This paper presents a thorough study of a time-dependent nonlinear Schrodinger (NLS) differential equation with a time-fractional derivative. The fractional time complex transform is used to conver...

The Fractional Complex Transform: a Novel Approach to the Time-Fractional SCHRÖDINGER Equation

Tunable negative stiffness spring using maxwell normal stress

The adverse effect of mechanical vibration is inevitable and can be observed in machine components either on the long- or short-term of machine life-span based on the severity of oscillation. This in turn motivates researchers to find solutions to the vibration and its harmful influences through developing and creating isolation structures. The isolation is of high importance in reducing and controlling the high-amplitude vibration. Over the years, porous materials have been explored for vibration damping and isolation. Due to the closed feature and the non-uniformity in the structure, the porous materials fail to predict the vibration energy absorption and the associated oscillation behavior, as well as other the mechanical properties. However, the advent of additive manufacturing technology opens more avenues for developing structures with a unique combination of open, uniform, and periodically distributed unit cells. These structures are called metamaterials, which are very useful in the real-life applications since they exhibit good competence for attenuating the oscillation waves and controlling the vibration behavior, along with offering good mechanical properties. This study provides a review of the fundamentals of vibration with an emphasis on the isolation structures, like the porous materials (PM) and mechanical metamaterials, specifically periodic cellular structures (PCS) or lattice cellular structure (LCS). An overview, modeling, mechanical properties, and vibration methods of each material are discussed. In this regard, thorough explanation for damping enhancement using metamaterials is provided. Besides, the paper presents separate sections to shed the light on single and 3D bandgap structures. This study also highlights the advantage of metamaterials over the porous ones, thereby showing the future of using the metamaterials as isolators. In addition, theoretical works and other aspects of metamaterials are illustrated. To this end, remarks are explained and farther studies are proposed for researchers as future investigations in the vibration field to cover the weaknesses and gaps left in the literature.

https://journals.sagepub.com/doi/pdf/10.1177/16878132221082872

Advances in mechanical metamaterials for vibration isolation: A review

This article presents an analytical approach to study the vibration control of rotating sandwich cylindrical shell-reinforced nanocomposite face sheet and porous core integrated with functionally graded magneto-electro-elastic layers using first-order shear deformation theory of shells. By considering the Coriolis and centrifugal force and also using Hamilton’s principle and Maxwell equations, the governing equations of motion for rotating sandwich cylindrical shell are derived. The differential quadrature method is employed to determine the forward and backward linear frequency of rotation sandwich cylindrical shell for different boundary conditions. Detailed parametric studies are carried out to investigate influences of volume fraction of carbon nanotube in face sheet layers, temperature, distribution types of porosity, different boundary conditions, angular velocity and electrical and magnetic control coefficients on vibration control of sandwich cylindrical shell. The results of the necessary parameters can be used as benchmarks for design in important industries such as low- or high-speed rotor and turbine manufacturing.

Vibration control of rotating sandwich cylindrical shell-reinforced nanocomposite face sheet and porous core integrated with functionally graded magneto-electro-elastic layers

Porous media have been a significant subject of research for a long time due to their applicability in various sciences. This paper investigates the heat transfer phenomenon in the porous media. A convergent solution is obtained for a two-dimensional time-fractional equation arising in a porous soil heat transfer. He's polynomial and He's variational iteration method are used to accomplish the required goals. The fractional derivative used in the article is described by He’s definition. He's fractional complex transform is used to convert the fractional differential equation into its traditional partner differential equation, which can be solved iteratively. Graphical representations of the results are provided to demonstrate the efficacy of the methods used.

Yao Sun

Papers

A theoretical analysis on the active structural acoustical control of a vibration isolation system with a coupled plate-shell foundation