Surface wrinkling, a film bonded on a pre-strained elastomeric substrate can form periodic wrinkling patterns, is a common phenomenon in daily life. In existing theoretical models, the film is much thinner than the su...Surface wrinkling, a film bonded on a pre-strained elastomeric substrate can form periodic wrinkling patterns, is a common phenomenon in daily life. In existing theoretical models, the film is much thinner than the substrate so that the substrate can be considered to be elastomeric with infinite thickness. In this paper, the effect of finite substrate thickness is analyzed theoretically for free boundary condition cases. Based on the minimum potential energy principle, a theoretical model is established, and the wave length and amplitude of the wrinkling pattern are obtained. When the thickness of the substrate is more than 200 times larger than the thickness of the film, the results of this study agree well with the results obtained from the previous models for infinite substrate thickness. However, for thin substrates, the effect of finite substrate thickness becomes significant. The model given in this paper accurately describes the effect of finite substrate thickness, providing important design guidelines for future thin-film-on-substrate systems such as stretchable electronic devices.展开更多
The patch antennas with an array of pins （pin array patch antennas） with excellent radiation characteristics are investigated for various substrate thicknesses. The radiation in the horizontal plane of a pin array p...The patch antennas with an array of pins （pin array patch antennas） with excellent radiation characteristics are investigated for various substrate thicknesses. The radiation in the horizontal plane of a pin array patch antenna is very small compared to that of a conventional patch antenna. And the increase of forward radiation and the decrease of backward radiation of a pin array patch antenna are obtained than those conventional one＇s. Also the half-power beamwidth of E -plane radiation pattern of a pin array patch antenna is narrower compared to that of the conventional so that the directivity is improved.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11572022 and 11172022)
文摘Surface wrinkling, a film bonded on a pre-strained elastomeric substrate can form periodic wrinkling patterns, is a common phenomenon in daily life. In existing theoretical models, the film is much thinner than the substrate so that the substrate can be considered to be elastomeric with infinite thickness. In this paper, the effect of finite substrate thickness is analyzed theoretically for free boundary condition cases. Based on the minimum potential energy principle, a theoretical model is established, and the wave length and amplitude of the wrinkling pattern are obtained. When the thickness of the substrate is more than 200 times larger than the thickness of the film, the results of this study agree well with the results obtained from the previous models for infinite substrate thickness. However, for thin substrates, the effect of finite substrate thickness becomes significant. The model given in this paper accurately describes the effect of finite substrate thickness, providing important design guidelines for future thin-film-on-substrate systems such as stretchable electronic devices.
文摘The patch antennas with an array of pins （pin array patch antennas） with excellent radiation characteristics are investigated for various substrate thicknesses. The radiation in the horizontal plane of a pin array patch antenna is very small compared to that of a conventional patch antenna. And the increase of forward radiation and the decrease of backward radiation of a pin array patch antenna are obtained than those conventional one＇s. Also the half-power beamwidth of E -plane radiation pattern of a pin array patch antenna is narrower compared to that of the conventional so that the directivity is improved.
