Spurious Response Due to Linear Interpolation of Input Load and Some Remedies

References

• ABAQUS. 2014. Analysis User’s Guide Volume V: Prescribed Conditions, Constraints & Interactions. Providence, RI: Dassault Systèmes.
   Google Scholar
• Arias-Trujillo, J., R. Blázquez, and S. López-Querol. 2012. “A Methodology Based on a Transfer Function Criterion to Evaluate Time Integration Algorithms.” Soil Dynamics and Earthquake Engineering 37:1–23. https://doi.org/10.1016/j.soildyn.2012.01.008.
   Web of Science ®Google Scholar
• Burden, R. L., and F. J. Douglas. 2011. Numerical Analysis. 9th ed. Boston, MA: Brooks/Cole, Cengage Learning.
   Google Scholar
• Cannillo, V., and M. Mancuso. 2000. “Spurious Resonances in Numerical Time Integration Methods for Linear Dynamics.” Journal of Sound and Vibration 238 (3): 389–399. https://doi.org/10.1006/jsvi.2000.3104.
   Web of Science ®Google Scholar
• Carr, A. J. 1997. “Damping Models for Inelastic Analyses.” Proceedings of the Asia-Pacific Vibration Conference, 42–48. Kyongju, Korea.
   Google Scholar
• Chang, T. L. 2022. Suanpan — an Open Source, Parallel and Heterogeneous Finite Element Analysis Framework. https://doi.org/10.5281/ZENODO.1285221.
   Google Scholar
• Chang, S.-Y. 2003. “Nonlinear Error Propagation Analysis for Explicit Pseudodynamic Algorithm.” Journal of Engineering Mechanics 129 (8): 841–850. https://doi.org/10.1061/(ASCE)0733-9399.
   Web of Science ®Google Scholar
• Chang, S.-Y. 2005. “Error Propagation in Implicit Pseudodynamic Testing of Nonlinear Systems.” Journal of Engineering Mechanics 131 (12): 1257–1269. https://doi.org/10.1061/(ASCE)0733-9399.
   Web of Science ®Google Scholar
• Chang, S.-Y. 2011. “Selection of Time Step for Pseudodynamic Testing.” Earthquake Engineering and Engineering Vibration 10 (3): 437–451. https://doi.org/10.1007/s11803-011-0079-8.
   Web of Science ®Google Scholar
• Chopra, A. K., and F. McKenna. 2015. “Modeling Viscous Damping in Nonlinear Response History Analysis of Buildings for Earthquake Excitation.” Earthquake Engineering & Structural Dynamics 45 (2): 193–211. https://doi.org/10.1002/eqe.2622.
   Web of Science ®Google Scholar
• Chrisp, D. J. 1980. Damping Models for Inelastic Structures, mathesis. NZ: University of Canterbury.
   Google Scholar
• Cui, W., and L. Caracoglia. 2016. “Physics-Based Method for the Removal of Spurious Resonant Frequencies in High-Frequency Force Balance Tests.” Journal of Structural Engineering 142 (2). https://doi.org/10.1061/(asce)st.1943-541x.0001414.
   PubMed Web of Science ®Google Scholar
• Hall, J. F. 2006. “Problems Encountered from the Use (Or Misuse) of Rayleigh Damping.” Earthquake Engineering & Structural Dynamics 35 (5): 525–545. https://doi.org/10.1002/eqe.541.
   Web of Science ®Google Scholar
• Houtte, C. V., S. Bannister, C. Holden, S. Bourguignon, and G. McVerry. 2017. “The New Zealand Strong Motion Database.” Bulletin of the New Zealand Society for Earthquake Engineering 50 (1): 1–20. https://doi.org/10.5459/bnzsee.50.1.1-20.
   Google Scholar
• Hulbert, G. M., and J. Chung. 1994. “The Unimportance of the Spurious Root of Time Integration Algorithms for Structural Dynamics.” Communications in Numerical Methods in Engineering 10 (8): 591–597. https://doi.org/10.1002/cnm.1640100803.
   Google Scholar
• Jehel, P. 2014. “A Critical Look into Rayleigh Damping Forces for Seismic Performance Assessment of Inelastic Structures.” Engineering Structures 78:28–40. https://doi.org/10.1016/j.engstruct.2014.08.003.
   Web of Science ®Google Scholar
• Lee, V. W. 1989. “Recent Developments on Data Processing of Strong-Motion Accelerograms: Interpolation of Uniform and Non-Uniform Sampling from Digitized Acceleration Data.” Soil Dynamics and Earthquake Engineering 8 (4): 202–212. https://doi.org/10.1016/s0267-7261(89)80021-1.
   Google Scholar
• Lee, V. W. 1990. “Efficient Algorithm for Computing Displacement, Velocity and Acceleration Responses of an Oscillator to Arbitrary Ground Motion.” Soil Dynamics and Earthquake Engineering 9 (6): 288–300. https://doi.org/10.1016/s0267-7261(05)80015-6.
   Google Scholar
• Maheo, L., V. Grolleau, and G. Rio. 2012. “Numerical Damping of Spurious Oscillations: A Comparison Between the Bulk Viscosity Method and the Explicit Dissipative Tchamwa–Wielgosz Scheme.” Computational Mechanics 51 (1): 109–128. https://doi.org/10.1007/s00466-012-0708-8.
   Web of Science ®Google Scholar
• Maheo, L., G. Rio, and V. Grolleau. 2011. “On the Use of Some Numerical Damping Methods of Spurious Oscillations in the Case of Elastic Wave Propagation.” Mechanics Research Communications 38 (2): 81–88. https://doi.org/10.1016/j.mechrescom.2011.01.006.
   Web of Science ®Google Scholar
• Mirbagheri, Y., H. Nahvi, J. Parvizian, and A. Düster. 2015. “Reducing Spurious Oscillations in Discontinuous Wave Propagation Simulation Using High-Order Finite Elements.” Computers & Mathematics with Applications 70 (7): 1640–1658. https://doi.org/10.1016/j.camwa.2015.06.022.
   Web of Science ®Google Scholar
• Noh, G., and K.-J. Bathe. 2019. “The Bathe Time Integration Method with Controllable Spectral Radius: The ρ∞-Bathe Method.” Computers & Structures 212:299–310. https://doi.org/10.1016/j.compstruc.2018.11.001.
   Web of Science ®Google Scholar
• Oppenheim, A. V., and R. W. Schafer. 2010. Discrete-Time Signal Processing. 3rd ed. Upper Saddle River, NJ: Pearson.
   Google Scholar
• Preumont, A. 1982. “Frequency Domain Analysis of Time Integration Operators.” Earthquake Engineering & Structural Dynamics 10 (5): 691–697. https://doi.org/10.1002/eqe.4290100506.
   Web of Science ®Google Scholar
• Rossi, D. F., W. G. Ferreira, W. J. Mansur, and A. F. G. Calenzani. 2014. “A Review of Automatic Time-Stepping Strategies on Numerical Time Integration for Structural Dynamics Analysis.” Engineering Structures 80:118–136. https://doi.org/10.1016/j.engstruct.2014.08.016.
   Web of Science ®Google Scholar
• Serfőző, D., and B. Pere. 2024. “An Effective Reduction Method with Caughey Damping for Spurious Oscillations in Dynamic Problems.” https://doi.org/10.21203/rs.3.rs-3930320/v1.
   Google Scholar
• Shing, P.-S. B., and S. A. Mahin. 1987. “Elimination of Spurious Higher-Mode Response in Pseudodynamic Tests.” Earthquake Engineering & Structural Dynamics 15 (4): 425–445. https://doi.org/10.1002/eqe.4290150403.
   Web of Science ®Google Scholar
• Söderström, T. 2002. Discrete-Time Stochastic Systems. London: Springer. https://doi.org/10.1007/978-1-4471-0101-7.
   Google Scholar
• Zhou, X., and K. K. Tamma. 2003. “Design, Analysis, and Synthesis of Generalized Single Step Single Solve and Optimal Algorithms for Structural Dynamics.” International Journal for Numerical Methods in Engineering 59 (5): 597–668. https://doi.org/10.1002/nme.873.
   Web of Science ®Google Scholar
• Zhou, X., and K. K. Tamma. 2006. “Algorithms by Design with Illustrations to Solid and Structural Mechanics/Dynamics.” International Journal for Numerical Methods in Engineering 66 (11): 1738–1790. https://doi.org/10.1002/nme.1559.
   Web of Science ®Google Scholar