures might be non-ideally clamped in engineering practice, and they can also vary with time due to damage or aging. Precise modelling of boundary conditions, in which both the boundary stiffness and the boundary mass should be modelled correctly, might be one of the most significant aspects in dynamic analysis and testing for such structures. However, only the boundary stiffness was considered in the most existing methods. In this paper, a boundary condition modelling and identification method for cantilever-like structures is proposed to precisely model both the boundary stiffness and the boundary mass using sensitivity analysis of natural frequencies. The boundary conditions of a cantilever-like structure can be parameterized by constant mass, constant rotational inertia,constant translational stiffness, and constant rotational stiffness. The relationship between natural frequencies and boundary parameters is deduced according to the vibration equation for the lateral vibration of a non-uniform beam. Then, an iterative identification formulation is established using the sensitivity analysis of natural frequencies with respect to the boundary parameters. The regularization technique is also used to solve the potential ill-posed problem in the identification procedure.Numerical simulations and experiments are performed to validate the feasibility and accuracy of the proposed method. Results show that the proposed method can be utilized to precisely model the boundary parameters of a cantilever-like structure.
The actual boundary conditions of cantilever-like structures might be non-ideally clamped in engineering practice, and they can also vary with time due to damage or aging. Precise modelling of boundary conditions, in which both the boundary stiffness and the boundary mass should be modelled correctly, might be one of the most significant aspects in dynamic analysis and testing for such structures. However, only the boundary stiffness was considered in the most existing methods. In this paper, a boundary condition modelling and identification method for cantilever-like structures is proposed to precisely model both the boundary stiffness and the boundary mass using sensitivity analysis of natural frequencies. The boundary conditions of a cantilever-like structure can be parameterized by constant mass, constant rotational inertia,constant translational stiffness, and constant rotational stiffness. The relationship between natural frequencies and boundary parameters is deduced according to the vibration equation for the lateral vibration of a non-uniform beam. Then, an iterative identification formulation is established using the sensitivity analysis of natural frequencies with respect to the boundary parameters. The regularization technique is also used to solve the potential ill-posed problem in the identification procedure.Numerical simulations and experiments are performed to validate the feasibility and accuracy of the proposed method. Results show that the proposed method can be utilized to precisely model the boundary parameters of a cantilever-like structure.
引文
1.Liu Y,Xie C,Yang C,Cheng J.Gust response analysis and wind tunnel test for a high-aspect ratio wing.Chin J Aeronaut 2016;29(1):91-103.
2.Ma X,Liu W,Chen L,Li X,Jia ZY,Shang ZL.Simulative technology for auxiliary fuel tank separation in a wind tunnel.Chin J Aeronaut 2016;29(3):608-16.
3.Qiu L,Yuan S,Mei H,Fang F.An improved Gaussian mixture model for damage propagation monitoring of an aircraft wing spar under changing structural boundary conditions.Sensors2016;16(3):291.
4.Ahmadian H,Mottershead JE,Friswell MI.Boundary condition identification by solving characteristic equations.J Sound Vib2001;247(5):755-63.
5.Ahmadian H,Esfandiar M,Jalali H.Boundary condition identification of a plate on elastic support.Int J Acoust Vibr 2014;19(4):282-6.
6.Pabst U,Hagedorn P.Identification of boundary conditions as a part of model correction.J Sound Vib 1995;182(4):565-75.
7.Akhtyamov AM,Utyashev IM.Identification of boundary conditions at both ends of a string from the natural vibration frequencies.Acoust Phys 2015;61(6):615-22.
8.Frikha S,Coffignal G,Trolle JL.Boundary condition identification using condensation and inversion-Application to operating piping network.J Sound Vib 2000;233(3):495-514.
9.Pai PF,Huang L,Gopalakrishnamurthy SH,Chung JH.Identification and applications of boundary effects in beams.Int J Solids Struct 2004;41(11):3053-80.
10.Waters TP,Brennan MJ,Sasananan S.Identifying the foundation stiffness of a partially embedded post from vibration measurements.J Sound Vib 2004;274(1):137-61.
11.Wang L,Yang ZC.Identification of boundary conditions of tapered beam-like structures using static flexibility measurements.Mech Syst Sig Process 2011;25(7):2484-500.
12.Yi WJ,Guo GH.Application of neural networks in recognizing the boundary conditions of beams.J Hunan Univ 1998;25(4):87-90.
13.Mignolet MP,Soize C,Avalos J.Nonparametric stochastic modeling of structures with uncertain boundary conditions/coupling between substructures.AIAA J 2013;51(6):1296-308.
14.Ritto TG,Sampaio R,Aguiar RR.Uncertain boundary condition Bayesian identification from experimental data:A case study on a cantilever beam.Mech Syst Sig Process 2016;68:176-88.
15.Rao SS,Yap FF.Mechanical vibrations.New York:AddisonWesley;1995.
16.Hsu JC,Lai HY,Chen CK.Free vibration of non-uniform EulerBernoulli beams with general elastically end constraints using Adomian modified decomposition method.J Sound Vib 2008;318(4):965-81.
17.Tikhonov AN,Arsenin VY.Solutions of ill-posed problems.New York:Wiley;1977.
18.Hansen PC.Regularization tools Version 4.0 for MATLABVersion 7.3.Numer Algorithms 2007;46:189-94.
2.Ma X,Liu W,Chen L,Li X,Jia ZY,Shang ZL.Simulative technology for auxiliary fuel tank separation in a wind tunnel.Chin J Aeronaut 2016;29(3):608-16.
3.Qiu L,Yuan S,Mei H,Fang F.An improved Gaussian mixture model for damage propagation monitoring of an aircraft wing spar under changing structural boundary conditions.Sensors2016;16(3):291.
4.Ahmadian H,Mottershead JE,Friswell MI.Boundary condition identification by solving characteristic equations.J Sound Vib2001;247(5):755-63.
5.Ahmadian H,Esfandiar M,Jalali H.Boundary condition identification of a plate on elastic support.Int J Acoust Vibr 2014;19(4):282-6.
6.Pabst U,Hagedorn P.Identification of boundary conditions as a part of model correction.J Sound Vib 1995;182(4):565-75.
7.Akhtyamov AM,Utyashev IM.Identification of boundary conditions at both ends of a string from the natural vibration frequencies.Acoust Phys 2015;61(6):615-22.
8.Frikha S,Coffignal G,Trolle JL.Boundary condition identification using condensation and inversion-Application to operating piping network.J Sound Vib 2000;233(3):495-514.
9.Pai PF,Huang L,Gopalakrishnamurthy SH,Chung JH.Identification and applications of boundary effects in beams.Int J Solids Struct 2004;41(11):3053-80.
10.Waters TP,Brennan MJ,Sasananan S.Identifying the foundation stiffness of a partially embedded post from vibration measurements.J Sound Vib 2004;274(1):137-61.
11.Wang L,Yang ZC.Identification of boundary conditions of tapered beam-like structures using static flexibility measurements.Mech Syst Sig Process 2011;25(7):2484-500.
12.Yi WJ,Guo GH.Application of neural networks in recognizing the boundary conditions of beams.J Hunan Univ 1998;25(4):87-90.
13.Mignolet MP,Soize C,Avalos J.Nonparametric stochastic modeling of structures with uncertain boundary conditions/coupling between substructures.AIAA J 2013;51(6):1296-308.
14.Ritto TG,Sampaio R,Aguiar RR.Uncertain boundary condition Bayesian identification from experimental data:A case study on a cantilever beam.Mech Syst Sig Process 2016;68:176-88.
15.Rao SS,Yap FF.Mechanical vibrations.New York:AddisonWesley;1995.
16.Hsu JC,Lai HY,Chen CK.Free vibration of non-uniform EulerBernoulli beams with general elastically end constraints using Adomian modified decomposition method.J Sound Vib 2008;318(4):965-81.
17.Tikhonov AN,Arsenin VY.Solutions of ill-posed problems.New York:Wiley;1977.
18.Hansen PC.Regularization tools Version 4.0 for MATLABVersion 7.3.Numer Algorithms 2007;46:189-94.