Abstract. In this paper, influence of boundary conditions on free vibrations of single-walled carbon nanotubes (SWCNTs) is examined. The Flügge's shell dynamical equations are utilized for governing vibrations for carbon nanotubes. The wave propagation approach (WPA) is engaged to determine vibration frequency equation in standard eigenvalue form. The axial modal dependence is measured by the complex exponential functions implicating the axial modal numbers. These numbers are associated with boundary conditions specified at edges of a carbon nanotube. Computer programming is performed to obtain solutions of vibration frequency equation. In our new investigation, the vibration frequency spectra are obtained and analyzed for various physical parameters e.g., length and thickness-to-radius ratio. A number of results are presented to influence of different boundary conditions on SWCNTs. They are shown graphically and have been compared with those available in the literature.

The vibration analysis, based on the Donnell thin shell theory, of single-walled carbon nanotubes (SWCNTs) has been investigated. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in SWCNTs. The complex exponential functions, with the axial modal numbers that depend on the boundary conditions stated at edges of a carbon nanotube, have been used to compute the axial modal dependence. In our new investigations, the vibration frequency spectra are obtained and calculated for various physical parameters like length-to-diameter ratios for armchair and zigzag SWCNTs for different modes and in-plane rigidity and mass density per unit lateral area for armchair and zigzag SWCNTs on the vibration frequencies. The computer software MATLAB is used in order to compute these frequencies of the SWCNTs. The results obtained from wave propagation method are found to be in satisfactory agreement with that obtained through the previously known numerical molecular dynamics simulations.

Carvacrol is a major natural constituent and is significantly present as an essential oil in aromatic plants and is well known for its numerous biological activities. Therapeutic properties of carvacrol have been demonstrated as anti‐oxidant, anticancer, diabetes prevention, cardioprotective, anti‐obesity, hepatoprotective and reproductive role, antiaging, antimicrobial, and immunomodulatory properties. The carvacrol biosynthesis has been mediated through mevalonate pathway. Carvacrol has the anticancer ability against malignant cells via decreasing the expressions of matrix metalloprotease 2 and 9, inducing apoptosis, enhancing the expression of pro‐apoptotic proteins, disrupting mitochondrial membrane, suppressing extracellular signal‐regulated kinase 1/2 mitogen‐activated protein kinase signal transduction, and also decreasing the phosphoinositide 3‐kinase/protein kinase B. It also decreased the concentrations of alanine aminotransferase, alkaline phosphatase and aspartate aminotransferase, and gamma‐glutamyl transpeptidase as well as also restored liver function, insulin level, and plasma glucose level. Carvacrol also has been found to exert antimicrobial activity against Staphylococcus aureus, Pseudomonas aeruginosa, Coagulase‐negative staphylococcus, Salmonella spp., Enterococcus sp. Shigella, and Escherichia coli. The current review article summarizes the health‐promoting perspectives of carvacrol through various pathways.

In this paper, vibration characteristics of rotating functionally graded cylindrical shell resting on Winkler and Pasternak elastic foundations have been investigated. These shells are fabricated from functionally graded materials. Shell dynamical equations are derived by using the Hamilton variational principle and the Langrangian functional framed from the shell strain and kinetic energy expressions. Elastic foundations, namely Winkler and Pasternak moduli are inducted in the tangential direction of the shell. The rotational motions of the shells are due to the Coriolis and centrifugal acceleration as well as the hoop tension produced in the rotating case. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in rotating functionally graded cylindrical shell. The complex exponential functions, with the axial modal numbers that depend on the boundary conditions stated at edges of a cylindrical shell, have been used to compute the axial modal dependence. In our new investigation, frequency spectra are obtained for circumferential wave number, length-to-radius ratio, height-to-radius ratio with simply supported–simply supported and clamped–clamped boundary conditions without elastic foundation. Also, the effect of elastic foundation on the rotating cylindrical shells is examined with the simply supported–simply supported edge. To check the validity of the present method, the fundamental natural frequencies of non-rotating isotropic and functionally graded cylindrical shells are compared with the open literature. Also, a comparison is made for infinitely long rotating with the earlier published paper.

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