Study of flexural wave propagation through a cable stayed beam subjected to a moving load

A physical perspective of the propagation and attenuation of flexural waves is presented in this paper for the dynamic behaviors of cable stayed beams subjected to a moving load. Based on the method of reverberation-ray matrix (MRRM), the waveform solutions of the wave equations of a simplified beam-cable system subjected to a moving load (hereinafter referred to as a beam-cable system) are given, and the theory is verified by a numerical example. The dynamic response of cable stayed beams is decomposed into nine kinds of flexural waves, including traveling waves, near-field waves, and nondispersive waves, according to the wavenumber characteristics. Numerical examples are analyzed to demonstrate the propagation characteristics of flexural waves through cable stayed beams. Numerical results show that the flexural waves in the cable stayed beams are mainly low-frequency waves whose frequencies are less than 3 times the structural fundamental frequency, which can be used to further improve the computational efficiency of response analysis method based on MRRM, and the proportion of high-frequency components increases gradually with increasing structural stiffness. The near-field wave can be transformed into a traveling shear wave when its frequency is larger than the critical frequency, which decreases with increasing radius of gyration and decreasing elastic modulus of the beam. With the increase in the radius of gyration and the elastic modulus of the beam, the attenuation effect of the near-field wave weakens. The wave velocity and the wave dispersion effect have a positive correlation with the stiffness-related parameters of the beam-cable system. The study of the effect of the beam-cable system parameters on flexural wave propagation characteristics can be applied to achieve a better dynamic design for engineering structures.

Propagation and Dispersion of Lightning-Generated Whistlers Measured From the Van Allen Probes

We study the propagation and attenuation of lightning-generated whistler (LGW) waves in near-Earth space (L ≤ 3) through the statistical study of three specific quantities extracted from data recorded by NASA’s Van Allen Probes mission, from 2012 to 2019: the LGW electric and magnetic power attenuation with respect to distance from a given lightning stroke, the LGW wave normal angle in space, and the frequency-integrated LGW refractive index. We find that LGW electric field wave power decays with distance mostly quadratically in space, with a power varying between -1 and -2, while the magnetic field wave power decays mostly linearly in space, with a power varying between 0 and -1. At night only, the electric wave power decays as a quadratic law and the magnetic power as a linear law, which is consistent with electric and magnetic ground measurements. Complexity of the dependence of the various quantities is maximal at the lowest L-shells (L < 1.5) and around noon, for which LGW are the rarest in Van Allen Probes measurements. In-space near-equatorial LGW wave normal angle statistics are shown for the first time with respect to magnetic local time (MLT), L-shell (L), geographic longitude, and season. A distribution of predominantly electrostatic waves is peaked at large wave normal angle. Conversely, the distribution of electromagnetic waves with large magnetic component and small electric component is peaked at small wave normal angle. Outside these limits, we show that, as the LGW electric power increases, the LGW wave normal angle increases. But, as the LGW magnetic power increases, the LGW wave normal angle distribution becomes peaked at small wave normal angle with a secondary peak at large wave normal angle. The LGW mean wave-normal angle computed over the whole data set is 41.6° with a ∼24° standard deviation. There is a strong MLT-dependence, with the wave normal angle smaller for daytime (34.4° on average at day and 46.7° at night). There is an absence of strong seasonal and continental dependences of the wave-normal angle. The statistics of the LGW refractive index show a mean LGW refractive index is 32 with a standard deviation of ∼26. There is a strong MLT-dependence, with larger refractive index for daytime 36) than for nighttime (28). Smaller refractive index is found during Northern hemisphere summer for L-shells above 1.8, which is inconsistent with Chapman ionization theory and consistent with the so-called winter/seasonal anomaly. Local minima of the mean refractive index are observed over the three continents. Cross-correlation of these wave parameters in fixed (MLT, L) bins shows that the wave normal angle and refractive index are anti-correlated; large (small) wave normal angles correspond with small (large) refractive indexes. High power attenuation during LGW propagation from the lightning source to the spacecraft is correlated with large refractive index and anti-correlated with small wave normal angle. Correlation and anti-correlation show a smooth and continuous path from one regime (i.e. large wave normal angle, small refractive index, low attenuation) to its opposite (i.e. small wave normal angle, large refractive index, large attenuation), supporting consistency of the results.

Lightning‐Generated Whistler Amplitudes Measured by the Van Allen Probes

<p>This talk will show a statistical analysis of both electric and magnetic field wave amplitudes of very low frequency lightning‐generated whistlers (LGWs) based on the equivalent of 11.5 years of observations made by the Van Allen Probes. We complement this analysis with data from the ground‐based World Wide Lightning Location Network (WWLLN) to explore differences between satellite and ground‐based measurements. We will discuss how LGW mean amplitudes were generally found to be low compared with other whistler mode waves even though there exists extreme events (1 out of 5,000) that can reach 100 pT and contribute strongly to the mean power below L = 2. We will reveal a region of low wave amplitude existing below L=2 thanks to the denser dayside ionosphere, which prevents the intense equatorial lightning VLF waves from propagating through it. Below L = 1.5 at all MLT, LGW amplitudes are found to be weak while the ground‐level lightning activity is maximal. This suggests a difficulty of lightning VLF waves to penetrate / propagate / remain at low L‐shells, certainly due at least to the denser ionosphere during daytime. On the contrary, the mean LGW magnetic power (or RMS) remains nearly constant with respect to L‐shell. We will explain that this is due to strong to extreme LGWs that dominate the wave mean power to the point of compensating the decay of LGW occurrence at low L‐shell. Even though extreme LGW were found to be very powerful, particularly at low L and during night, the mean electric/magnetic power remains low compared with other whistler waves. This implies that LGW resonant effects on electrons are consequently long‐term effects that contribute to “age” trapped inner belt electron populations.</p>

Michell Investigation of the Significant Influence on the Hydrodynamic of a Warp-Chine Pentamaran

This study attempted to investigate the hydrodynamic performance of various pentamaran configurations with a focus on the interference flow around the component hulls. A computer simulation was conducted based on Michell’s thin ship theory alongside a commercial CFD computation as a comparison. Experiments in the towing tank were performed to validate the numerical calculations, resulting in some hydrodynamic characteristics on the far-field wave pattern, wave interference, wave resistance, and total resistance. Analyses on both transversal and divergent waves were performed to assess the magnitude of wave resistance occurring due to the placement of the side hull to the main hull. Analyses on both waves were also conducted to assess the magnitude of wave resistance due to the placement of outriggers. Looking at the results, numerical calculations based on Michell’s theory were in parallel with experimental data, particularly at Fn greater than .4. Michell’s theory was observed as doing a little preferable agreement with the results of experiments than CFD. Besides, flow patterns obtained numerically from Michell’s and CFD analyses appeared as identical to photographs observed in a towing tank. This investigation identified that a configuration with aligning placement of the main to side hull on the formation of arrow tri-hull, near the Kelvin angle, would cancel the wave formed by the leading hull and can be used as a practical setting to reduce the total wave resistance.