Bibi Farhat, Ali Hashmat, Azhar Ehtsham, Jamal Muhammad, Ahmed Iftikhar, Ragab Adham E
Department of Mathematics, PMAS Arid Agriculture University, Rawalpindi, Pakistan.
Department of Mathematics, COMSATS University Islamabad (CUI), Park Road, Tarlai Kalan, Islamabad, 45550, Pakistan.
Sci Rep. 2023 Oct 17;13(1):17703. doi: 10.1038/s41598-023-44712-4.
This investigation relates to the research on Hall current on propagation and reflection of elastic waves through non-local fractional-order thermoelastic rotating medium with voids. The system is split up into longitudinal and transverse components using the Helmholtz vector rule. It is observed that, through the frequency dispersion relation four coupled quasi-waves exist in the medium. The rotating solid modifies the nature of purely longitudinal and transverse waves toward the quasi-type waves. All the propagating waves are dispersive as they depend upon angular frequency. The quasi-longitudinal wave qP and quasi-transverse wave qSV faces cut-off frequencies. The nonlocal parameter affect all the waves except the quasi void wave. Analytically, the reflection coefficients of the wave are computed using suitable boundary conditions. MATLAB software is used to perform numerical computations for a chosen solid material. The amplitude ratios and the speed of propagation of the wave are plotted graphically for rotational frequency, nonlocal, fractional order, and Hall current parameter. The significant effect of the physical parameters on the computed results has been observed. The cut-off frequency of the waves is also presented graphically. The energy conservation law is proved in the form of energy ratios. The earlier findings in the literature are obtained as special case in the absence of rotation, Hall current parameter and porous voids.
本研究涉及弹性波在含孔隙的非局部分数阶热弹性旋转介质中传播和反射时的霍尔电流研究。利用亥姆霍兹矢量法则将该系统分解为纵向和横向分量。观察到，通过频散关系，介质中存在四个耦合准波。旋转固体将纯纵向波和横向波的性质改变为准型波。所有传播波都是色散的，因为它们取决于角频率。准纵波qP和准横波qSV面临截止频率。非局部参数影响除准孔隙波之外的所有波。通过合适的边界条件，解析计算了波的反射系数。使用MATLAB软件对选定的固体材料进行数值计算。针对旋转频率、非局部、分数阶和霍尔电流参数，绘制了波的振幅比和传播速度的图形。观察到物理参数对计算结果有显著影响。还以图形形式给出了波的截止频率。以能量比的形式证明了能量守恒定律。文献中的早期研究结果是在没有旋转、霍尔电流参数和多孔孔隙的情况下作为特殊情况得到的。
