Our official English website, www.x-mol.net, welcomes your
feedback! (Note: you will need to create a separate account there.)
Waves in nonlocal thermoelastic solids of type III
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-05-10 , DOI: 10.1002/zamm.201900074 Nihar Sarkar 1 , Mitali Bachher 2 , Narayan Das 3 , Soumen De 4 , Nantu Sarkar 4
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-05-10 , DOI: 10.1002/zamm.201900074 Nihar Sarkar 1 , Mitali Bachher 2 , Narayan Das 3 , Soumen De 4 , Nantu Sarkar 4
Affiliation
|
In this paper, the propagation of time‐harmonic thermoelastic plane waves is studied in an infinite nonlocal elastic continuum. The type III Green‐Naghdi model (with energy dissipation) of generalized thermoelasticity and the Eringen's nonlocal elasticity model are adopted to address this problem. We found two sets of the coupled longitudinal waves which are dispersive in nature and experience attenuation. In addition to the coupled waves, there also exists one independent vertically shear‐type wave which is dispersive but experiences no attenuation. All these waves are found to be influenced by the elastic nonlocality parameter. Furthermore, the shear‐type wave is found to face a critical frequency, while the coupled longitudinal waves may face critical frequencies conditionally. Reflection phenomenon of an incident coupled longitudinal waves from a rigid and thermally insulated boundary surface of a homogeneous and isotropic nonlocal thermoelastic half‐space is investigated. Using these boundary conditions, the formulae for various reflection coefficients and their respective energy ratios are presented. For a particular model, various graphs are plotted to analyze the behavior of the phase speeds, reflection coefficients and their respective energy ratios. The amplitude ratios of the reflected waves and their respective energy ratios are determined analytically. For a particular model, the effect of elastic nonlocality parameter on the variations of phase speeds, attenuation coefficients, amplitude ratios and corresponding energy ratios of the reflected waves are presented graphically. Finally, analysis of the various results have been interpreted.
中文翻译：
III型非局部热弹性固体中的波
在本文中，研究了时域热弹性平面波在无限局部非弹性连续体中的传播。广义热弹性的III型Green-Naghdi模型（具有能量耗散）和Eringen的非局部弹性模型被用来解决这个问题。我们发现了两组耦合的纵波，它们在本质上是分散的，并且会衰减。除了耦合波，还存在一个独立的垂直剪切型波，该波是分散的但没有衰减。发现所有这些波都受弹性非局部性参数的影响。此外，发现剪切型波面对临界频率，而耦合的纵波可能有条件地面对临界频率。研究了均匀均质各向同性非局部热弹性半空间的刚性隔热边界表面入射耦合纵波的反射现象。利用这些边界条件，给出了各种反射系数的公式及其各自的能量比。对于特定模型，绘制了各种图表以分析相速度，反射系数及其各自的能量比的行为。通过解析确定反射波的振幅比及其各自的能量比。对于特定的模型，以图形方式显示了弹性非局部性参数对相速度，衰减系数，振幅比和相应的能量比变化的影响。最后，
更新日期：2020-05-10
中文翻译：
III型非局部热弹性固体中的波
在本文中，研究了时域热弹性平面波在无限局部非弹性连续体中的传播。广义热弹性的III型Green-Naghdi模型（具有能量耗散）和Eringen的非局部弹性模型被用来解决这个问题。我们发现了两组耦合的纵波，它们在本质上是分散的，并且会衰减。除了耦合波，还存在一个独立的垂直剪切型波，该波是分散的但没有衰减。发现所有这些波都受弹性非局部性参数的影响。此外，发现剪切型波面对临界频率，而耦合的纵波可能有条件地面对临界频率。研究了均匀均质各向同性非局部热弹性半空间的刚性隔热边界表面入射耦合纵波的反射现象。利用这些边界条件，给出了各种反射系数的公式及其各自的能量比。对于特定模型，绘制了各种图表以分析相速度，反射系数及其各自的能量比的行为。通过解析确定反射波的振幅比及其各自的能量比。对于特定的模型，以图形方式显示了弹性非局部性参数对相速度，衰减系数，振幅比和相应的能量比变化的影响。最后，
京公网安备 11010802027423号