Thermal Science

International Scientific Journal

Find this paper on

STABILITY OF INITIAL RESPONSE OF EXPONENTIALLY DAMPED OSCILLATORS

ABSTRACT

A damping system always results in energy consumption. This paper studies an exponentially damped oscillator with historical memory for a viscoelastic damper structure, its stability under an initial response is analyzed analytically and verified numerically.

KEYWORDS

exponentially damped oscillators, initial response, stability, convolutional nonviscously damped model

PAPER SUBMITTED: 2022-12-30

PAPER REVISED: 2023-03-10

PAPER ACCEPTED: 2023-03-20

PUBLISHED ONLINE: 2024-05-18

DOI REFERENCE: https://doi.org/10.2298/TSCI2403179X

CITATION EXPORT: view in browser or download as text file

THERMAL SCIENCE YEAR 2024, VOLUME 28, ISSUE No. 3, PAGES [2179 - 2188]

REFERENCES

[1] Cacopardo, L., et al., Characterizing and Engineering Biomimetic Materials for Viscoelastic Mechanotransduction Studies, Tissue Engineering Part B: Reviews, 28 (2022), 4, pp. 912-925, 10.1089/ten.teb.2021.0151

[2] He, C. H., et al., A Novel Bond Stress-Slip Model for 3-D Printed Concretes, Discrete and Continuous Dynamical Systems, 15 (2022), 7, pp. 1669-1683, 10.3934/dcdss.2021161

[3] Zuo, Y. T., Liu, H. J., Is the Spider a Weaving Master or a Printing Expert? Thermal Science, 26 (2022), 3B, pp. 2471-2475, 10.2298/tsci2203471z

[4] He, J.-H., et al., The Maximal Wrinkle Angle During the Bubble Collapse and Its Application to the Bubble Electrospinning, Frontiers in Materials, 8 (2022), 800567, 10.3389/fmats.2021.800567

[5] Qian, M. Y., He, J.-H., Collection of Polymer Bubble as a Nanoscale Membrane, Surfaces and Interface, 28 (2022), 101665, 10.1016/j.surfin.2021.101665

[6] Hu, M. B., et al., Experimental Study of Energy Absorption Properties of Granular Materials Under Low Frequency Vibrations, International Journal of Modern Physics B, 18 (2004), 17-19, pp. 2708-2712, 10.1142/s0217979204025956

[7] Mekid, S., Kwon, O. J. Nervous Materials: A New Approach for Better Control, Reliability and Safety of Structures, Science of Advanced Materials, 1 (2009), 3, pp. 276-285, 10.1166/sam.2009.1055

[8] He, C. H., et al., Controlling the Kinematics of a Spring-Pendulum System Using an Energy Harvesting Device, Journal of Low Frequency Noise, Vibration & Active Control, 41 (2022), 3, pp. 1234-1257, 10.1177/14613484221077474

[9] Liang, Y. H., Wang, K. J., A New Fractal Viscoelastic Element: Promise and Applications to Maxwell-Rheological Model, Thermal Science, 25 (2021), 2B, pp. 1221-1227, 10.2298/tsci200301015l

[10] Qian, M. Y., He, J.-H., Two-Scale Thermal Science for Modern Life - Making the Impossible Possible, Thermal Science, 26 (2022), 3B, pp. 2409-2412, 10.2298/tsci2203409q

[11] He, J.-H., et al., A Tutorial Introduction to the Two-Scale Fractal Calculus and Its Application to the Fractal Zhiber-Shabat Oscillator, Fractals, 29 (2021), 8, 2150268, 10.1142/s0218348x21502686

[12] Xiu, G. Z., et al., Integral Representation of the Viscoelastic Relaxation Function, Journal of Shanghai Normal University (Natural Sciences), 48 (2019), 3, pp. 242-251

[13] Adhikari, S., Woodhouse, J., Quantification of Non-viscous Damping in Discrete Linear Systems, Journal of Sound and Vibration, 260 (2003), 3, pp. 499-518, 10.1016/s0022-460x(02)00952-5

[14] Li, L., et al., Inclusion of Higher Modes in the Eigensensitivity of Non-viscously Damped Systems, AI-AA Journal, 52 (2014), 6, pp. 1316-1322, 10.2514/1.j052797

[15] He, J.-H., El-Dib, Y. O., Periodic Property of the Time-Fractional Kundu-Mukherjee-Naskar Equation, Results in Physics, 19 (2020), 103345, 10.1016/j.rinp.2020.103345

[16] Li, L., et al., Design Sensitivity Analysis of Dynamic Response of Non-viscously Damped Systems, Mechanical Systems and Signal Processing, 41 (2013), 1-2, pp. 613-638, 10.1016/j.ymssp.2013.08.009

[17] Shen, H. Y., et al., Time History Analysis Method for Response of Convoluted Non-viscous Damping System Based on Taylor Expansion of Volterra Integral Equation (in Chinese), Chinese Journal of Applied Mechanics, 35 (2018), 2, pp. 261-266

[18] Meng, L., Zhongdong, D., Wind Effect Analysis of Super-High Structure Based on Convolutional Non-viscously Damped System, Chinese Journal of Computational Mechanics, 34 (2017), 6, pp. 763-769

[19] Lazaro, M., Perez-Aparicio, J. L., Characterization of Real Eigenvalues in Linear Viscoelastic Oscillators and the Non-viscous Set, Journal of Applied Mechanics, 81 (2014), 2, pp. 021016-1-021016-14, 10.1115/1.4025400

[20] Guedria, N., Smaoui, H., A Direct Algebraic Method for Eigensolution Sensitivity Computation of Damped Asymmetric Systems, International Journal for Numerical Methods in Engineering, 68 (2006), 6, pp. 674-689, 10.1002/nme.1732

[21] Xiu, G. Z., et al., Optimal Control Designs for a Class of Non-viscously Damped Systems, Journal of Donghua University (English Edition), 37 (2020), 2, pp. 137-142

[22] Benjamin, D., et al., Transition from Exponentially Damped to Finite-Time Arrest Liquid Oscillations Induced by Contact Line Hysteresis, Physical Review Letters, 124 (2020), 10, pp. 104502.1-104502.5, 10.1103/physrevlett.124.104502

[23] Lazaro, M., Eigensolutions of Non-viscously Damped Systems Based on the Fixed-Point Iteration, Journal of Sound and Vibration, 418 (2018), Mar., pp. 100-121, 10.1016/j.jsv.2017.12.025

[24] He, J. H., et al., Homotopy Perturbation Method for Fractal Duffing Oscillator with Arbitrary Conditions, Fractals, 30 (2022), 9, 22501651, 10.1142/s0218348x22501651

[25] Anjum, N., et al., Two-Scale Fractal Theory for the Population Dynamics, Fractals, 29 (2021), 7, 2150182, 10.1142/s0218348x21501826

[26] El-Shahed, M., Application of He's Homotopy Perturbation Method to Volterra's Integro-differential Equation, International Journal of Non-linear Sciences and Numerical Simulation, 6 (2005), 2, pp. 163-168, 10.1515/ijnsns.2005.6.2.163

[27] Nadeem, M., Li, F. Q., He-Laplace Method for Non-linear Vibration Systems and Non-linear Wave Equations, Journal of Low Frequency Noise, Vibration and Active Control, 38 (2019), 3-4, pp. 1060-1074, 10.1177/1461348418818973

[28] He, J.-H., et al., Fractal Oscillation and Its Frequency-Amplitude Property, Fractals, 29 (2021), 4, 2150105, 10.1142/s0218348x2150105x

[29] He, J.-H., et al., Forced Non-linear Oscillator in a Fractal Space, Facta Universitatis, Series: Mechanical Engineering, 20 (2022), 1, pp. 1-20, 10.22190/fume220118004h

[30] Tian, D., et al., Fractal N/MEMS: from Pull-in Instability to Pull-in Stability, Fractals, 29 (2021), 2, 2150030, 10.1142/s0218348x21500304

[31] Tian, D., He, C. H., A Fractal Micro-Electromechanical System and Its Pull-in Stability, Journal of Low Frequency Noise Vibration and Active Control, 40 (2021), 3, pp. 1380-1386, 10.1177/1461348420984041

[32] He, C. H., A Variational Principle for a Fractal Nano/Microelectromechanical (N/MEMS) System, International Journal of Numerical Methods for Heat & Fluid Flow, 33 (2023), 1, pp. 351-359, 10.1108/hff-03-2022-0191

[33] He, J.-H., et al., Pull-down Instability of the Quadratic Non-linear Oscillators, Facta Universitatis, Series: Mechanical Engineering, 21 (2023), 2, pp. 191-200, 10.22190/fume230114007h

PDF VERSION [DOWNLOAD]

Stability of initial response of exponentially damped oscillators

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence

THERMAL SCIENCE

Find this paper on

Guozhong Xiu

Hongmei Liu

Jianjing Mao

STABILITY OF INITIAL RESPONSE OF EXPONENTIALLY DAMPED OSCILLATORS