Quantification of Site City Interaction Effects on Responses of Buildings and Basin Under Realistic Earthquake Loading for Development of Economic Smart City

The paper presents the quantification of site-city-interaction (SCI) effects on the responses of buildings of a city and free field motion under realistic earthquake loading for the economic development of a smart city. The state of the art pseudo-dynamic earthquake rupture is implemented in the existing fourth-order viscoelastic staggered-grid SH-wave finite-difference program, and simulated results validated. SH-wave responses of various homogeneous and heterogeneous cities situated on horizontal sediment layer as well as in 2D heterogeneous basins are simulated and analyzed for different dynamic parameters of the buildings. The simulated SCI effects using realistic earthquake loading reveals a reduction of transfer function (TF) of buildings in a wide frequency bandwidth. This finding is conflicting with the reported splitting of bandwidth of the FoSB in the past SCI studies, carried out using simple plane incident wave-front with a single zero-phase wavelet. The obtained largest SCI effects on a building was highly dependent on the building type, city and basin heterogeneity in contrast to the general perception that it should be maximum at centre of city. It is also obtained that SCI effects are always beneficial to buildings when fundamental frequency of building on rock FoSR <1.4FoB( FoB is the fundamental frequency of basin/sediment layer). The obtained reduction of of building of city as well as free field motion due to the effects of SCI corroborates with the past SCI studies. The increase of coupling between the buildings and basin due to an increase of building density causes an increase of SCI effects on the responses of both the buildings and free field motion. The SCI effects in the case of buildings with low damping are beneficial during an earthquake. It is recommended that the smart city should be homogeneous in nature and of buildings should be less than around 1.4 times the of the underlying basin/sediment deposit and buildings should preferably be a steel one.

Acoustic scattering by a semi-infinite angular sector with impedance boundary conditions, II: the far-field asymptotics

This work is a natural continuation of our recent study devoted to the scattering of a plane incident wave by a semi-infinite impedance sector. We develop an approach that enables us to compute different components in the far-field asymptotics. The method is based on the Sommerfeld integral representation of the scattered wave field, on the careful study of singularities of the integrand and on the asymptotic evaluation of the integral by means of the saddle point technique. In this way, we describe the waves reflected from the sector, diffracted by its edges or scattered by the vertex as well as the surface waves. Discussion of the far-field in the so-called singular directions (or in the transition zones) is also addressed.

Graded resonator arrays for spatial frequency separation and amplification of water waves

A structure capable of substantially amplifying water waves over a broad range of frequencies at selected locations is proposed. The structure consists of a small number of C-shaped cylinders in a line array, with the cylinder properties graded along the array. Using linear potential-flow theory, it is shown that the energy carried by a plane incident wave is amplified within specified cylinders for wavelengths comparable to the array length and for a range of incident directions. Transfer-matrix analysis is used to attribute the large amplifications to excitation of local Rayleigh–Bloch waves and gradual slowing down of their group velocity along the array.

On the dynamic interaction between a microdefect and a main crack

A generalized theoretical approach is presented for the dynamic interaction between an arbitrarily located and oriented microdefect and a finite main crack subjected to a plane incident wave. The analysis is based upon the use of integral transform techniques and an appropriate superposition procedure. The resulting dynamic stress intensity factors ( K * I and K * II ) at the main crack are obtained by solving the appropriate singular integral equations, using Chebyshev polynomi­als, for different incident waves. The resulting solution is verified by comparison with existing results, and numerical examples are provided to show the effect of the location and orientation of the microdefect and the frequency of the incident wave upon K * I and K * II of the main crack. The results advanced here can be used as building blocks in the fields of micromechanics, damage and non-destructive characterization of defects in solids.

Integral Equation Method via Domain Decomposition and Collocation for Scattering Problems

In this paper an exterior domain decomposition (DD) method based on the boundary element (BE) formulation for the solutions of two or three-dimensional time-harmonic scattering problems in acoustic media is described. It is known that the requirement of large memory and intensive computation has been one of the major obstacles for solving large scale high-frequency acoustic systems using the traditional nonlocal BE formulations due to the fully populated resultant matrix generated from the BE discretization. The essence of this study is to decouple, through DD of the problem-defined exterior region, the original problem into arbitrary subproblems with data sharing only at the interfaces. By decomposing the exterior infinite domain into appropriate number of infinite subdomains, this method not only ensures the validity of the formulation for all frequencies but also leads to a diagonalized, blockwise-banded system of discretized equations, for which the solution requires only O(N) multiplications, where N is the number of unknowns on the scatterer surface. The size of an individual submatrix that is associated with a subdomain may be determined by the user, and may be selected such that the restriction due to the memory limitation of a given computer may be accommodated. In addition, the method may suit for parallel processing since the data associated with each subdomain (impedance matrices, load vectors, etc.) may be generated in parallel, and the communication needed will be only for the interface values. Most significantly, unlike the existing boundary integral-based formulations valid for all frequencies, our method avoids the use of both the hypersingular operators and the double integrals, therefore reducing the computational effort. Numerical experiments have been conducted for rigid cylindrical scatterers subjected to a plane incident wave. The results have demonstrated the accuracy of the method for wave numbers ranging from 0 to 30, both directly on the scatterer and in the far-field, and have confirmed that the procedure is valid for critical frequencies.

The current distribution on a circular disc

In this paper we derive the surface-current distribution on a perfectly conducting circular disc. The current is obtained by calculating the limit of the surface currents on an oblate spheroid as the thickness goes to zero. The null-field approach is used. We show that it is possible to calculate all quantities in terms of the spherical basis functions, thus avoiding the cumbersome spheroidal basis functions. Furthermore, it is shown that the correct edge behaviour appears very naturally within the formulation. We compute the surface field on the disc for a plane incident wave, the surface current (eigencurrents) at the complex resonances of the disc, and the induced current on a subterranean disc excited by a circular antenna loop on the ground.

Theory for Absorption of Wave Power by a System of Interacting Bodies

Wave power absorption by a system of interacting bodies is analyzed within linear theory. A general expression for the wave power absorbed by the system, in terms of far-field velocity potentials, is derived. The optimum power absorption by a system of identical bodies from a plane incident wave is obtained. The theory is applied to various configurations of bodies oscillating in one or two modes. It is shown that the interaction between properly spaced bodies may raise the absorbed power per body by a substantial factor. It is also demonstrated that a single row of oscillating bodies may absorb 50 percent of the incident power if the bodies are operated in one mode and 100 percent if operated in two modes.

Radiation and scattering of water waves by rigid bodies

Schwinger's variational formulation is applied to the radiation of surface waves due to small oscillation of bodies. By means of Haskind's theorem the wave forces on a stationary body due to a plane incident wave are found using only far-field properties. Results for horizontal rectangular and vertical circular cylinders are presented.