Presence of predictable cavities inside the structure is often preferable as it will reduce the vibration amplitude. Inspired by the traditional mass attached to the beam system, in order to solve the problem of free vibration of the steel liquid storage tank with a column made of porosity material and perforated material using an exact analytical continuum model to replace the lumped mass system. The free vibration response of the column under porosities and holes with an attached mass is established by using a new analytical method known as Fourier series with Stokes’ transform. The free vibration frequencies are obtained by using an eigen-value approximation, and the influence of number of holes, filling ratio, porosity effect and other parameters on the free vibration response is explored. It is shown that an increase in the mass parameter, filling ratio and porosity parameter of the column with an attached mass system could significantly affect the free vibration of response of the system.

With the development of nanotechnology, interest in nanomaterials has increased significantly in recent years. This study examines the bending analysis of a nanobeam with modified couple stress theory and weighted residual methods. The formulas derived for calculating bending analysis results in the article has been found by using Weighted Residual Method. The results have compared to show effects on nanobeam and the calculated values are shown in the graphs and tables. The results which is obtained in the article are compared with the results already found in the literature and it was observed that they are consistent.

Nanobeams are now widely used in numerous vibration frequency research. In this study, an eigenvalue problem has used to determine the vibration frequency analysis of the buckyball and spring attached to the end of the nanobeam. The vibration frequencies of the system may be discovered using a single (2x2) matrix in this eigenvalue problem. A mathematical method for analyzing sensors has attached to nanobeams is presented in this paper. The results, which is obtained in this study, has showed a result that has compatible with the flicker frequency studies conducted in the literature, and the results have presented in tables and graphics.