Analysis of models for viscoelastic wave propagation

Abstract

We consider the problem of waves propagating in a viscoelastic solid. For the material properties of the solid we consider both classical and fractional differentiation in time versions of the Zener, Maxwell, and Voigt models, where the coupling of different models within the same solid are covered as well. Stability of each model is investigated in the Laplace domain, and these are then translated to time-domain estimates. With the use of semigroup theory, some time-domain results are also given which avoid using the Laplace transform and give sharper estimates. We take the time to develop and explain the theory necessary to understand the relation between the equations we solve in the Laplace domain and those in the time-domain which are written using the language of causal tempered distributions. Finally we offer some numerical experiments that highlight some of the differences between the models and how different parameters effect the results.

Experimental study on anti‐crystallization law of tunnel transverse flocking drainpipe at different velocities

“…At low flow velocity, the roughness has a great impact on the flow pattern, so the total amount of crystallization attached to the villi is relatively small . [19][20][21] With the increase of flow velocity, the influence of roughness on the flow pattern disturbance is gradually weakened. [22][23][24][25][26] When the flow velocity exceeds the threshold of 5.46 cm/s, the flow action overcomes the influence of roughness on the flow pattern and then reduces the crystallization attached to the villi.…”

Optimal design of nozzle for filter bag cleaning device of combined air-conditioning based on fluid mechanics

“…As shown in fig. 7, large droplets of high-speed jet flow are mainly concentrated in the middle region [10][11][12], which is an energy concentration region, which conforms to the observed jet flow state in practice.…”

Automatic testing method for static pressure drive performance of electronic hydraulic brake system

“…The isolation valve is closed under normal working condition, and when the EHB power supply device fails, the isolation valve opens without flow. The driver can still send the brake fluid in the main brake cylinder to the brake wheel cylinder through the isolation valve and the brake pipeline through the brake pedal to achieve a certain intensity of braking [11][12][13].…”