A proof is offered for the equivalence of the energy velocity and the group velocity in the case where the group velocity may be negative while the wavenumber is positive. The explicit expression for both the energy ...A proof is offered for the equivalence of the energy velocity and the group velocity in the case where the group velocity may be negative while the wavenumber is positive. The explicit expression for both the energy velocity and the group velocity is obtained for waves in an isotropic homogeneous plate waveguide. Calculations show the values of the group velocity or the energy velocity to be negative for some frequencies.展开更多
The one-dimensional monoatomic lattice chain connected by nonlinear springs is investigated, and the asymptotic solution is obtained through the Lindstedt-Poincar′e perturbation method. The dispersion relation is der...The one-dimensional monoatomic lattice chain connected by nonlinear springs is investigated, and the asymptotic solution is obtained through the Lindstedt-Poincar′e perturbation method. The dispersion relation is derived with the consideration of both the nonlocal and the active control effects. The numerical results show that the nonlocal effect can effectively enhance the frequency in the middle part of the dispersion curve.When the nonlocal effect is strong enough, zero and negative group velocities will be evoked at different points along the dispersion curve, which will provide different ways of transporting energy including the forward-propagation, localization, and backwardpropagation of wavepackets related to the phase velocity. Both the nonlinear effect and the active control can enhance the frequency, but neither of them is able to produce zero or negative group velocities. Specifically, the active control enhances the frequency of the dispersion curve including the point at which the reduced wave number equals zero, and therefore gives birth to a nonzero cutoff frequency and a band gap in the low frequency range. With a combinational adjustment of all these effects, the wave propagation behaviors can be comprehensively controlled, and energy transferring can be readily manipulated in various ways.展开更多
文摘A proof is offered for the equivalence of the energy velocity and the group velocity in the case where the group velocity may be negative while the wavenumber is positive. The explicit expression for both the energy velocity and the group velocity is obtained for waves in an isotropic homogeneous plate waveguide. Calculations show the values of the group velocity or the energy velocity to be negative for some frequencies.
基金Project supported by the National Natural Science Foundation of China(Nos.11532001and 11621062)the Fundamental Research Funds for the Central Universities of China(No.2016XZZX001-05)
文摘The one-dimensional monoatomic lattice chain connected by nonlinear springs is investigated, and the asymptotic solution is obtained through the Lindstedt-Poincar′e perturbation method. The dispersion relation is derived with the consideration of both the nonlocal and the active control effects. The numerical results show that the nonlocal effect can effectively enhance the frequency in the middle part of the dispersion curve.When the nonlocal effect is strong enough, zero and negative group velocities will be evoked at different points along the dispersion curve, which will provide different ways of transporting energy including the forward-propagation, localization, and backwardpropagation of wavepackets related to the phase velocity. Both the nonlinear effect and the active control can enhance the frequency, but neither of them is able to produce zero or negative group velocities. Specifically, the active control enhances the frequency of the dispersion curve including the point at which the reduced wave number equals zero, and therefore gives birth to a nonzero cutoff frequency and a band gap in the low frequency range. With a combinational adjustment of all these effects, the wave propagation behaviors can be comprehensively controlled, and energy transferring can be readily manipulated in various ways.
