Journal of Computational & Applied Research in Mechanical Engineering (JCARME)

Articles in Press

Document Type : Research Paper

Authors

Jalal Akbari ¹
Samaneh Mirzaei ²

¹ Department of Civil Engineering, Bu-Ali Sina University, Hamedan, Iran

² Genova University, Savona Compose, Genova, Italy,

10.22061/jcarme.2026.8939.2206

Abstract

The numerical techniques involve difficulties, e.g., conditional stability, period elongation error, amplitude decay error, and the appearance of spurious frequencies in solving dynamic structural problems. Recently, several first-order precise integration methods (PIM) have been introduced to overcome the mentioned problems; however, in these methods, the error of state matrix inversion still is a problem. This paper utilizes the capabilities of the singular value decomposition (SVD) technique to improve the efficiency of the PIM algorithm and remove the singularity of the state matrix. The robustness of the proposed method was investigated for various transient dynamic problems, and the results show that the error of traditional methods e.g. Newark is dramatically high and, in some cases, more than 150 %. Finally, the most important outcome of this research is that appropriate estimation of the dynamic response of MDF systems under impact loading requires careful attention, and the available methods e.g. Newmark average acceleration techniques should not be applied blindly.

Graphical Abstract

Keywords

Main Subjects

Dynamic Response

References

[1] Paultre, " Dynamics of structures ", John Wiley and Sons, 3^rd, (2003).

[2] X. Zhong, and F. W. Williams, "A precise time step integration method." Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., Vol. 208, No. 6, pp. 427-430, (1994).

[3] Yuanxian, C. Biaosong and Z. Hongwu, "precise time-integration with dimension expanding method", Acta Mech. Sin., Vol. 4, No. 4, pp. 456-463, (2000).

[4] Wang and X. Zhou, "Modified precise time step integration method of structural dynamic analysis", J. Earthquake Eng. Eng .Vib., Vol. 4, No. 2, pp. 287-294, (2005).

[5] Wang and F. T. K. Au, "Assessment and improvement of precise time step integration method", Comput. Struct, Vol. 84, No. 12, pp. 779-786, (2006).

[6] H. Fu and W. Z. Zhang, "Precise integration method for solving ill-conditioned algebraic equations ", Chinese", J. Comput. Mech, Vol. 28, No. 4, pp. 530-534, (2011).

[7] Z. Zhang and P. Y. Huang, "Precise integration method for a class of singular two-point boundary value problems", Acta Mech. Sin., Vol. 29, No. 2, pp. 233-240, (2013).

[8] FU and Y. Li, "A Preconditioned Precise Integration Method for Solving ill-conditioned Linear Equations", Appl. Math. Mech.,Vol. 4, No. 8, pp. 462-469, (2018).

[9] Gao, S. J. Tan, W. X. Zhong and H. W. Zhang, "Improved precise integration method for differential Riccati equation", Appl. Math. Mech., Vol. 34, No. 1, pp. 1-14, (2013).

[10] J. Tan, H. J. Peng, W. Y. Zhou and Z. G. Wu, "A novel extended precise integration method based on Fourier series expansion for the H2-norm of linear time-varying periodic systems", Int. J. Control, Vol. 89, No. 10, pp. 2083-2095, (2016).

[11] S. J. Tan, H. J. Peng, W. Y. Zhou and Z. G. Wu, "A novel extended precise integration method based on Fourier series expansion for periodic Riccati differential equations", Control. Appl. Methods, Vol. 38, No. 6, pp. 896-907, (2017).

[12] F. Wang, "Reduced‐order precise integration methods for structural dynamic equations", Int. J. Numer. Methods Biomed. Eng., Vol. 27, No. 10, pp. 1569-1582, (2011).

[13] L. Wu and C. C. Chuang, "Application of an innovative precise integration method in solving equilibrium equation of motion for structural dynamic problems", 15WCEE, LISBOA, (2012).

[14] Wu and C. C. Chuang. "An Innovative Precise Integration Method in Solving Structural Dynamic Problems" In Pressure Vessels and Piping Conference, Vol. 55669, p. V002T02A008. American Society of Mechanical Engineers, (2013).

[15] Gao, F. Wu, H. W. Zhang, J. H. Lin and W. X. Zhong,"A fast precise integration method for large-scale dynamic structures", Chi. J. Comput. Mech, Vol. 28, No. 4, pp. 493-498, (2011).

[16] Gao, F. Wu, H. W. Zhang, W. X. Zhong, W. P. Howson and F. W. Williams, "A fast precise integration method for structural dynamics problems", Struct. Eng. Mech., Vol. 43, No. 1, pp. 1-13, (2012).

[17] Cai, Y. Zhang, X. Li, and B. Jin, "Research on the Vibration Control Algorithms for Large Space Truss Structure Based on Precise Integration Method", J. Comput. Methods, Vol. 13, No. 4, pp. 121-146, (2016).

[18] Cong, X. Ren, Y. Yang and W. Deng, "A modified precise integration method based on Magnus expansion for transient response analysis of time varying dynamical structure." Chaos. Solitons Fract., Vol. 89, pp. 40-46, (2016).

[19] Ding, L. Li and Y. Hu, "A modified precise integration method for transient dynamic analysis in structural systems with multiple damping models", Mech. Syst. Sig. Process., Vol. 9, No. 8, pp. 613-633, (2016).

[20] C. Caprani, "A modal precise integration method for the calculation of footbridge vibration response." Comput. Struct., Vol. 128, pp. 116-127, (2013).

[21] Xingkun, M. Duan and J. Jurado Granados, "Precise integration method for natural frequencies and mode shapes of ocean risers with elastic boundary conditions." Appl. Math. Model., Vol. 61, pp. 709-725, (2018).

[22] Qiping and W. Ying, "A Precise Integration Method for Dynamic Time-History Analysis of Frame-Shear Wall Structures." J. Hebei Univ. Eng. (Nat. Sci. Edit.) Vol. 28, No. 1, pp. 1-4, (2011).

[23] I. A. Lingling and H. A. N. Yang, "Study on Dynamic Load Identification Based on Precise Integration Method", Sub. Eng., Vol. 5, pp. 15-23, (2011).

[24] B. Wang and R. Liu, "Precise Integration Method of Pseudo-dynamic Testing of Structures", J. Appl. Mech , Vol. 580, No. 2, pp. 1574-1580, (2014).

[26] J. Han, G. Lin and J. B. Li, "Dynamic response of footings on stratified soil using the Precise Integration Method", 15WCEE, LISBOA, (2012).

[27] E. I. Qingguan, C. H. E. N. Dong, W. A. N. G. Jianguo and S. H. E. N. Xiaopu, "State-space precise integration method based dynamic response analysis on bottom slab of gate chamber", Water Resour. Hydr. Eng., Vol. 43, No. 4, pp. 45-48, (2012).

[28] Zhang, Q. Gao, S. J. Tan and W. X. Zhong, "A precise integration method for solving coupled vehicle–track dynamics with nonlinear wheel-rail contact", J. Sound Vib., Vol. 331, No. 21, pp. 4763-4773, (2012).

[29] U. Xian-ting, X. I. A. He, L. I. Hui-le, and C. U. I. Kun-peng. "Dynamic analysis framework of train-bridge system based on improved gauss precise integration method" Vol. 30, No. 9, pp. 171-176, (2013).

[30] Shigao, "Precise Time-Step Integration for Dynamic Response of Vehicle-Bridge Coupling Systems" Sci. Technol. Eng., Vol. 13, No. 11, pp. 1-10, (2013).

[31] Y. Fang, J. Liu and F. M. Wang, "A precise integration method for modeling GPR wave propagation in layered pavement structure", CMES-Comp. Model. Eng. Sci, Vol. 99, No. 6, pp. 473-490, (2014).

[32] J. Zhang, Q. N. Li and J. H. Yin, "Precise integration method for the solution of contact element model in earthquake pounding analysis", Shock Vib., Vol. 28, No. 3, pp. 20-38, (2016).

[33] Zhang, Q. Li, T. Wang, Y. Ye and J. Sun, " Elastic-plastic seismic collision analysis of adjacent structures based on the precise integration method", Shock Vib., Vol. 37, No. 14, (2018).

[34] Wu, Q. Gao and W. X. Zhong, "Subdomain precise integration method for periodic structures", Shock Vib., , Vol. 2014, No. 1, pp. 657589, (2014).

[35] Chen, J. Zeng, H. Zhou, J. Zhao and X.Wang, " Sensitivity analysis for the time-domain response of transmission lines based on the precise integration method", 12th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD), (pp. 1347-1351), IEEE, (2016).

[36] C. Cui, X. S. He, Z. R. Lu, Y. M. Chen and J.K.Liu, "Dynamic responses of a beam with breathing cracks by precise integration method", Struct. Eng. Mech, Vol. 60, No. 5, pp. 891-902, (2016).

[38] Moler and C. Van Loan, "Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later", SIAM Review, Vol. 45, No. 1, pp. 3-49, (2003).

[39] Preumont, "Frequency domain analysis of time integration operators", Earthquake Eng. Struct. Dyn., Vol. 10, No. 5, pp. 691-697, (1982).

[40] Michel and P. Gueguen, "Interpretation of the velocity measured in buildings by seismic interferometry based on Timoshenko beam theory under weak and moderate motion", Soil. Dyn. Earthquake Eng., Vol. 104, No. 2, pp. 131-142, (2018).

[41] MATLAB, The MathWorks, Inc., Natic, (2018)

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Journal of Computational & Applied Research in Mechanical Engineering (JCARME)

Articles in Press, Accepted Manuscript
Available Online from 31 January 2026

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