USING FREDHOLM INTEGRAL EQUATION OF THE SECOND KINDTO SOLVE THE VERTICAL VIBRATION OF ELASTICPLATE ON AN ELASTIC HALF SPACE

The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By applying Abel transformation the dual integral equations are reduced to Fredholm integral equation of the second kind which is solved numerically.

UNIQUENESS FOR THE SOLUTIONS OF ELASTIC THIN PLATES AND SHALLOW SHELLS AS WELL AS THEIR CONTACT PROBLEM WITH HALF SPACE

The uniqueness for the solutions mentioned in the subject is proved by using the uniqueness of the solution for the internal boundary problem of Laplace and bi-Laplace equations of the first kind as well as of the second.

Driving Mechanism of Urban Space Expansion in Luoyang, China

Urban space expansion is the result of the interaction between internal and external forces of the urban. Based on the remote sensing image data of 1990, 2000, 2010, and 2020, and the social and economic development data, this paper analyzes the driving mechanism of the Luoyang space expansion characteristics and its correlation characteristics. By using urban land use efficiency index, urban expansion elastic index;urban allometric growth index, and grey correlation analysis in 4 times sections and 3 periods. The research results show that the urban space expansion of Luoyang mainly comes from the needs and support of economic development, the coordination between urban space expansion and population development is poor, and urban space expansion effectively attracts the inflow of external funds, and the settlement of migrants, drives the development of the tertiary industry, and increases the local revenue.

An eigen theory of waves in piezoelectric solids

Based on the standard spaces of the physical presentation, both the quasi-static mechanical approximation and the quasi-static electromagnetic approximation of piezoelectric solids are studied here. The complete set of uncoupled elastic wave and electromagnetic wave equations are deduced. The results show that the number and propagation speed of elastic waves and electromagnetic waves in anisotropic piezoelectric solids are determined by both the subspaces of electromagnetically anisotropic media and ones of mechanically anisotropic media. Based on these laws, we discuss the propagation behaviour of elastic waves and electromagnetic waves in the piezoelectric material of class 6 mm.

A new method to calculate near-field radiation excited by heterogeneous fault rupture

This paper derives from the representation theory the formula for calculating the radiation excited by heterogeneous fault rupture based on box-like discretization scheme. Preliminary validation indicates that our algorithm has very high computation precision and efficiency; therefore, it is a very practical tool to investigate strong ground motion problems. Additionally, the equations given in this study can also be used to invert the fault rupture process.

SCATTERING OF SH-WAVE BY CRACKS ORIGINATING AT AN ELLIPTIC HOLE AND DYNAMIC STRESS INTENSITY FACTOR

The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Green's function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.

Static loading and vertical displacement at southern Siberia

Seismic method is usually used for elastic parametric estimation. This is why this method presents dynamic parameters of Earth. Frequency seismic range changes greatly from geodynamic modelling time. Now we have opportunity to use geodesy result for some years for elastic parameters estimation. Static solution from elastic theory may be used for the interpretation of long term results. It presents static elastic parameter. The inverse problem for different types of vertical surface loading on one year period is calculated. Two cases of loading with maximal and minimal area are presented. Results are determined by space geodesy and leveling methods. Current relation between atmospheric pressure and vertical displacements was estimated at the center of Siberian Anti Cyclone with size varied from 2000 km to 3000 kin. Pressure-displacement coefficients （PDC） can be achieved by three years obser- vation （0.997 mm/mbar for NVSK GPS station）. It is used for elastic module study of geology medium with maximum thickness up to 600 km. In the context of elastic model, the modulus of rigidity is estimated to be 113 GPa. Vast expanse of anti-cyclone may relate with rheology of crust and upper mantle. Smaller size of surface loading - local loading is seasonal variation of water reservoir. Annual vertical changes were obtained by leveling near the dam of the reservoir. PDC ratio was 1.15 mm/bar for these places. In elastic theory, the Young modulus E = 80 GPa （Poisson ratio = 0.25, the modulus of rigidity - 32 GPa） was calculated by sixteen years of leveling measurements. This result can effectively be represented for upper crust. Our results were checked by solution for coseismic displacement of Chyia- Altai earthquake （Sep. 27, 2003, M = 7.3）. Coseismic results calculated by static modules agree with experimental coseismic GPS data at 10% level.