On propagation of axisymmetric waves in pressurized functionally graded elastomeric hollow cylinders

Abstract

Soft materials can be designed with a functionally graded (FG) property for specific applications.Such material inhomogeneity can also be found in many soft biological tissues whose functionality is only partly understood to date. In this paper, we analyze the axisymmetric guided wave propagation in a pressurized FG elastomeric hollow cylinder. The cylinder is subjected to a combined action of axial pre-stretch and pressure difference applied to the inner and outer

Forced Vibration of the Non-Homogeneously Pre-Stressed System Consisting of the Hollow Cylinder and Surrounding Medium

“…Despite the significance of the related investigations, up to now such investigations, i.e. investigations regarding the dynamics of the structural elements with non-homogeneous pre-stresses are almost completely absent (except for a few works carried out in the investigations [Engin and Suhubi (1978); Shearer, Abrahams, Parnel et al (2013); Wu, Su, Liu et al (2018); Akbarov and Bagirov (2019); Bagirov, Akbarov and Seyfullayev (2018)]. Notwithstanding this, the corresponding problems related to the stability loss of mine workings with inhomogeneous initial stresses have been studied by Guz and his students, the results of which are detailed in the monograph by Guz [Guz (1977)] and a review of which is given in the paper by Guz [Guz (2003)].…”

“…At the same time, it should be noted that in these investigations, the mine workings are modelled as an infinite homogeneous elastic or elastoplastic medium containing a cylindrical cavity and having initial nonhomogeneous axisymmetric stresses and the variational method is developed for the solution to the corresponding eigenvalue problems. Now we attempt to detail the investigations made in the aforementioned works [Engin and Suhubi (1978); Shearer, Abrahams, Parnell et al (2013); Wu, Su, Liu et al (2018); Akbarov and Bagirov (2019); Bagirov, Akbarov and Seyfullayev (2018)]. Note that in the papers [Engin and Suhubi (1978); Shearer, Abrahams, Parnell et al (2013)], torsional waves in the hollow cylinder made of incompressible highly elastic materials are studied and it is assumed that the non-homogeneous pre-stresses therein are caused by static internal and external uniformly distributed compressional radial forces.…”

“…Note that in the papers [Engin and Suhubi (1978); Shearer, Abrahams, Parnell et al (2013)], torsional waves in the hollow cylinder made of incompressible highly elastic materials are studied and it is assumed that the non-homogeneous pre-stresses therein are caused by static internal and external uniformly distributed compressional radial forces. Unlike the foregoing papers, the paper by Wu et al [Wu, Su, Liu et al (2018)] has studied the longitudinal axisymmetric wave propagation and dispersion in the hollow cylinder made of functionally graded highly elastic material. As in the previous last two papers, this study is also made for the case where the cylinder is pre-stressed with the compressional uniformly distributed forces acting on the internal and external face surfaces of the cylinder.…”

“…Numerical results presented and discussed in these works illustrate the influence of the non-homogeneity of the pre-stresses on the torsional wave dispersion propagated in the hollow cylinder. In the case considered in the paper by Wu et al [Wu, Su, Liu et al (2018)], the analytical determination of the initial stress-strain state is more difficult, and separate works, such as the papers by Batra et al [Batra and Bahrami (2009)] and Chen et al [Chen, Liu, Kitipornchai et al (2017)], are devoted to this determination. Consequently using the results obtained in these works, the paper by Wu et al [Wu, Su, Liu et al (2018)] solves the wave propagation equations by utilizing the state-space formalism for these equations with the approximate laminate or multi-layer technique.…”

“…In the case considered in the paper by Wu et al [Wu, Su, Liu et al (2018)], the analytical determination of the initial stress-strain state is more difficult, and separate works, such as the papers by Batra et al [Batra and Bahrami (2009)] and Chen et al [Chen, Liu, Kitipornchai et al (2017)], are devoted to this determination. Consequently using the results obtained in these works, the paper by Wu et al [Wu, Su, Liu et al (2018)] solves the wave propagation equations by utilizing the state-space formalism for these equations with the approximate laminate or multi-layer technique. The paper by Akbarov et al [Akbarov and Bagirov (2019)] studies the longitudinal axisymmetric wave dispersion in a bi-layered (bi-material) hollow cylinder with nonhomogeneous pre-stresses caused by the hydrostatic pressures acting on the faces of that.…”