The wave finite element method (WFEM) is developed to simulate the wave propagation in one-dimensional problem of nonhomogeneous linear micropolar rod of variable cross-section. For this purpose, t...

Stress Wave Propagation Analysis in One-Dimensional Micropolar Rods with Variable Cross-Section Using Micropolar wave Finite Element Method

In this work, the longitudinal wave propagation in stressed rock with variable cross-section is investigated analytically. Considered the stress-sensibility of dynamic elastic modulus and the viscosity of rock, a modified viscoelastic stress-strain relationship is established. Based on the continuity equation, motion equation and stress-strain relation equations, the wave propagation equation for a stressed rock with variable cross-section is obtained. The harmonic wave propagation is discussed in detail by calculating the attenuation coefficient in amplitude. The combined effects of static stress and geometry on the wave attenuation are analyzed. The results show that due to the variable static stress along the propagation path, the wave attenuation is space-dependent, and the distribution of attenuation coefficients may be remarkably different under different levels of static stress. The wave attenuation in a stressed rock with variable cross-section is also frequency-dependent, and the influence of static stress on the lower-frequency wave components is more obvious compared with that on the higher-frequency wave components. Comparing the wave attenuation among rocks with three different geometries, we conclude that the wave attenuation depends on actual normal static stress, the cross-sectional areas and the changing rates of cross-sectional area.

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Theoretical Analysis of Longitudinal Wave Attenuation in a Stressed Rock With Variable Cross-Section

A wave approach to finite element analysis of solids

In this article, the wave finite element method (WFEM) is developed for analyzing the wave propagation of one-dimensional micropolar elastic beams at small strain. The micropolar WFEM (MWFEM) equat...

Wave propagation analysis of micropolar elastic beams using a novel micropolar wave finite element method

A numerical procedure to study one-dimensional waves in a rod, taking into account arbitrary rheological properties, is considered. The procedure is based on direct mathematical modelling of wave propagation in a rod of variable crosssection. Elastic-viscoplastic waves resulting from the impact of a rigid body, including repeated collisions and rebounds, are analyzed.

Mathematical Modelling of Wave Propagation in a Rod of Time-Dependent Material

A numerical procedure to study one-dimensional waves in solids is considered in application to longitudinal loading of elastic-plastic rods of a variable cross section. The procedure assumes direct mathematical modelling of mechanical perturbations. Multiple reflections of waves from the rod ends, alternating signs of stress, influence of isotropic and anisotropic hardening, and the Bauschinger effect are taken into account. A detailed description of stress waves in elastic-plastic rods of a variable cross section at the impact of a rigid body is presented.

B. F. Shorr

Papers

Analysis of wave propagation in elastic-plastic rods of a variable cross section using direct mathematical modelling