An analytical approach is investigated to model ground-plate interaction based on modal decomposition and the two-dimensional Fourier transform. A finite rectangular plate subjected to flexural vibration is coupled with the ground and modeled with the Kirchhoff hypothesis. A Navier equation represents the stratified ground, assumed infinite in the x- and y-directions and free at the top surface. To obtain an analytical solution, modal decomposition is applied to the structure and a Fourier Transform is applied to the ground. The result is a new tool for analyzing ground-plate interaction to resolve this problem: ground cross-modal impedance. It allows quantifying the added-stiffness, added-mass, and added-damping from the ground to the structure. Similarity with the parallel acoustic problem is highlighted. A comparison between the theory and the experiment shows good matching. Finally, specific cases are investigated, notably the influence of layer depth on plate vibration.
Mitigation measures against railway vibration in buildings include elastomeric mounts or springs inserted between building foundations and upper-structures. This paper aims at evaluating on site the field performance of such building base isolation. Two performance indicators are defined
and used, both expressed as insertion gain: a Power Flow insertion Gain (PFIG) based on the power transmitted to the building upper-structure, and a Building Insertion Gain Indicator (BIGI) based on the building floor velocities. The paper shows that both indicators can be used to evaluate
the field performance of base-isolated buildings: the PFIG can be indirectly obtained from local measurements of the isolator transmissibility and some knowledge of the mobility magnitudes of the building structures in contact and the BIGI indirectly obtained from measurements of the treated
building transmissibility (as defined in ISO/TS 14837-31) and some knowledge of the transmissibility of similar but untreated buildings. The methods are successfully validated using a numerical model of a 2D ground-building configuration easy to calculate and assumed realistic enough. The
paper ends with a discussion on the practicality of obtaining these performances on- site in real buildings.
The aim of this article is to introduce a method to mitigate ground surface vibration through a flexural plate coupled to the ground and acting as a horizontal wave barrier. Using the thin plate hypothesis, two flexural plates are coupled to the ground, the first plate being the excited plate and the second plate the horizontal wave barrier. For instance, the first plate may represent a slab track and be excited by the tramway wheels. A solution to the problem can be found using a spatial two-dimensional Fourier transform of the elastodynamics equation for the ground and a modal decomposition for the flexural plate vibration. The authors show that vibration is substantially mitigated by the horizontal wave barrier and depends on its thickness and width. When the top surface wavelength becomes smaller than twice the plate width, the horizontal wave barrier acts as a wave barrier in the frequency range of interest, i.e., from 20 Hz.
Anew kind of inter modal impedance has recently been developed taking into account plate-ground interaction. This impedance is called the ground inter modal impedance. The inter modal impedance allows to understand the transfer of energy from as tructure to the surrounding medium. The aim of this paper is to compare two types of inter modal impedance in different cases of plate/medium coupling on the top surface. The twot ypes of impedance are acoustical inter modal impedance and the recently developed ground inter modal impedance. An extension of the usual coupling case with fluid will be introduced for afinite simply supported plate coupled with asemi-infinite ground medium. Inter modal impedance can be used to adapt the interpretation made in the acoustical case for the ground case, and to exhibit differences between acoustical and ground media. The paper points out major differences at the origin of the flat plate velocity response when coupled with aground medium, principally due to the excitation of the shear wave in the ground medium which do not exist in the acoustic medium. The influence of the plate surface on the RMS plate velocity is presented as well as the influence of the ground stratification PACS no. 43.40.Dx, 43.40.Rj
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