Dynamic analysis of an elastic plate on a cross-anisotropic elastic half-space under a rectangular moving load

2020 ◽  
Vol 231 (11) ◽  
pp. 4735-4759 ◽  
Author(s):  
Niki D. Beskou ◽  
Edmond V. Muho ◽  
Jiang Qian
Keyword(s):  
Dynamic Analysis ◽  
Half Space ◽  
Elastic Plate ◽  
Moving Load ◽  
Elastic Half Space ◽  
Anisotropic Elastic

scholarly journals Reduced model for the surface dynamics of a generally anisotropic elastic half-space

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190590 ◽  
Author(s):  
Yibin Fu ◽  
Julius Kaplunov ◽  
Danila Prikazchikov
Keyword(s):  
Surface Wave ◽  
Half Space ◽  
Travelling Waves ◽  
Moving Load ◽  
Multiple Scale ◽  
Elastic Half Space ◽  
Surface Dynamics ◽  
Near Surface ◽  
Surface Resonance ◽  
Anisotropic Elastic

Near-surface resonance phenomena often arise in semi-infinite solids. For instance, when a moving load with a speed v close to the surface wave speed v R is applied to the surface of an elastic half-space, it will give rise to a large-amplitude disturbance inversely proportional to v  −  v R . The latter can be determined by a multiple-scale approach using an extra slow time variable. It has also been shown for isotropic elastic half-spaces that the reduced governing equation thus derived is capable of describing the surface wave contribution even for arbitrary dynamic loading. In this paper, we first derive the analogous evolution equation for a generally anisotropic elastic half-space, and then assess its applicability in the study of travelling waves in a half-space that is coated with a continuous array of spring-like vertical resonators or bonded to an elastic layer of different properties. Our results are validated by comparison with previously known results, and illustrative calculations are carried out for a fibre-reinforced half-space and a coated half-space that is subjected to a finite deformation.

Nonuniformly Moving Loads on an Anisotropic Elastic Half-Space

2003 ◽  
Vol 19 (1) ◽  
pp. 217-224
Author(s):  
Kuang-Chong Wu
Keyword(s):  
Half Space ◽  
Moving Load ◽  
Constant Load ◽  
Elastic Half Space ◽  
Reciprocal Theorem ◽  
Line Load ◽  
Surface Displacements ◽  
Anisotropic Elastic ◽  
The Reciprocal Theorem ◽  
Rayleigh Wave Speed

ABSTRACTThe transient motion in an anisotropic elastic half-space due to a moving surface line load is considered. The load is applied suddenly on the surface and moves off in a fixed direction with nonuniform speed. Integral expressions for the displacements are derived using the reciprocal theorem. The waves generated by the moving load are discussed. Special attention is paid to the singularities in surface displacements generated as the load moves through the Rayleigh wave speed. Explicit expression is obtained for the particle velocity due to a constant load moving with constant speed.

scholarly journals The first boundary value problem of the dynamics of an anisotropic elastic half-space under the action of subsonic transport loads

2020 ◽  
Vol 4 (78) ◽  
pp. 45-52
Author(s):  
G. K. ZAKIR’YANOVA ◽  
◽  
L. A. ALEXEYEVA ◽  
Keyword(s):  
Rock Mass ◽  
Boundary Value Problem ◽  
Half Space ◽  
Wide Class ◽  
Boundary Value ◽  
Operator Method ◽  
Elastic Half Space ◽  
Theory Of Elasticity ◽  
Wide Range ◽  
Anisotropic Elastic

The first boundary value problem of the theory of elasticity for an anisotropic elastic half-space is solved when a transport load moves along its surface. The subsonic Raleigh case is considered, when the velocity of motion is less than the velocity of propagation of bulk and surface elastic waves. The Green’s tensor of the transport boundary value problem is constructed and on its basis the solution of boundary value problems for a wide class of distributed traffic loads is given. To solve the problem, the methods of tensor and linear algebra, integral Fourier transform, and operator method for solving systems of differential equations were used. The obtained solution makes it possible to investigate the dynamics of the rock mass for a wide class of transport loads, in a wide range of velocities, both low velocities and high velocities, and to evaluate the strength properties of the rock mass under the influence of road transport. In particular, determine the permissible velocities of its movement and carrying capacity. In addition, a investigation on its basis of the movement of the day surface along the route will make it possible to establish criteria for the seismic resistance of ground structures and the permissible distances of their location from the route.

scholarly journals Dynamics of inhomogeneous elastic half-space under moving load

2019 ◽  
Vol 97 ◽  
pp. 05048
Author(s):  
Bakhtiyor Yuldashev ◽  
Sagdulla Abdukadirov
Keyword(s):  
Half Space ◽  
Numerical Solutions ◽  
Moving Load ◽  
Elastic Base ◽  
Elastic Half Space ◽  
Thin Elastic Plate ◽  
Wave Processes ◽  
Load Effect ◽  
Time Period ◽  
Resonant Processes

Wave processes in an elastic half-space covered with an elastic layer and (or) a thin elastic plate are considered in the paper. External load moves along the free surface. In the stationary statement, the waveguide properties of the system are determined. The multiple roots of the dispersion equations are revealed and the critical load velocities, leading to the initiation of resonant processes, are determined. In the case when the load moves with the velocity of the Rayleigh wave, additional resonances determined by the structure can be realized in the structure under consideration. It is revealed that Rayleigh resonance exists for long waves only. Numerical solutions are obtained that make it possible to trace the development of resonant excitations. The models of simple structures that have dispersive properties in the medium wave zone are analyzed, such as a thin plate on an elastic base; a model with an attached inertial medium. Analytical solutions have been obtained for these models. Computer simulations conducted simultaneously allow us to analyze the quantitative features of process throughout the entire time period of the load effect. The numerical and asymptotic solutions are compared.

The Effect of an Axial Force on the Response of an Anisotropic Elastic Half Space to a Rolling Cylinder

1973 ◽  
Vol 40 (1) ◽  
pp. 251-256 ◽  
Author(s):  
D. L. Clements
Keyword(s):  
Half Space ◽  
Axial Force ◽  
Elastic Half Space ◽  
Applied Force ◽  
Finite Width ◽  
Infinite Length ◽  
Anisotropic Elastic

The problem of an inflated cylindrical tire of infinite length and constant finite width steadily rolling over the surface of an anisotropic elastic half space is examined. The influence of an applied force, acting along the axis of the cylinder, on the width of the region of slip at each end of the tire is determined. In particular, it is shown numerically that when a material exhibits certain anisotropy the presence of an axial force can considerably reduce the width of the zones of slip.

Sign in / Sign up

Export Citation Format

Share Document