Vibrations of rotating cylindrical shells with functionally graded material using wave propagation approach

2018 ◽  
Vol 232 (23) ◽  
pp. 4342-4356 ◽  
Author(s):  
Muzammal Hussain ◽  
M Nawaz Naeem ◽  
Aamir Shahzad ◽  
Mao-Gang He ◽  
Siddra Habib
Keyword(s):  
Wave Propagation ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Wave Number ◽  
Type I ◽  
Rotating Speed ◽  
Simply Supported ◽  
Fundamental Frequencies

Fundamental natural frequencies of rotating functionally graded cylindrical shells have been calculated through the improved wave propagation approach using three different volume fraction laws. The governing shell equations are obtained from Love’s shell approximations using improved rotating terms and the new equations are obtained in standard eigenvalue problem with wave propagation approach and volume fraction laws. The effects of circumferential wave number, rotating speed, length-to-radius, and thickness-to-radius ratios have been computed with various combinations of axial wave numbers and volume fraction law exponent on the fundamental natural frequencies of nonrotating and rotating functionally graded cylindrical shells using wave propagation approach and volume fraction laws with simply supported edge. In this work, variation of material properties of functionally graded materials is controlled by three volume fraction laws. This process creates a variation in the results of shell frequency. MATLAB programming has been used to determine shell frequencies for traveling mode (backward and forward) rotating motions. New estimations show that the rotating forward and backward simply supported fundamental natural frequencies increases with an increase in circumferential wave number, for Type I and Type II of functionally graded cylindrical shells. The presented results of backward and forward simply supported fundamental natural frequencies corresponding to Law I are higher than Laws II and III for Type I and reverse effects are found for Type II, depending on rotating speed. Our investigations show that the decreasing and increasing behaviors are noted for rotating simply supported fundamental natural frequencies with increasing length-to-radius and thickness-to-radius ratios, respectively. It is found that the fundamental frequencies of the forward waves decrease with the increase in the rotating speed, and the fundamental frequencies of the backward waves increase with the increase in the rotating speed. This investigation has been made with three different volume fraction laws of polynomial (Law I), exponential (Law II), and trigonometric (Law III). The presented numerical results of nonrotating isotropic and rotating functionally graded simply supported are in fair agreement with parts of other earlier numerical results.

Effect of Winkler and Pasternak elastic foundation on the vibration of rotating functionally graded material cylindrical shell

2018 ◽  
Vol 232 (24) ◽  
pp. 4564-4577 ◽  
Author(s):  
Muzamal Hussain ◽  
Muhammad Nawaz Naeem ◽  
Mohammad Reza Isvandzibaei
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Radius Ratio ◽  
Wave Number ◽  
Simply Supported ◽  
Elastic Foundations

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.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Rabia Anwar ◽  
Madiha Ghamkhar ◽  
Muhammad Imran Khan ◽  
Rabia Safdar ◽  
Muhammad Zafar Iqbal ◽  
...  
Keyword(s):  
Functionally Graded Materials ◽  
Natural Frequencies ◽  
Constitutive Relations ◽  
Cylindrical Shells ◽  
Frequency Equation ◽  
Functionally Graded ◽  
Graded Materials ◽  
Simply Supported ◽  
Love’S Shell Theory ◽  
Graded Material

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.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

scholarly journals Solving nonlinear stability problem of imperfect functionally graded circular cylindrical shells under axial compression by Galerkin's method

2012 ◽  
Vol 34 (3) ◽  
pp. 139-156 ◽  
Author(s):  
Dao Van Dung ◽  
Le Kha Hoa
Keyword(s):  
Axial Compression ◽  
Nonlinear Stability ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Geometrical Nonlinearity ◽  
Functionally Graded ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Method Effects ◽  
Circular Cylindrical Shells

This paper presents an analytical approach to analyze the nonlinear stability of thin closed circular cylindrical shells under axial compression with material properties varying smoothly along the thickness in the power and exponential distribution laws. Equilibrium and compatibility equations are obtained by using Donnel shell theory taking into account the geometrical nonlinearity in von Karman and initial geometrical imperfection.  Equations to find the critical load and the load-deflection curve are established by Galerkin's method. Effects of buckling modes, of imperfection, of dimensional parameters and of volume fraction indexes to buckling loads and postbuckling load-deflection curves of cylindrical shells are investigated. In case of perfect cylindrical shell, the present results coincide with the ones of the paper  [13] which were solved by Ritz energy method.

Dynamic Behavior of FGM Doubly Curved Panel due to Mechanical Loading

2019 ◽  
Vol 950 ◽  
pp. 200-204
Author(s):  
Guang Ping Zou ◽  
Nadiia Dergachova
Keyword(s):  
Mechanical Loading ◽  
Volume Fraction ◽  
Equivalent Stress ◽  
Functionally Graded ◽  
Excitation Mode ◽  
Simply Supported ◽  
Curved Panel ◽  
Von Mises Equivalent Stress ◽  
Von Mises ◽  
Doubly Curved

This study presents the dynamic response analyze of a simply supported and isotropic functionally graded (FG) double curved panel under mechanical loading. The aim of the research was to investigate mechanical behavior in a FGM curved panel due to different excitation mode of dynamic loading. The novelty of this research is an investigation of von Mises equivalent stress distribution in double curved panel due to different excitation mode. Computed results are found to agree well with the results reported in the literature. Moreover, influence of volume fraction of the material is studied.

Wave propagation analysis of thermoelastic functionally graded nanotube conveying nanoflow

2020 ◽  
pp. 107754632097704
Author(s):  
Jiayin Dai ◽  
Yongshou Liu ◽  
Guojun Tong
Keyword(s):  
Wave Propagation ◽  
Temperature Variation ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Nonuniform Temperature ◽  
Propagation Analysis ◽  
Graded Material ◽  
The Stability ◽  
Volume Fraction Function ◽  
Better Than

As a hollow cylindrical structure, a nanotube has potential to convey nanoflow, which has opened up a field of research. Functionally graded nanotube as a designable structure with continuous variation of material properties can perform better than uniform nanotube, especially in physical field without introducing large stress concentration. In this article, we take the thermal effect into account and investigated the wave propagation characteristics of functionally graded material nanotube conveying nanoflow. In particular, we compared the effects of different kinds of volume fraction function and also the cases of uniform and nonuniform temperature variation. According to the numerical results, we can conclude that as we decrease the exponent n of the volume fraction function, the system is enhanced and larger enhancement can be observed in the case of the power volume fraction function. In addition, there is a positive correlation between the stability and both the temperature variation and the nonuniformity of temperature variation.

Free vibration analysis of porous laminated rotating circular cylindrical shells

2019 ◽  
Vol 25 (18) ◽  
pp. 2494-2508 ◽  
Author(s):  
Ahmad Reza Ghasemi ◽  
Mohammad Meskini
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Equilibrium Equations ◽  
Rotating Speed ◽  
Simply Supported ◽  
Numerical Result ◽  
Love’S Shell Theory ◽  
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.

ON THE FUNDAMENTAL FREQUENCIES AND MODES OF FREE VIBRATION OF CYLINDRICAL SHELLS

1991 ◽  
Vol 15 (2) ◽  
pp. 147-159
Author(s):  
J.L. Urrutia-Galicia ◽  
L.J. Arango
Keyword(s):  
Free Vibration ◽  
Elastic Material ◽  
Cylindrical Shells ◽  
Simply Supported ◽  
Fundamental Frequencies ◽  
Circular Cylindrical Shells

The fundamental frequencies and modes of free vibration of simply supported circular cylindrical shells are explored. The results include the fundamental frequencies ωmn and the modes (m,n) of steel cylindrical shells which are presented in the form of a nomogram, see Figure 6. Besides, single more general formulas are given for cylindrical shells made out of any elastic material which turn out to be very suitable for design and analysis purposes.

scholarly journals Vibration and Buckling Analysis of Cylindrical Shells Made of Functionally Graded Materials under Combined Static and Periodic Axial Forces

2010 ◽  
Vol 19 (2) ◽  
pp. 096369351001900 ◽  
Author(s):  
F. Ebrahimi ◽  
H.A. Sepiani
Keyword(s):  
Transverse Shear ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Deformation Mode ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Axial Forces ◽  
Graded Material

In this study, a formulation for the free vibration and buckling of cylindrical shells made of functionally graded material (FGM) subjected to combined static and periodic axial loadings are presented. The properties are temperature dependent and graded in the thickness direction according to a volume fraction power law distribution. The analysis is based on two different methods of first-order shear deformation theory (FSDT) considering the transverse shear strains and the rotary inertias and the classical shell theory (CST). The results obtained show that the effect of transverse shear and rotary inertias on vibration and buckling of functionally graded cylindrical shells is dependent on the material composition, the temperature environment, the amplitude of static load, the deformation mode, and the shell geometry parameters.

Sign in / Sign up

Export Citation Format

Share Document