A new formal solution for the multiple scattering of plane harmonic waves by a group of arbitrary configuration tubular piles in an elastic total space is derived. Each order of scattering satisfies prescribed boundary conditions at the interface of tubular piles, which is delivered as the sum of incident and scattering waves. The first order performs the scattering wave by each scattered pile and the subsequent orders resulted from the excitation of each pile of first order of scattering from the remaining tubular piles. Advanced scattering orders can be regarded as the same manners. Several series of scattering coefficients are figured out with the aids of addition theorem so that the exact steady-state solution for the scattered displacement and stress is obtained. Particularly, when internal diameter of tubular piles tends to be infinitely small, it degenerates to a solid pile problem. By imposing the normalized displacement amplitudes and transmissibility indices, the influences of specific parameters such as scattering orders, internal and external diameter ratio of piles, pile material rigidity, position and distances between tubular pile and pile rows, and pile numbers are discussed. Certain recommended conclusions have been drawn as the guidelines of practical engineering design for discontinuous barrier of tubular piles.
The text visualization in 3D environment is quite complex due to the characteristics of 3D scene. In this paper we propose to study a group of 3D text information visualization based on parameter study. The primary text information visualization position is set as an initial point. Then, several different level-of-details for the texts are designed as the Event LoDs. Firstly, the parameter study for different EventLoDs is conducted, followed by the parameter study for the different size value. Based on the two groups of parameter study result, a use case is applied to test the effect. Finally, the summary and future work is given.
Based on Biot's saturated soil wave theory, using wave function expansion method, theoretical solutions of multiple scattering of plain P 1 waves are achieved by rows of cavities as barrier with arbitrarily arranged cavities in saturated soil. Undetermined complex coefficients after wave function expansion are obtained by cavities-soil stress and displacement free boundary conditions. Numerical examples are used to investigate variation of dimensionless displacement amplitude at the back and force of cavities barrier under P 1 wave incident, and it is also discussed that the main parameters influenced isolation effect such as scattering orders, separation of cavities, distances between cavity rows, numbers of cavities, and arrangement of barriers. The results clearly demonstrate optimum design proposals with rows of cavities: with the multiple scattering order increases, the displacement amplitude tends to converge and the deviation caused by subsequent scattering cannot be neglected; it will obtain higher calculation accuracy when the order of scattering is truncated at = 4; it is considered to select 2.5 ≤ p / ≤ 3.0 and 2.5 ≤ ℎ/ ≤ 3.5, while designing cavity spacing and row-distance, respectively. The isolation properties of elastic waves with rectangular arrangement (counterpoint) are weaker than that with hexagonal arrangement (counterchanged) when the row-distance of barrier is uniform.
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