The motion of guided waves in viscoelastic waveguides is generally accompanied by energy transport and dissipation. Envisioned applications demand an accurate understanding of both propagating and evanescent of waves related to dispersive properties. This paper uses the isogeometric analysis to consider wave characteristics in stressed viscoelastic waveguides based on the Floquet’s principle. Parameterized wave equation considering the acoustoelasticity and viscoelasticity is obtained from the virtual power principle and the updated Lagrangian format. In addition, the energy velocity of a guided wave mode is derived in the linear incremental theory. Error estimations of cutoff frequencies for flexural wave modes are shown for the comparison between the wave isogeometric analysis method and the classic wave finite element method. The results indicate the former can provide smaller error compared with the latter. Then, phase velocity, energy velocity, and wave attenuation are presented for two kinds of viscoelastic structures (double cylindrical rods, functionally graded material plates) under different loaded cases. The effects of stress and viscoelasticity are also demonstrated in detail.
BiotMA.The influence of initial stress on elastic waves. J Appl Phys1940; 11: 522–530.
6.
HayesM.Wave propagation and uniqueness in prestressed elastic solids. Proc Roy Soc Lond1963; 274: 500–506.
7.
WilliamsRAMalvernLE.Harmonic dispersion analysis of incremental waves in uniaxially prestressed plastic and viscoplastic bars, plates, and unbounded media. J Appl Mech1969; 36: 59–64.
8.
MottG.Elastic waveguide propagation in an infinite isotropic solid cylinder that is subjected to a static axial stress and strain. J Acoust Soc Am1973; 53: 268–273.
9.
WillsonAJ.Wave propagation in thin pre-stressed elastic plates. Int J Eng Sci1977; 15: 245–251.
10.
CookLPHolmesM.Waves and dispersion relations for hydroelastic systems. SIAM J Appl Math1981; 41: 271–287.
11.
CavigliaGMorroA.Energy flux and dissipation in pre-stressed solids. Acta Mech1998; 128: 209–216.
12.
ChenFWilcoxPD.The effect of load on guided wave propagation. Ultrasonics2007; 47: 111–122.
13.
FrikhaATreyssedeFCartraudP.Effect of axial load on the propagation of elastic waves in helical beams. Wave Motion2011; 48: 83–92.
14.
DubucBEbrahimkhanlouASalamoneS.The effect of applied stress on the phase and group velocity of guided waves in anisotropic plates. J Acoust Soc Am2017; 142: 3553.
15.
YuJGZhangCZ.Effects of initial stress on guided waves in orthotropic functionally graded plates. Appl Math Model2014; 38: 464–478.
16.
LovedayPW.Semi-analytical finite element analysis of elastic waveguides subjected to axial loads. Ultrasonics2009; 49: 298.
17.
LovedayPWWilcoxPD. Guided wave propagation as a measure of axial loads in rails, Health Monitoring of Structural and Biological Systems, Proc SPIE 2010; 7650: 765023-1-765023-8.
18.
MazzottiMMarzaniABartoliI, et al. Guided waves dispersion analysis for prestressed viscoelastic waveguides by means of the safe method. Int J Solids Struct2012; 49: 2359–2372.
19.
TreyssedeFFrikhaACartraudP.Mechanical modeling of helical structures accounting for translational invariance. Part 2: Guided wave propagation under axial loads. Int J Solids Struct2013; 50: 1383–1393.
PeddetiKSanthanamS.Dispersion curves for Lamb wave propagation in prestressed plates using a semi-analytical finite element analysis. J Acoust Soc Am2018; 143: 829.
22.
MeadDM.Wave propagation in continuous periodic structures: Research contributions from Southampton, 1964–1995. J Sound Vib1996; 190: 495–524.
23.
GryLGontierC.Dynamic modelling of railway track: A periodic model based on a generalized beam formulation. J Sound Vib1997; 199: 531–558.
24.
ThompsonDJ.Wheel–rail noise generation, part I: Introduction and interaction model. J Sound Vib1993; 161: 387–400.
25.
ZhouWJIchchouMN.Wave propagation in mechanical waveguide with curved members using wave finite element solution. Comput Meth Appl Mech Eng2010; 199: 2099–2109.
26.
WakiYMaceBRBrennanMJ.Numerical issues concerning the wave and finite element method for free and forced vibrations of waveguides. J Sound Vib2009; 327: 92–108.
27.
MencikJM.A model reduction strategy for computing the forced response of elastic waveguides using the wave finite element method. Comput Meth Appl Mech Eng2012; 229–232: 68–86.
28.
LiCLHanQLiuYJ, et al. Investigation of wave propagation in double cylindrical rods considering the effect of prestress. J Sound Vib2015; 353: 164–180.
29.
LiuYJHanQLiCL, et al. Numerical investigation of dispersion relations for helical waveguides using the scaled boundary finite element method. J Sound Vib2014; 333: 1991–2002.
30.
GravenkampHManHSongC, et al. The computation of dispersion relations for three-dimensional elastic waveguides using the scaled boundary finite element method. J Sound Vib2013; 332: 3756–3771.
31.
LiuYJHanQLiCL, et al. Numerical modeling of wave propagation for damped elbow pipes using Fourier–Legendre spectral element method in polar coordinates. Arch Appl Mech2016; 86: 1–14.
XuGMourrainBDuvigneauR, et al. Parameterization of computational domain in isogeometric analysis: Methods and comparison. Comput Meth Appl Mech Eng2011; 200: 2021–2031.
34.
XuGMourrainBDuvigneauRGalligoA.Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications. CAD Comput Aided Design2013; 45: 395–404.
35.
ChristensenRM.Theory of Viscoelasticity. 2nd Ed.Mineola, NY: Dover Publications, 2010.
36.
AuldB.Acoustic Fields and Waves in Solids, Vol. II. Malabar, FL: Robert E. Krieger, 1990.
