Hollow cylinders often exhibit backward propagation modes whose group and phase velocities have opposite directions, and these exhibit a minimum possible frequency at which the group velocity vanishes at a nonzero wavenumber. These zero-group-velocity (ZGV) points are associated with resonant conditions in the medium. On the basis of ZGV resonances, a non-contact and laser ultrasound technique has been developed to measure elastic constants of hollow pipes. This paper provides a theoretical and numerical investigation of the influence of the contained liquid on backward waves and associated ZGV modes, in order to explore whether this ZGV technique is suitable for in-service non-destructive evaluations of liquid-filled pipes. Dispersion spectra and excitation properties have been analyzed. It is found that the presence of the liquid causes an increased number of backward modes and ZGVs which are highly excitable by a point source. In addition, several guided modes twice undergo a change of sign in the slopes of their dispersion curves, leading to two ZGV points. This phenomenon of double ZGVs in one backward wave, which is caused by strong mode repulsions, has not been found in isotropic hollow cylinders, but it can be observed in a fluid-filled thin-walled pipe.

It is known that modes in axially uniform waveguides exhibit backward-propagation characteristics for which group and phase velocities have opposite signs. For elastic plates, group velocities of backward Lamb waves depend only on Poisson's ratio. This paper explores ways to achieve a large group velocity of a backward mode in hollow cylinders by changing the outer to inner radius ratio, in order that such a mode with strong backward-propagation characteristics may be used in acoustic logging tools. Dispersion spectra of guided waves in hollow cylinders of varying radii are numerically simulated to explore the existence of backward modes and to choose the clearly visible backward modes with high group velocities. Analyses of group velocity characteristics show that only a small number of low order backward modes are suitable for practical use, and the radius ratio to reach the highest group velocity corresponds to the accidental degeneracy of neighboring pure transverse and compressional modes at the wavenumber k = 0. It is also shown that large group velocities of backward waves are achievable in hollow cylinders made of commonly encountered materials, which may bring cost benefits when using acoustic devices which take advantage of backward-propagation effects.

The dispersion and excitation characteristics of the guided waves in a rod surrounded by an infinite solid medium (cladding) are investigated. First, the bisection technique is employed to find all the roots of the dispersion function on the basis of theoretical analysis and to obtain the complex phase and group velocity dispersion curves of the guided modes. Second, according to their different dispersion characteristics, the guided modes are divided into two categories: normal modes and Stoneley modes. And it is concluded that the normal modes merely exist in the “hard cladding” model in which the cladding’s shear velocity is larger than the rod’s; while the Stoneley modes in cylindrical interface are highly dispersive and merely exist in the model whose acoustical parameters satisfied the existence condition of the Stoneley waves. Third, the seldom discussed issue, the excitation mechanisms of the guided waves, excited by three source models: symmetric point source, axial and radial force sources, are simulated respectively. Attention is paid on the dominant mode which has better excitation sensitivity and the suitable excitation frequency range. Moreover, the propagation characteristics of the Stoneley modes, ignored in previous references, are analyzed and compared with those of the normal modes.

Temperature has a complex effect on acoustic dispersion in dilute gases. In this paper, the effect of temperature on the acoustic dispersion of dilute gases is analyzed theoretically and experimentally. Theoretically, the Navier–Stokes (NS) equation and the Greenspan's theory, which includes the rotational-relaxation correction, are applied to calculate the dispersive sound speed. It is concluded that the temperature affects the molecular translational relaxation and the rotational relaxation by influencing the average molecular collision frequency and the relaxation collision number, respectively, and thus, change the amplitude of the acoustic dispersion. Numerical calculations led to the conclusion that both translational and rotational dispersions weakened as the temperature decreased. Experimentally, sound speed measurements of 21–40 kHz acoustic waves were also carried out in gaseous nitrogen at temperatures ranging from −70 °C to 20 °C and pressures of 150–10⁵ Pa. Theoretical predications indicate that the speed of sound should increase with decreasing pressure at all temperatures, and the degree of dispersion should diminish at lower temperatures. The experimental observation of dispersion is consistent with theory within experimental error (1%) but was not able to distinguish the small (0.01%) increase in sound speed expected at 150 Pa.

In clad rods, the dispersion properties of firstorder flexural [F(1, 1)] modes can differ from other modes. Normal and Stoneley modes and the existence criteria for four F(1, 1) modes are investigated. We focus on low-frequency anomalous dispersion, which occurs only in F(1, 1) modes and is sensitive to shear velocity.

火星声探测技术逐渐成为火星探测的一种重要手段。为了探测火星声源，需研究稀薄低温火星大气中的声速和声衰减、建立分层大气中的声传播模型。本文提出了一种结合Navier-Stokes (NS)声波方程和变组分混合气体的声速模型，考虑了火星极端稀薄大气中的声频散，将火星声速剖面模拟计算拓展到0-250 km海拔范围，并讨论了NS声速剖面的适用条件。本文实验验证了低压、低温环境中，在分子平动、旋转和振动弛豫作用下，三原子二氧化碳中存在明显声频散。随后分别基于频散NS声速和无频散理想气体声速剖面，模拟了地面声源和高空声源产生的不同频率声波的传播路径。研究发现声频散显著影响了声传播路径，降低了声线首次折返高度、缩短了声线折回火星地表的距离、减小了第一声影区的范围等。而且频率越高、声源海拔高度越高，频散对声传播的影响越剧烈，NS方程的连续性假设失效，更高频的声波需要基于Boltzmann方程和分子模拟法建立声频散模型。