Materials or structures made of polymers or composites often exhibit non-viscous damping behavior. The non-viscous damping forces that depend on the history velocity can be expressed by the exponential non-viscous damping model. Some polymer or composite materials can be used as damping materials for kinetic energy absorption in the dynamic systems. Vibration isolator and absorber are usually considered for shock absorption. In this study, transfer ratios of vibration isolator and absorber with exponential non-viscous damping system are derived by using the Laplace transform. The dimensionless amplitude of vibration absorber with exponential non-viscous damping is derived too. Compared to viscous damping system, transfer ratio and dimensionless amplitude of exponential non-viscous damping system are influenced by the ratio of the relaxation parameter and natural frequency or the frequency of the external load. With the non-viscous damping material used in vibration control, the ratio is therefore a non-negligible factor which should be considered in analysis.
AdhikariS (2001) Eigenrelations for nonviscously damped systems. AIAA Journal39: 1624–1630.
2.
AdhikariS (2005) Qualitative dynamic characteristics of a non-viscously damped oscillator. Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences461: 2269–2288.
3.
AdhikariS (2008) Dynamic response characteristics of a nonviscously damped oscillator. Journal of Applied Mechanics75: 011003.
4.
AdhikariSWoodhouseJ (2001) Identification of damping: Part 2, non-viscous damping. Journal of Sound and Vibration243: 63–88.
5.
BandstraJP (1983) Comparison of equivalent viscous damping and nonlinear damping in discrete and continuous vibrating systems. Journal of Vibration and Acoustics-transactions of The Asme105: 382–392.
6.
CortésFMateosMElejabarrietaMJ (2009) A direct integration formulation for exponentially damped structural systems. Computers & Structures87: 391–394.
7.
CrandallSH (1970) The role of damping in vibration theory. Journal of Sound and Vibration11: 3–18.
8.
FanRMengGYangJ, et al. (2009) Experimental study of the effect of viscoelastic damping materials on noise and vibration reduction within railway vehicles. Journal of Sound and Vibration319: 58–76.
9.
García-BarruetabeñaJCortésFAbeteJM (2012) Dynamics of an exponentially damped solid rod: analytic solution and finite element formulations. International Journal of Solids and Structures49: 590–598.
10.
GaulLKleinPKempleS (1991) Damping description involving fractional operators. Mechanical Systems and Signal Processing5: 81–88.
11.
GhiringhelliGLTerraneoMVigoniE (2013) Improvement of structures vibroacoustics by widespread embodiment of viscoelastic materials. Aerospace Science and Technology28: 227–241.
LázaroM (2016) Eigensolutions of non-proportionally damped systems based on continuous damping sensitivity. Journal of Sound and Vibration363: 532–544.
14.
LázaroM (2019a) Approximate critical curves in exponentially damped nonviscous systems. Mechanical Systems and Signal Processing122: 720–736.
15.
LázaroM (2019b) Critical damping in nonviscously damped linear systems. Applied Mathematical Modelling65: 661–675.
16.
LeeC-L (2020a) Proportional viscous damping model for matching damping ratios. Engineering Structures207: 110178.
17.
LeeC-L (2020b) Sparse proportional viscous damping model for structures with large number of degrees of freedom. Journal of Sound and Vibration478: 115312.
LiLHuY (2016) State-space method for viscoelastic systems involving general damping model. AIAA Journal54: 3290–3295.
20.
LiLHuYDengW, et al. (2015) Dynamics of structural systems with various frequency-dependent damping models. Frontiers of Mechanical Engineering10: 48–63.
21.
LiLHuYWangX (2014) Harmonic response calculation of viscoelastic structures using classical normal modes: an iterative method. Computers & Structures133: 39–50.
22.
LinRMNgTY (2019) An iterative method for exact eigenvalues and eigenvectors of general nonviscously damped structural systems. Engineering Structures180: 630–641.
23.
LiuQ (2014) Computational method of the dynamic response for nonviscously damped structure systems. Journal of Engineering Mechanics140.
24.
LiuQ (2018) Stationary random response of non-viscously damped polymer matrix composite structure systems. Composite Structures202: 1–8.
25.
MouritzAPGellertEBurchillP, et al. (2001) Review of advanced composite structures for naval ships and submarines. Composite Structures53: 21–42.
26.
NaylorVD (1970) Some fallacies in modern damping theory. Journal of Sound and Vibration11: 278–280.
27.
PalmeriAMuscolinoG (2011) A numerical method for the time-domain dynamic analysis of buildings equipped with viscoelastic dampers. Structural Control and Health Monitoring18: 519–539.
28.
PanYWangY (2015) Iterative method for exponential damping identification. Computer-Aided Civil and Infrastructure Engineering30: 229–243.
29.
PapouliaKDKellyJM (1997) Visco-hyperelastic model for filled rubbers used in vibration isolation. Journal of Engineering Materials and Technology-transactions of The Asme119: 292–297.
30.
PuthanpurayilAMCarrAJDhakalRP (2014) A generic time domain implementation scheme for non-classical convolution damping models. Engineering Structures71: 88–98.
31.
RaoMD (2003) Recent applications of viscoelastic damping for noise control in automobiles and commercial airplanes. Journal of Sound and Vibration262: 457–474.
32.
ReggioADe AngelisMBettiR (2013) A state-space methodology to identify modal and physical parameters of non-viscously damped systems. Mechanical Systems and Signal Processing41: 380–395.
33.
ShenRQianXZhouJ (2019) Direct integration for non-viscous structural systems and its simplification. Mechanics Research Communications95: 8–15.
34.
ShenRQianXZhouJ (2020) Identification of linear non-viscous damping with different kernel functions in the time domain. Journal of Sound and Vibration487: 115623.
35.
ShenRQianXZhouJ, et al. (2021) A time integration method based on the weak form Galerkin method for non-viscous damping systems. Mechanical Systems and Signal Processing151: 107361.
36.
ShenRQianXZhouJ, et al. (2022) Study on experimental identification and alternative kernel functions of non-viscous damping in time domain. International Journal of Applied Mechanics. (Accepted).
37.
SieberJWaggDJAdhikariS (2008) On the interaction of exponential non-viscous damping with symmetric nonlinearities. Journal of Sound and Vibration314: 1–11.
38.
SuLMeiS-QPanY-H, et al. (2019) Experimental identification of exponential damping for reinforced concrete cantilever beams. Engineering Structures186: 161–169.
39.
WagnerNAdhikariS (2003) Symmetric state-space method for a class of nonviscously damped systems. AIAA Journal41: 951–956.
40.
WangM-FWangZ-H (2018) Time-domain integration methods of exponentially damped linear systems. International Journal for Numerical Methods in Engineering114: 347–374.
41.
WoodhouseJ (1998) Linear damping models for structural vibration. Journal of Sound and Vibration215: 547–569.
42.
WuC (2008) Fundamentals of Analysis and Control for Engineering Vibration in Chinese. Beijing: China Machine Press.
43.
WuXHeHChenG (2019) A new state-space method for exponentially damped linear systems. Computers & Structures212: 137–144.
44.
ZhouXQYuDYShaoXY, et al. (2016) Research and applications of viscoelastic vibration damping materials: a review. Composite Structures136: 460–480.
