Abstract
In practical engineering, the changing structural temperature distribution has been considered as an important factor influencing the structural vibration property. By treating the uncertainties in material properties, boundary conditions and external loads as interval variables, this paper proposes a dual-stage uncertainty analysis framework to evaluate the variation of structural natural frequency associated with transient non-uniform temperature distribution. Based on the subinterval dividing strategy, a modified interval vertex method is firstly proposed to predict the uncertain temperature field. As the material mechanical properties are temperature dependent, the components with different temperatures are consequently employed to discrete the structural model. Then by using the Taylor series, an interval perturbation method is developed to solve the generalized eigenvalue problem for the natural frequency prediction. By introducing the traditional Monte Carlo simulations as reference, a 3D plate structure with uncertain parameters is adopted to verify the proposed method.
Similar content being viewed by others
References
Ibrahim HH, Yoo HH, Tawfik M, Lee KS (2010) Thermo-acoustic random response of temperature-dependent functionally graded material panels. Comput Mech 46(3):377–386
Zhou H, Ni Y, Ko J (2011) Eliminating temperature effect in vibration-based structural damage detection. J Eng Mech 137(12):785–796
Xia Y, Chen B, Weng S, Ni Y, Xu Y (2012) Temperature effect on vibration properties of civil structures: a literature review and case studies. J Civil Struct Health Monit 2(1):29–46
Limongelli M (2010) Frequency response function interpolation for damage detection under changing environment. Mech Syst Signal Process 24(8):2898–2913
Zhang S, Oskay C (2017) Reduced order variational multiscale enrichment method for thermo-mechanical problems. Comput Mech 59(6):887–907
Zhao X, Liew KM (2010) A mesh-free method for analysis of the thermal and mechanical buckling of functionally graded cylindrical shell panels. Comput Mech 45(4):297–310
Ebrahimi F, Salari E (2015) Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions. Compos Part A Eng 78:272–290
Guzman-Maldonado E, Hamila N, Boisse P, Bikard J (2015) Thermomechanical analysis, modelling and simulation of the forming of pre-impregnated thermoplastics composites. Compos Part A Appl Syst 78:211–222
Balzani D, Gandhi A, Tanaka M, Schroder J (2015) Numerical calculation of thermo-mechanical problems at large strains based on complex step derivative approximation of tangent stiffness matrices. Comput Mech 55(5):861–871
Petersen D, Rolfes R, Zimmermann R (2001) Thermo-mechanical design aspects for primary composite structures of large transport aircraft. Aerosp Sci Technol 5(2):135–146
Gu L, Qin Z, Chu F (2015) Analytical analysis of the thermal effect on vibrations of a damped Timoshenko beam. Mech Syst Signal Process 60:619–643
Marzani A, Salamone S (2012) Numerical prediction and experimental verification of temperature effect on plate waves generated and received by piezoceramic sensors. Mech Syst Signal Process 30:204–217
Xia Y, Xu Y, Wei Z, Zhu H, Zhou X (2011) Variation of structural vibration characteristics versus non-uniform temperature distribution. Eng Struct 33(1):146–153
Brown AM (2002) Temperature-dependent modal test/analysis correlation of X-34 FASTRAC composite rocket nozzle. J Propul Power 18(2):284–288
Yang J, Shen H (2002) Vibration characteristics and transient response of shear-deformable functionally graded plates in thermal environments. J Sound Vib 255(3):579–602
Nayeri RD, Masri SF, Ghanem RG, Nigbor RL (2008) A novel approach for the structural identification and monitoring of a full-scale 17-story building based on ambient vibration measurements. Smart Mater Struct 17(2):1–19
Sun K, Zhao Y, Hu H (2015) Identification of temperature-dependent thermal-structural properties via finite element model updating and selection. Mech Syst Signal Process 52:147–161
Peeters B, Maeck J, De Roeck G (2001) Vibration-based damage detection in civil engineering: excitation sources and temperature effects. Smart Mater Struct 10(3):518–527
Wang C, Qiu Z, Xu M (2017) Collocation methods for fuzzy uncertainty propagation in heat conduction problem. Int J Heat Mass Trans 107:631–639
Ezvan O, Batou A, Soize C, Gagliardini L (2017) Multilevel model reduction for uncertainty quantification in computational structural dynamics. Comput Mech 59(2):219–246
Wang C, Matthies HG, Xu M, Li Y (2018) Hybrid reliability analysis and optimization for spacecraft structural system with random and fuzzy parameters. Aerosp Sci Technol 77:353–361
Xu M, Du J, Wang C, Li Y (2017) Hybrid uncertainty propagation in structural-acoustic systems based on the polynomial chaos expansion and dimension-wise analysis. Comput Methods Appl Mech Eng 320:198–217
Qiu Z, Yang D, Elishakoff I (2008) Probabilistic interval reliability of structural systems. Int J Solids Struct 45(10):2850–2860
Moens D, Vandepitte D (2006) Recent advances in non-probabilistic approaches for non-deterministic dynamic finite element analysis. Arch Comput Methods Eng 13(3):389–464
Ben-Haim Y, Elishakoff I (2013) Convex models of uncertainty in applied mechanics. Elsevier, Amsterdam
Muhanna RL, Mullen RL (2001) Uncertainty in mechanics problems-interval-based approach. J Eng Mech 127(6):557–566
Wang C, Qiu Z, Wang X, Wu D (2014) Interval finite element analysis and reliability-based optimization of coupled structural-acoustic system with uncertain parameters. Finite Elem Anal Des 91:108–114
Qiu Z, Elishakoff I (1998) Antioptimization of structures with large uncertain-but- non-random parameters via interval analysis. Comput Methods Appl Mech Eng 152(3):361–372
Wang C, Qiu Z, Xu M, Li Y (2017) Novel reliability-based optimization method for thermal structure with hybrid random, interval and fuzzy parameters. Appl Math Model 47:573–586
Chen S, Lian H, Yang X (2003) Interval eigenvalue analysis for structures with interval parameters. Finite Elem Anal Des 39(5):419–431
Chen S, Yang X (2000) Interval finite element method for beam structures. Finite Elem Anal Des 34(1):75–88
Xia B, Yu D (2012) Interval analysis of acoustic field with uncertain-but-bounded parameters. Comput Struct 112:235–244
Xia B, Yu D (2012) Modified sub-interval perturbation finite element method for 2D acoustic field prediction with large uncertain-but-bounded parameters. J Sound Vib 331(16):3774–3790
Ben-Haim Y (1994) A non-probabilistic concept of reliability. Struct Saf 14(4):227–245
Jiang C, Ni B, Han X, Tao Y (2014) Non-probabilistic convex model process: a new method of time-variant uncertainty analysis and its application to structural dynamic reliability problems. Comput Methods Appl Mech Eng 268:656–676
Jiang C, Han X, Liu G (2008) Uncertain optimization of composite laminated plates using a nonlinear interval number programming method. Comput Struct 86(17):1696–1703
Wang C, Qiu Z (2015) Hybrid uncertain analysis for steady-state heat conduction with random and interval parameters. Int J Heat Mass Trans 80:319–328
Mendes MAA, Ray S, Pereira JMC, Pereira JCF, Trimis D (2012) Quantification of uncertainty propagation due to input parameters for simple heat transfer problems. Int J Therm Sci 60:94–105
Wang C, Qiu Z, Yang Y (2016) Collocation methods for uncertain heat convection-diffusion problem with interval input parameters. Int J Therm Sci 107:230–236
Xue Y, Yang H (2013) Interval identification of thermal parameters for convection-diffusion heat transfer problems. In: Asia-Pacific congress for computational mechanics, Singapore
Tao W (2001) Numerical heat transfer. Xi’an Jiaotong University Press, Xi’an
Smith GD (1985) numerical solutions of partial differential equations (finite difference methods). Clarendon Press, Oxford
Rump SM (1992) On the solution of interval linear systems. Computing 47(3–4):337–353
Wang C, Qiu Z (2016) Subinterval perturbation methods for uncertain temperature field prediction with large fuzzy parameters. Int J Therm Sci 100:381–390
Fujimoto RM (2000) Parallel and distributed simulation systems. Wiley, New York
Shackelford JF, Han YH, Kim S, Kwon SH (2016) CRC materials science and engineering handbook. CRC Press, Boca Raton
Acknowledgements
This work was supported by the Alexander von Humboldt Foundation.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, C., Matthies, H.G. Dual-stage uncertainty modeling and evaluation for transient temperature effect on structural vibration property. Comput Mech 63, 323–333 (2019). https://doi.org/10.1007/s00466-018-1596-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00466-018-1596-3