Oscillating Nonlinear Acoustic Waves in a Mooney–Rivlin Rod
Anastasia Karakozova,
Sergey Kuznetsov
Abstract:Harmonic wave excitation in a semi-infinite incompressible hyperelastic 1D rod with the Mooney–Rivlin equation of state reveals the formation and propagation of the shock wave fronts arising between faster and slower moving parts of the initially harmonic wave. The observed shock wave fronts result in the collapse of the slower moving parts being absorbed by the faster parts; hence, to the attenuation of the kinetic and the elastic strain energy with the corresponding heat generation. Both geometrically and ph… Show more
“…Rubber is an isotropic material that can be simulated using the Mooney-Rivlin [28] constitutive model with tensile strain smaller than 100% and compressive strain smaller than 30%. The strain energy of rubber materials could break down into two parts: strain bias energy as well as voluminal strain energy.…”
A novel three-dimensional isolation system consisting of thick rubber bearing (TNRB), disc spring bearing (DSB), and laminated rubber bearing (LRB) in series combination was designed, and its composition, principle, and isolation effect were comprehensively analyzed. By combining numerical examples, the whole structure method is used to compare and analyze the dynamic characteristics, dynamic response, and structural damage of large-span isolation structures containing new three-dimensional systems, large-span horizontal isolation structures based on LRB, and corresponding non-isolation structures under multi-dimensional seismic excitation. The results show that compared with the horizontal isolation structure based on LRB, the structure of the new three-dimensional isolation system has a 33% longer vertical natural vibration period, a 17.85% attenuation in the overall damage index, and a 36.86% increase in vertical energy dissipation capacity. It can achieve good isolation effects in both horizontal and vertical directions, which can form a favorable complement to the horizontal isolation structure based on LRB in terms of vertical isolation and energy dissipation.
“…Rubber is an isotropic material that can be simulated using the Mooney-Rivlin [28] constitutive model with tensile strain smaller than 100% and compressive strain smaller than 30%. The strain energy of rubber materials could break down into two parts: strain bias energy as well as voluminal strain energy.…”
A novel three-dimensional isolation system consisting of thick rubber bearing (TNRB), disc spring bearing (DSB), and laminated rubber bearing (LRB) in series combination was designed, and its composition, principle, and isolation effect were comprehensively analyzed. By combining numerical examples, the whole structure method is used to compare and analyze the dynamic characteristics, dynamic response, and structural damage of large-span isolation structures containing new three-dimensional systems, large-span horizontal isolation structures based on LRB, and corresponding non-isolation structures under multi-dimensional seismic excitation. The results show that compared with the horizontal isolation structure based on LRB, the structure of the new three-dimensional isolation system has a 33% longer vertical natural vibration period, a 17.85% attenuation in the overall damage index, and a 36.86% increase in vertical energy dissipation capacity. It can achieve good isolation effects in both horizontal and vertical directions, which can form a favorable complement to the horizontal isolation structure based on LRB in terms of vertical isolation and energy dissipation.
Acoustic Emission (AE) testing is a non-destructive evaluation technique that has gained significant attention in pipeline monitoring. Pencil-lead breaks (PLBs) are commonly used in reproducing and characterising sensors used in AE applications and have emerged as a valuable tool for calibration processes. This technique involves breaking a pencil lead by pressing it on the surface of the test structure and applying a bending moment at a given angle on a surface. The applied force produces a local deformation on the test surface, which is released when the lead breaks. The fracture in these PLBs is assumed to be a step unload; however, this is not the case. In this work, a series of PLB source experiments complemented with parallel numerical simulations were carried out to investigate the actual unload rate by correlating the relationship between AE speed, frequency, and power from PLBs. This was achieved by varying the simulation unload rates recorded over a duration of 2 s on a steel pipe and comparing to the experiment. Analysis of the investigated results from the experimental and numerical models suggests that although the AE line structure of a PLB can be reproduced by simulation for short times only (1 µs), the actual unload rate for PLBs is in the region of 10–8 s. It is concluded that FEA has the potential to help in the recovery of the temporal structure from real AE structures. The establishment of this model will provide a theoretical basis for future studies on the monitoring of non-impulsive AE sources such as impact on pipelines using finite element analysis.
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