Thin elastic coatings and interfaces arise in numerical engineering applications, including high contrast laminates involving soft layers. Forced time-harmonic motions are considered not making any restriction on the vibration frequency. Long wave, multimode approximations are derived from the original 3D setup. It is governed by 2D equations with coefficients depending on trigonometric functions of the frequency parameter. The related explicit dispersion relations appear to be of general interest as well. Although formulations are oriented to the analysis of the effect of prescribed stresses slowly varying along the faces, they are also useful of various resonance responses due to concentrated loading. Numerical comparisons between exact results and asymptotic predictions are demonstrated.
References
[1] Erbaş, B., Itskov, M., Kaplunov, J. and Prikazchikov, D., 2024. Multimode long-wave approximation for a viscoelastic coating subject to antiplane shear. Zeitschrift für angewandte Mathematik und Physik, 75(6), p.234.
[2] Ege, N., Erbaş, B., Kaplunov, J., Yücel, H., Dynamics of a thin elastic coating, to be submitted to International Journal of Engineering Science.
[3] Prikazchikova, L., Rege, A., Kaplunov, J. and Prikazchikov, D., 2024. Low-frequency propagating and evanescent waves in strongly inhomogeneous sandwich plates. Zeitschrift für angewandte Mathematik und Physik, 75(6), pp.1-14.
[4] Cherednichenko, K., Kaplunov, J. and Prikazchikov, D., 2020, October. Global long wave approximations for elastic wave guides. In 11th International Conference on Structural Dynamic, EURODYN (pp. 2464-2474). ICMES.
| Subject : | : | oral |
| Topics | : | 6-3 - Dynamic and transient phenomena, dynamic phase transitions, nonlinear waves |
| PDF version | : |  PDF version |
