Dynamic stability of cantilevered functionally graded cylindrical shells under axial follower forces (original) (raw)
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International Journal of Civil Engineering, 2015
The effect of axial deformation of shell particles on the dynamic instability (flutter) of cantilevered cylindrical shells made of functionally graded materials (FGM) under an end axial follower force is addressed. To this end, at first, results for free vibration of FGM cylindrical shells were verified with previous outcomes and they were in very good agreement. Then, the effect of axial deformation of the shell, acting like a reducing linearly-distributed follower load, on the critical circumferential mode number and the flutter load of FGM shells was accounted for. Finally, the effect of axial deformation of the shell particles on the critical circumferential mode number and the flutter load of FGM shells were investigated. In this case, three homogeneous shells with different elasticity moduli and densities and two FGM materials were considered: nickel-stainless steel and stainless steel-alumina. Results include the increasing critical circumferential mode number and the increas...
Journal of Mechanical Science and Technology, 2009
In the present work, study of the vibration of thin cylindrical shells with ring supports made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. Effects of boundary conditions and ring support on the natural frequencies of the FGM cylindrical shell are studied. The cylindrical shells have ring supports which are arbitrarily placed along the shell and which imposed a zero lateral deflection. The study is carried out using different shear deformation shell theories. The analysis is carried out using Hamilton's principle. The governing equations of motion of a FGM cylindrical shells are derived based on various shear deformation theories. Results are presented on the frequency characteristics, influence of ring support position and the influence of boundary conditions. The present analysis is validated by comparing results with those available in the literature.
Mechanical stability of functionally graded stiffened cylindrical shells
Applied Mathematical Modelling, 2009
This paper is concerned with the elastic buckling of stiffened cylindrical shells by rings and stringers made of functionally graded materials subjected to axial compression loading. The shell properties are assumed to vary continuously through the thickness direction. Fundamental relations, the equilibrium and stability equations are derived using the Sander's assumption. Resulting equations are employed to obtain the closed-form solution for the critical buckling loads. The results show that the inhomogeneity parameter and geometry of shell significantly affect the critical buckling loads. The analytical results are compared and validated using the finite element method.
Vibration Characteristics of Ring-Stiffened Functionally Graded Circular Cylindrical Shells
ISRN Mechanical Engineering, 2012
The vibration characteristics of ring stiffened cylindrical shells are analyzed. These shells are assumed to be structured from functionally graded materials (FGM) and are stiffened with isotropic rings. The problem is formulated by coupling the expressions for strain and kinetic energies of a circular cylindrical shell with those for rings. The Lagrangian function is framed by taking difference of strain and kinetic energies. The Rayleigh-Ritz approach is employed to obtain shell dynamical equations. The axial model dependence is approximated by characteristic beam functions that satisfy the boundary conditions. The validity and efficiency of the present technique are verified by comparisons of present results with the previous ones determined by other researchers.
Materials & Design, 2010
This research investigates the free vibration and buckling of a two-layered cylindrical shell made of inner functionally graded (FG) and outer isotropic elastic layer, subjected to combined static and periodic axial forces. Material properties of functionally graded cylindrical shell are considered as temperature dependent and graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. Theoretical formulations are presented 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 transverse shear and rotary inertias have considerable effect on the fundamental frequency of the FG cylindrical shell. The results for nondimensional natural frequency are in a close agreement with those in literature. It is inferred from the results that the geometry parameters and material composition of the shell have significant effect on the critical axial force, so that the minimum critical load is obtained for fully metal shell. Good agreement between theoretical and finite element results validates the approach. It is concluded that the presence of an additional elastic layer significantly increases the nondimensional natural frequency, the buckling resistance and hence the elastic stability in axial compression with respect to a FG hollow cylinder.
Dynamic Stability of FGM Cylindrical Shells
hypersciences.org
In this study, a formulation for the stability 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 dynamic stability 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.
2017
In the present work, study of the vibration of a functionally graded (FG) cylindrical shell made up of stainless steel, zirconia, and nickel is presented. Free vibration analysis is presented for FG cylindrical shells with simply supported-simply supported and clamped–clamped boundary condition based on temperature independent material properties. The equations of motion are derived by Hamilton’s principle. Material properties assume to be graded in the thickness direction according to a simple power law distribution in terms of the volume fraction of the constituents. Effects of boundary conditions and volume fractions (power law exponent) on the natural frequencies of the FG cylindrical shell are studied. Frequency characteristics of the FG shell are found to be similar to those of isotropic cylindrical shells. Furthermore, natural frequencies of these shells are observed to be dependent on the constituent volume fractions and boundary conditions. Strain displacement relations fro...
In this paper, the nonlinear vibrations of functionally graded (FGM) cylindrical shells under different constituent volume fractions and configurations are analyzed. The Sanders-Koiter theory is applied to model nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. Displacement fields are expanded by means of a double mixed series based on Chebyshev orthogonal polynomials for the longitudinal variable and harmonic functions for the circumferential variable. Both driven and companion modes are considered, allowing for the travelling-wave response of the FGM shell. The functionally graded material considered is made of stainless steel and nickel; the properties are graded in the thickness direction, according to a real volume fraction power-law distribution. In the nonlinear model, the shells are subjected to an external radial excitation. Nonlinear vibrations due to large amplitude excitation are considered. Specific modes are selected in the modal expansions; a dynamical nonlinear system is obtained. Lagrange equations are used to reduce nonlinear partial differential equations to a set of ordinary differential equations, from the potential and kinetic energies, and the virtual work of the external forces. Different geometries are analyzed; amplitude-frequency curves are obtained. Convergence tests are carried out considering a different number of asymmetric and axisymmetric modes. The effect of the material distribution on the natural frequencies and nonlinear responses of the shells is analyzed.
Dynamic response of functionally graded circular cylindrical shells subjected to radial impulse load
International Journal of Mechanics and Materials in Design, 2012
Dynamic response of simply supported circular cylindrical shell made of functionally graded material (FGM) subjected to lateral impulse load is investigated. The effective material properties are assumed to vary continuously along the thickness direction according to a volume fraction power law distribution. First order shear deformation theory and Love's first approximation theory are utilized in the equilibrium equations. Finally time response of displacement components is derived using mode superposition method. The influence of material composition, FGM configuration and geometrical parameters (length-to-radius and thickness-to-radius ratios) on the dynamic response is investigated. The results show that even though the shell is thin, the value of power law exponent has a considerable effect on the natural frequencies as well as the dynamic response of the functionally graded shell. Verification of the results of natural frequencies and time response of the FGM shell is achieved by making comparison with those available in the literature and those obtained using commercial software.