The device generates probing ultrasonic waves

The device generates probing ultrasonic waves [7] (one longitudinal and two transverse, polarized in mutually perpendicular directions) by piezoelectric transducers (PETs) serving as piezo-actuators. The reflected elastic waves excited in the material of the controlled object are also received by the same PETs via converting mechanical vibrations to a potential difference. Compared to the known approaches [8,9], the specific features of this problem are both direct numerical simulation of a high-frequency vibration process (the frequency of exposure is 5 MHz) by numerically solving the problem of propagation of elastic strain waves from the solution of a system of elastic equations and accounting for the relations for simulating the related electroelastic problem. Small-sized finite elements of the computational domain and a small retinoid x receptor step should be used for properly describing such a process. It should be noted that simulation studies on piezoelectric materials are mainly concerned with finding the natural frequencies of piezoelectric elements, or with determining the compression-rarefaction waves in materials [8,9]. In this paper we propose an approach that consists of simultaneously solving the conjugated problems and involves no simplifying assumptions about the absence of environmental effect on the generation of vibrations. This is a novel approach (or at least we are unware of any similar studies).
The process of measuring the mechanical stresses by the acoustoelastic method As the wave propagates through the bulk of the layer and is reflected from the surface opposite to the sensor, vibrations of the metal surface lead to deformations of the plate and to a potential difference arising between the electrodes. The potential difference is registered by a unit processing the incoming information as part of the IN-5101A device. The time delay between the transmitted and the reflected pulses is measured. Next, the mechanical stresses are calculated by the formulas that relate the delay in the propagation of the elastic wave with coefficients of elastic-acoustic coupling [10]. The reflected pulse can be approximated by the following expression: where A(t) is the signal envelope; t is the time counted from the moment the wave arrives at the sensor; f is the oscillation frequency. The shape of the envelope of the signal registered in the measurements is described by an exponential power function [11]: where is the time interval from the start of the pulse to its peak; A0 is the maximum signal amplitude; δ is the approximation coefficient. The level of the reflected signal displayed on the screen of the device is set automatically by specifying the gain. Because of this, for the sake of convenience, from now on we shall only consider the normalized signal of the form A/A0. A full-scale experiment involved registering the signal caused by propagation of longitudinal waves in a 16-mm-thick steel sample. The envelope of the first reflected pulse was approximated by expression (2) at = 3·(1/f), where f = 5 MHz and δ = 2.0. The obtained dependence is shown in Fig. 1.
Problem setting Fig. 2 shows the schematic for the problem setting. A sample of 14ХГНДЦ steel (a Cr–Mn–Ni–Cu–Zr alloy) is simulated by a h×l-sized rectangular area. The dimension h = 16 mm corresponds to the thickness of the sample used for measurements in Ref. [12]. The dimension l is taken to exceed h by five times. It was established through solving a series of auxiliary problems that at this value of l, the results are not distorted by rereflection from the right-hand boundary of the computational domain. Young\'s modulus E = 200 GPa; Poisson\'s ratio ν = 0.3; Density ρ = 7700 kg/m3; Frequency of exposure = 5 MHz. Fig. 2 also shows a schematic of the kinematic boundary conditions. The outer edge of the layer is fixed. A transient potential difference U(t), which is sawtooth-shaped in accordance with instructions [7], is applied to the upper surface of the piezoelectric element. The frequency of exposure = 5 MHz.