Frequency Analysis for Functionally Graded Material Cylindrical Shells: A Significant Case Study

Cylindrical shells play an important role for the construction of functionally graded materials (FGMs). Functionally graded materials are valuable in order to develop durable materials. They are made of two or more materials such as nickel, stainless steel, zirconia, and alumina. They are extremely beneficial for the manufacturing of structural elements. Functionally graded materials are broadly used in several fields such as chemistry, biomedicine, optics, and electronics. In the present research, vibrations of natural frequencies are investigated for different layered cylindrical shells, those constructed from FGMs. The behavior of shell vibration is based on different parameters of geometrical material. The problem of the shell is expressed from the constitutive relations of strain and stress with displacement, as well as it is adopted from Love’s shell theory. Vibrations of natural frequencies (NFs) are calculated for simply supported-simply supported (SS-SS) and clamped-free (C-F) edge conditions. The Rayleigh–Ritz technique is employed to obtain the shell frequency equation. The shell equation is solved by MATLAB software.

Dynamic stability of anisotropic fiber-reinforced plate

The dynamic stability problem of an anisotropic fiber-reinforced plate under increasing compressing load is considered in a geometrically nonlinear formulation using the Kirchhoff-Love’s shell theory. The problem is solved using the Bubnov-Galerkin method based on a polynomial approximation of the deflections in combination with a numerical method based on quadrature formulas. For a wide range of variations of physical, mechanical, and geometrical parameters, the dynamic behavior of the plate is studied.

Free vibration analysis of porous laminated rotating circular cylindrical shells

In this research, investigations are presented of the free vibration of porous laminated rotating circular cylindrical shells based on Love’s shell theory with simply supported boundary conditions. The equilibrium equations for circular cylindrical shells are obtained using Hamilton’s principle. Also, Navier’s solution is used to solve the equations of the cylindrical shell due to the simply supported boundary conditions. The results are compared with previous results of other researchers. The numerical result of this study indicates that with increase of the porosity coefficient the nondimensional backward and forward frequency decreased. Then the results of the free vibration of rotating cylindrical shells are presented in terms of the effects of porous coefficients, porous type, length to radius ratio, rotating speed, and axial and circumferential wave numbers.

Effect of Power Law-Index for Accurate Natural Frequencies of Rotating Isotropic SWCNTs with Ring Supports

Vibration analysis of carbon nanotubes (CNTs) is very essential field owing to their many promising applications in tiny instruments. The unique and interesting properties of CNTs, particularly their mechanical and electrical features, have fascinated industries and researchers to implement CNTs for production of different electromechanical devices. Research on vibration behavior of CNTs was done for a few decades ago. Vibrations of isotropic rotating zigzag and chiral single-walled carbon nanotube (SWCNTs) with ring supports are established using the Love’s shell theory. To discretize the governing equations of current model, Galerkin’s method is utilized for frequency equations of single-walled carbon nanotubes (SWCNTs). The unknown axial functions have assumed by characteristic beam functions which fulfill boundary conditions applied at the tube ends. Effects of different parameters with ring supports on the fundamental natural frequencies versus ratio of length-to-radius, angular speed and height-to-radius ratio have been investigated. The frequencies curves decrease as the length-to-diameter ratio increases. With the increase of angular speed the frequency curve of backward waves increases and forward wave decreases for rotating zigzag and chiral tubes. On the other hand, the phenomena of frequency versus height-to-radius ratio are counterpart of length-to-radius ratio for rotating boundary conditions. The frequency phenomena have been observed very pronounced with ring support. Frequency value of C-C end condition is higher than those of C-F computations. The results of single-walled carbon nanotube are computed by using MATLAB software. To validate the accuracy of present model, the results have been compared with earlier modeling/simulations.

Thermo-Electro-Mechanical Vibrations of Porous Functionally Graded Piezoelectric Nanoshells

In this work, we aim to study free vibration of functionally graded piezoelectric material (FGPM) cylindrical nanoshells with nano-voids. The present model incorporates the small scale effect and thermo-electro-mechanical loading. Two types of porosity distribution, namely, even and uneven distributions, are considered. Based on Love’s shell theory and the nonlocal elasticity theory, governing equations and corresponding boundary conditions are established through Hamilton’s principle. Then, natural frequencies of FGPM nanoshells with nano-voids under different boundary conditions are analyzed by employing the Navier method and the Galerkin method. The present results are verified by the comparison with the published ones. Finally, an extensive parametric study is conducted to examine the effects of the external electric potential, the nonlocal parameter, the volume fraction of nano-voids, the temperature rise on the vibration of porous FGPM cylindrical nanoshells.

Traveling Wave Vibration of Rotating Thin Circular Cylindrical Shell

In this paper, the vibration characteristics of the rotating thin circular cylindrical shell subjected to the radial excitation are presented. Based on the Love’s shell theory, the governing equation of the rotating thin circular cylindrical shell is derived by using the Hamilton’s principle. Then, the amplitude-frequency responses for traveling wave vibration of the circular cylindrical shell are investigated. The results indicate that there exists the traveling wave vibration for the rotating thin circular cylindrical shell, namely: the forward wave and the backward wave. The effects of the damping and excitation on the amplitude-frequency response are analyzed.

Hydro-Elastic Vibration of Partially Liquid-Filled or Partially Liquid- Surrounded Composite Cylindrical Shells

Vibration characteristics of partially liquid-filled or partially liquid-surrounded composite cylindrical shells are investigated in this paper. Using Rayleigh-Ritz energy method and Love’s shell theory, eigenvalue equation of the problem is derived, and the polynomial for natural frequencies of such shells is further obtained. The external work by the hydrodynamic pressure, which is introduced by liquid sloshing, is taken into account in the energy function. Hydro-elastic vibration characteristics of a composite cylindrical shell are studied by using the present method. Effects of liquid level, liquid density, fiber orientation, length-to-radius ratio, and thickness-to-radius ratio on the natural frequencies are analyzed and graphically presented.