Asymmetric Large Deformation Superharmonic and Subharmonic Resonances of Spiral Stiffened Imperfect FG Cylindrical Shells Resting on Generalized Nonlinear Viscoelastic Foundations

2020 ◽  
Vol 12 (05) ◽  
pp. 2050052
Author(s):  
Kamran Foroutan ◽  
Habib Ahmadi ◽  
Mohammad Shariyat
Keyword(s):  
Multiple Scales ◽  
Cylindrical Shells ◽  
Viscoelastic Model ◽  
Excitation Amplitude ◽  
Functionally Graded ◽  
Function Concept ◽  
Nonlinear Viscoelastic ◽  
Foundation Type ◽  
Nonlinear Elastic ◽  
Subharmonic Resonances

This paper is devoted to superharmonic and subharmonic behavior investigation of imperfect functionally graded (FG) cylindrical shells with external FG spiral stiffeners under large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation, which is composed of a two-parameter Winkler–Pasternak foundation augmented by a Kelvin–Voigt viscoelastic model with a nonlinear cubic stiffness, to account for the vibration hardening/softening phenomena and damping considerations. The von Kármán strain-displacement kinematic nonlinearity is employed in the constitutive laws of the shell and stiffeners. The external spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. The coupled governing equations are solved by using Galerkin’s method in conjunction with the stress function concept. The multiple scales method is utilized to detect the subharmonic and superharmonic resonances and the frequency–amplitude relations of the 1/3 and 1/2 subharmonic and 3/1 and 2/1 superharmonic resonances of the system. Finally, the influences of the stiffeners helical angles, foundation type, coefficient of the nonlinear elastic foundation, material distribution, and excitation amplitude on the system resonances are investigated comprehensively.

Superharmonic and Subharmonic Resonances of Spiral Stiffened Functionally Graded Cylindrical Shells under Harmonic Excitation

2019 ◽  
Vol 19 (10) ◽  
pp. 1950114 ◽  
Author(s):  
Habib Ahmadi ◽  
Kamran Foroutan
Keyword(s):  
Multiple Scales ◽  
Plate Theory ◽  
Cylindrical Shells ◽  
Harmonic Excitation ◽  
Functionally Graded ◽  
Classical Plate Theory ◽  
Geometrical Properties ◽  
Hardening Nonlinearity ◽  
Subharmonic Resonances ◽  
Theory Of Shells

This paper presents the superharmonic and subharmonic resonances of spiral stiffened functionally graded (SSFG) cylindrical shells under harmonic excitation. The stiffeners are considered to be externally or internally added to the shell. Also, it is assumed that the material properties of the stiffeners are continuously graded in the thickness direction. In order to model the stiffeners, the smeared stiffener technique is used. Within the context of the classical plate theory of shells, the von Kármán nonlinear equations are derived for the shell and stiffeners based on Hooke’s law and the relations of stress-strain. Using Galerkin’s method, the equation of motion is discretized. The superharmonic and subharmonic resonances are analyzed by the method of multiple scales. The influence of the material parameters and various geometrical properties on the superharmonic and subharmonic resonances of SSFG cylindrical shells is investigated. Considering these results, the hardening nonlinearity behavior and jump value of cylindrical shell is less and more than others, when the angle of stiffeners is [Formula: see text] and [Formula: see text], respectively.

Nonlinear Static and Dynamic Buckling Analyses of Imperfect FGP Cylindrical Shells Resting on Nonlinear Elastic Foundation Under Axial Compression

2020 ◽  
Vol 20 (07) ◽  
pp. 2050074
Author(s):  
Kamran Foroutan ◽  
Habib Ahmadi
Keyword(s):  
Elastic Foundation ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
Dynamic Buckling ◽  
Functionally Graded ◽  
Porosity Distribution ◽  
Nonlinear Elastic Foundation ◽  
Special Cases ◽  
Nonlinear Static ◽  
Nonlinear Elastic

In this paper, semi-analytical and analytical methods for the nonlinear static and dynamic buckling analyses of imperfect functionally graded porous (FGP) cylindrical shells subjected to axial compression are presented. The structure is embedded within a generalized nonlinear elastic foundation, treated as a two-parameter Winkler–Pasternak foundation augmented by a nonlinear cubic stiffness. The material property of the shell changes continuously through the thickness. Two types of FGP distributions, i.e. uniform porosity distribution (UPD) and nonuniform porosity distribution (NPD), are considered. By applying the Galerkin’s method to the von Kármán equations, the buckling of the shells was solved. The fourth-order Runge–Kutta method is utilized to obtain the responses of nonlinear dynamic buckling (NDB). The results obtained for some special cases are compared with those available elsewhere. The effects of various geometrical properties, material parameters and elastic foundation coefficients are investigated on the nonlinear static buckling (NSB) and dynamic buckling (DB) analyses of the shells. It was shown that various types of porosity, imperfection and the elastic foundation parameters have a strong effect on the buckling behaviors of the FGP cylindrical shells.

Large Amplitude Dynamic Analysis of FGM Cylindrical Shells on Nonlinear Elastic Foundation Under Thermomechanical Loads

2017 ◽  
Vol 09 (07) ◽  
pp. 1750105 ◽  
Author(s):  
Abbas Hadi ◽  
Hamid Reza Ovesy ◽  
Saeed Shakhesi ◽  
Jamshid Fazilati
Keyword(s):  
Elastic Foundation ◽  
Shell Thickness ◽  
Thermal Environment ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Governing Equations ◽  
Nonlinear Elastic Foundation ◽  
Nonlinear Dynamic Characteristics ◽  
Linear And Nonlinear ◽  
Nonlinear Elastic

Nonlinear dynamic characteristics of functionally graded material (FGM) cylindrical shells surrounded by nonlinear elastic foundation under axial static and lateral dynamic loads in thermal environment are investigated in the current paper. The main emphasis is on the simulation of the elastic foundation model and thermal loads. Nonlinear tri-parametric elastic foundation including linear and nonlinear parameters is used to model the reaction of the elastic foundation on the cylindrical shell. Different thermal loading scenarios are applied to the system to study the effects of thermal environment, including uniform, linear and nonlinear temperature distribution across the shell thickness. Governing equations are derived based on the Donnell’s thin shell theory. Material properties of the FGM are assumed to be variable through the shell thickness according to a power law function. Discretization of the obtained governing equations is performed using the Galerkin’s method. An averaging method and the Runge–Kutta method are applied to obtain the frequency–amplitude relation and time–deflection relation, respectively. Comprehensive numerical results are given for investigating the effects of thermo-mechanical loads, material and geometrical properties and nonlinear elastic foundation parameters on nonlinear dynamic characteristics of the functionally graded cylindrical shells (FGCSs). Present formulations are validated by comparing the results with the published data for some specific cases.

scholarly journals Anomalous Nonlinear Dynamics Behavior of Fractional Viscoelastic Beams

2021 ◽  
Author(s):  
Jorge L. Suzuki ◽  
Ehsan Kharazmi ◽  
Pegah Varghaei ◽  
Maryam Naghibolhosseini ◽  
Mohsen Zayernouri
Keyword(s):  
Nonlinear Dynamics ◽  
Differential Equation ◽  
Free Vibration ◽  
Multiple Scales ◽  
Viscoelastic Model ◽  
Primary Resonance ◽  
Decay Rates ◽  
Distribution Functions ◽  
Analytical Scheme ◽  
Nonlinear Viscoelastic

Abstract Fractional models and their parameters are sensitive to intrinsic microstructual changes in anomalous materials. We investigate how such physics-informed models propagate the evolving anomalous rheology to the nonlinear dynamics of mechanical systems. In particular, we study the vibration of a fractional, geometrically nonlinear viscoelastic cantilever beam, under base excitation and free vibration, where the viscoelasticity is described by a distributed-order fractional model. We employ Hamilton's principle to obtain the equation of motion with the choice of specific material distribution functions that recover a fractional Kelvin-Voigt viscoelastic model of order $\alpha$. Through spectral decomposition in space, the resulting time-fractional partial differential equation reduces to a nonlinear time-fractional ordinary differential equation, where the linear counterpart is numerically integrated through a direct L1-difference scheme. We further develop a semi-analytical scheme to solve the nonlinear system through a method of multiple scales, yielding a cubic algebraic equation in terms of the frequency. Our numerical results suggest a set of $\alpha$-dependent anomalous dynamic qualities, such as far-from-equilibrium power-law decay rates, amplitude super-sensitivity at free vibration, and bifurcation in steady-state amplitude at primary resonance.

scholarly journals A New Analytical Approach for Nonlinear Global Buckling of Spiral Corrugated FG-CNTRC Cylindrical Shells Subjected to Radial Loads

2020 ◽  
Vol 10 (7) ◽  
pp. 2600
Author(s):  
Tho Hung Vu ◽  
Hoai Nam Vu ◽  
Thuy Dong Dang ◽  
Ngoc Ly Le ◽  
Thi Thanh Xuan Nguyen ◽  
...  
Keyword(s):  
Analytical Approach ◽  
Cylindrical Shells ◽  
Equation System ◽  
Functionally Graded ◽  
Governing Equations ◽  
Reinforced Composite ◽  
Global Buckling ◽  
Homogenization Model ◽  
Corrugated Structure ◽  
The Galerkin Method

The present paper deals with a new analytical approach of nonlinear global buckling of spiral corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells subjected to radial loads. The equilibrium equation system is formulated by using the Donnell shell theory with the von Karman’s nonlinearity and an improved homogenization model for spiral corrugated structure. The obtained governing equations can be used to research the nonlinear postbuckling of mentioned above structures. By using the Galerkin method and a three term solution of deflection, an approximated analytical solution for the nonlinear stability problem of cylindrical shells is performed. The linear critical buckling loads and postbuckling strength of shells under radial loads are numerically investigated. Effectiveness of spiral corrugation in enhancing the global stability of spiral corrugated FG-CNTRC cylindrical shells is investigated.

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