Initial Hoop Tension Research Articles

Free vibration analysis of rotating thin-walled cylindrical shells with hard coating based on Rayleigh-Ritz method

This paper focuses on the free vibration analyses of the rotating hard-coating cylindrical shells with various boundary conditions and the effects of hard coating on the vibration behaviors of the rotating shells. To accurately predict more natural characteristics, the characteristic orthogonal polynomials are taken as the admissible displacement functions. Considering the influences of Coriolis force, centrifugal force and initial hoop tension caused by rotation, the equations of motion of the shells are established by the use of the Rayleigh-Ritz method. Based on the state vector method, an efficient method is developed to solve the equations. By comparing with the results of both the finite element analysis and published literatures, the high accuracy and good convergence of the proposed model are verified. In addition, the effects of the boundary conditions, parameters of hard coating, rotating speed and number of circumferential waves on the vibration behaviors of the hard-coating shells are evaluated. This study may provide a reference for the application of hard-coating damping treatment to the vibration suppression of rotating thin-walled structures.

Free vibration analysis of rotating functionally graded GPL-reinforced truncated thick conical shells under different boundary conditions

In this article, the forward and backward wave frequencies of rotating truncated conical thick shells are investigated. The shell is composed of epoxy as the matrix and functionally graded (FG) graphene nanoplatelets (GPLs) as the reinforcement, which are dispersed with four different patterns through the thickness direction. The effective material properties are estimated using the Halpin-Tsai model and the rule of mixture. The influence of shear deformation in the shell is taken into account based on the third-order shear deformation theory (TSDT). By considering a constant angular velocity, and also considering the effects of the initial hoop tension, Coriolis and centrifugal accelerations, a set of governing equations is derived using Hamilton’s principle and is solved for different boundary conditions using generalized differential quadrature method (GDQM). A parametric study is carried out to investigate the influences of various parameters on the forward and backward traveling wave frequencies with respect to the following cases: the boundary conditions, circumferential wave number, rotating speed, geometrical parameters of the shell as well as the mass fraction, distribution pattern, and width and thickness of the GPLs. The numerical results indicates that dispersing more GPL reinforcements near the inner and outer surfaces of the rotating shells leads to a remarkable increase in both forward and backward wave frequencies.

Effect of graphene nanoplatelet reinforcements on the dynamics of rotating truncated conical shells

In this paper, a parametric study is presented for free vibration analysis of rotating truncated conical shells reinforced with graphene nanoplatelets (GNPs). The composite shell is considered to be composed of epoxy as the matrix and the GNPs which are distributed along the thickness direction based on the various distribution patterns. The shell is modeled based on the first-order shear deformation theory (FSDT), and effective material properties are calculated based on the Halpin–Tsai model and the rule of mixture. Incorporating centrifugal and Coriolis accelerations along with initial hoop tension, the set of the governing equations and boundary conditions are derived using Hamilton’s principle and are solved numerically using generalized differential quadrature method. Convergence and accuracy of the presented solution are confirmed, and influences of various parameters on the forward and backward frequencies are investigated including circumferential mode number, boundary conditions, rotational speed, semi-vertex angle and also mass fraction, distribution pattern, width and thickness of the GNPs. It is noteworthy that for the first time, the initial hoop tension is incorporated for a rotating conical shell modeled based on the FSDT.

Parametric resonances of rotating composite laminated nonlinear cylindrical shells under periodic axial loads and hygrothermal environment

This paper focuses on nonlinear parametric resonance behaviors of rotating composite laminated cylindrical shells subjected to periodic axial loads and hygrothermal environment. With effects of the time-varying axial loads, hygrothermal expansion deformation, Coriolis and centrifugal forces as well as the rotation-induced initial hoop tension taken into account, the nonlinear dynamic equations of the shell are obtained on the base of Love’s nonlinear shell theory and Hamilton’s principle. Then, an analytical formulation on the steady state response of the shell is derived by the method of multiple scales, and the stability conditions of trivial and nontrivial solutions are determined by the Routh–Hurwitz criterion. Some numerical results are utilized to conduct detailed parametric studies on vibration characteristics, amplitude–frequency response curves and instability regions of forward and backward travelling waves of the shell. Of particular interest in the process is the combined effect of dynamic axial loads and hygrothermal effects on the resonance behaviors of the rotating nonlinear cylindrical shell.

Active vibration control of rotating laminated composite truncated conical shells through magnetostrictive layers based on first-order shear deformation theory

In this paper, for the first time active vibration control of rotating laminated composite truncated conical shells containing magnetostrictive layers by employing first-order shear deformation theory is investigated. The active vibration control task is done through magnetostrictive layers employing velocity feedback control law. The effects of initial hoop tension and centrifugal and Coriolis forces are considered in extraction of the partial differential equations through Hamilton principle. The ordinary differential equations are derived by employing modified Galerkin method. This study agrees with the mentioned results of the literature. Finally, the effects of several parameters on the vibration suppression are investigated.

Harmonic resonances of graphene-reinforced nonlinear cylindrical shells: effects of spinning motion and thermal environment

This work investigates nonlinear harmonic resonance behaviors of graded graphene-reinforced composite spinning thin cylindrical shells subjected to a thermal load and an external excitation. The volume fraction of graphene platelets varies continuously in the shell’s thickness direction, which generates position-dependent useful material properties. Natural frequencies of shell traveling waves are derived by considering influences of the initial hoop tension, centrifugal and Coriolis forces, thermal expansion deformation, and thermal conductivity. A new Airy stress function is introduced. Harmonic resonance behaviors and their stable solutions for the spinning cylindrical shell are analyzed based on an equation of motion which is established by adopting Donnell’s nonlinear shell theory. The necessary and sufficient conditions for the existence of the subharmonic resonance of the spinning composite cylindrical shell are given. Besides the shell’s intrinsic structural damping, the Coriolis effect due to the spinning motion has a contribution to the damping terms of the system as well. Comparisons between the present analytical results and those in other papers are made to validate the existing solutions. Influences of main factors on vibration characteristics, primary resonance, and subharmonic resonance behaviors of the novel composite cylindrical shell are discussed. Furthermore, the mechanism of how the spinning motion affects the amplitude–frequency curves of harmonic resonances of the cylindrical shell is analyzed.

Influence of Rotation on Vibration Behavior of a Functionally Graded Moderately Thick Cylindrical Nanoshell Considering Initial Hoop Tension

In this research, the effect of rotation on the free vibration is investigated for the size-dependent cylindrical functionally graded (FG) nanoshell by means of the modified couple stress theory (MCST). MCST is applied to make the design and the analysis of nano actuators and nano sensors more reliable. Here the equations of motion and boundary conditions are derived using minimum potential energy principle and first-order shear deformation theory (FSDT). The formulation consists of the Coriolis, centrifugal and initial hoop tension effects due to the rotation. The accuracy of the presented model is verified with literatures. The novelty of this study is the consideration of the rotation effects along with the satisfaction of various boundary conditions. Generalized differential quadrature method (GDQM) is employed to discretize the equations of motion. Then the investigation has been made into the influence of some factors such as the material length scale parameter, angular velocity, length to radius ratio, FG power index and boundary conditions on the critical speed and natural frequency of the rotating cylindrical FG nanoshell.

The influences of magnetostrictive layers on active vibration control of laminated composite rotating cylindrical shells based on first-order shear deformation theory

In this paper for the first time, active vibration control of rotating laminated composite cylindrical shells embedded with magnetostrictive layers as actuators by means of first-order shear deformation theory is studied. Vibration equations of the rotating shell are extracted using Hamilton principle considering the effects of initial hoop tension, Coriolis, and centrifugal forces. The vibration differential equations are reduced to algebraic ones through Galerkin method. The validity of the study is proved by the comparison of some results with the literature results. Eventually, the influence of several parameters on damping characteristics and vibration responses are investigated in detail.

Analytical prediction of the impact response of graphene reinforced spinning cylindrical shells under axial and thermal loads

• An analytical study on impact responses of a cylindrical shell is presented. • Effects of the spinning motion, thermal load and external axial load on results are studied. • Reinforcement effect of graded GPLs is investigated. • A gratifying GPL distribution pattern for impact responses of cylindrical shells is carried out. This paper presents an analytical study that predicts the low-velocity impact response of a spinning functionally graded (FG) graphene reinforced cylindrical shell subjected to impact, external axial and thermal loads. The nanocomposite cylindrical shell is constructed based on a multiplayer model with graphene platelet (GPL) nanofillers whose weight fraction is constant in each concentric cylindrical layer but follows a layer-wise variation in the thickness direction, resulting in the position-dependent elastic moduli, mass density, Poisson's ratio and thermal expansion coefficient through the shell thickness. With effects of the thermal expansion deformation, external axial loads, centrifugal and Coriolis forces as well as the spin-induced initial hoop tension taken into account, the natural frequency of the cylindrical shell is derived on the base of differential equations of motion which are established according to the Donnell's nonlinear shell theory and the Hamilton's principle. The time-dependent contact force between a foreign impactor and the cylindrical shell is calculated by adopting a single spring-mass model. In addition, on the base of the other second-order differential equation, time-dependent displacements and strains are obtained by using the Duhamel integration. In numerical analyses, validation examples are carried out to verify the present solution, and then comprehensive parametric investigations are given to study effects of the GPL weight fraction, dispersion patterns, spinning speeds, temperature variations, geometrical sizes of the shell, the external axial load, radius of the impactor and the impact velocity on the contact force, contact duration and time histories of displacements and strains of the nanocomposite cylindrical shell.

Vibration control of the rotating sandwich cylindrical shell considering functionally graded core and functionally graded magneto-electro-elastic layers by using differential quadrature method

In this paper, the vibration control of the rotating sandwich cylindrical shell considering functionally graded core and functionally graded magneto-electro-elastic (FGMEE) layers is studied. The Hamilton principle, first-order shear deformation theory of shells, constitutive equation considering coupling effect between mechanical, electric, magnetic are considered to derive the equations of motion and distribution of electrical potential, magnetic potential of FGMEE sandwich cylindrical shell. This formulation considers the Coriolis and centrifugal forces and the initial hoop tension resulting from rotation. The differential quadrature method is used for solving the differential equation of motion and also for studying all the boundary conditions. The effects of various parameters such as power low index of core, inner and outer layers, electrical and magnetic control coefficients, different boundary conditions, angular velocity and geometrical coefficient considering the vibration control of sandwich cylindrical shell are also investigated.

Absolute frequency analysis of traveling waves in a thin-wall laminated composite cylindrical shell rotating on two-ending elastic supports

In this paper, some methods to determine the absolute frequencies of traveling waves in a rotating cross-ply laminated cylindrical shell with elastic supports are investigated. Based on the Sanders’ shell theory and by taking into account the Hamilton principle, the governing equations of motion are derived in the rotating coordinate system, which considers the effects of initial hoop tension, the centrifugal and the Coriolis forces due to the rotation as well. The constraint equations of elastic supports are modelled by using artificial distributed elastic springs in the possible directions. By substitution of mode shape profile functions into equations and using the differential quadrature method, the eigenvalue equations of the rotaing shell are derived in both rotating and fixed systems. To make more comparison, the eigenvalue equation of synchronous critical speeds is also derived. Convergence and comparison of the proposed method is investigated through comparing its results with available literature. The comparison results shows that the direction of the corresponding traveling waves and the graphical determination of critical speeds are determined by a more convenient criteria with easier physical interpretation in the fixed system, specially by using the direct method which is more efficient in computation than the converting method.

Nonlinear Dynamic Modeling and Model Reduction Strategy for Rotating Thin Cylindrical Shells

Nonlinear dynamic modeling and model reduction strategy are studied in this paper for a rotating thin cylindrical shell. The nonlinear dynamic model is first established in terms of ordinary differential equations, in which the effects of Coriolis and centrifugal forces are considered, as well as the initial hoop tension due to rotation. This model describes both the in‐plane vibrations and the flexural vibration and reflects the coupling effects of those deformations. Based on this original model, a novel model reduction strategy is proposed to reduce the degrees of freedom by neglecting vibration modes predominated by in‐plane vibrations. Meanwhile, for the reduced‐order model, the in‐plane vibrations’ contributions to the rotating shell’s response are still preserved. To validate the dynamic model and the model reduction strategy, comparisons and simulations are carried out. Subsequently, nonlinear dynamic behaviors are investigated preliminarily by analyzing the rotating cylindrical shell’s amplitude‐frequency responses under different excitation levels.

Vibration characteristics of a rotating composite laminated cylindrical shell in subsonic air flow and hygrothermal environment

This paper focuses on vibration characteristics of a rotating composite laminated cylindrical shell subjected to both subsonic air flow and hygrothermal effects. Based on Love's nonlinear shell theory, and introducing hygrothermal strains into the constitutive relation of single layer material, the dynamic equations of the shell considering rotation, subsonic air flow and hygrothermal effects are obtained by Hamilton's principle. The frequency parameters of the equations are derived by means of Galerkin's method. Some numerical results are performed to conduct detailed parametric studies on vibration characteristics of the shell. In particular, combined effects of subsonic air flow and hygrothermal environment on natural frequencies of forward and backward travelling waves and critical rotating velocity of the shell are discussed, and the influence of initial hoop tension on those frequencies is also carried out. From the results it is shown that rotating angular velocity, subsonic air flow velocity and hygrothermal effects show the significant influence on vibration characteristics of the shell.

Nonlinear free vibration of graded graphene reinforced cylindrical shells: Effects of spinning motion and axial load

This paper presents an analytical study on linear and nonlinear free vibration characteristics and dynamic responses of spinning functionally graded (FG) graphene reinforced thin cylindrical shells with various boundary conditions and subjected to a static axial load. The weight fraction of graphene platelet (GPL) nanofillers in each concentric cylindrical layer is constant but follows a layer-wise variation through thickness direction, resulting in position-dependent elastic moduli, mass density and Poisson's ratio along the shell thickness. Based on the Donnell's nonlinear shell theory, the nonlinear partial differential equations of motion for the cylindrical shell are established by using the Hamilton's principle with the effects of centrifugal and Coriolis forces as well as the spin-induced initial hoop tension taken into account. The governing equations for nonlinear vibration of the nanocomposite cylindrical shell with different GPL dispersion patterns are derived from a set of nonlinear ordinary differential equations which are derived by employing the Galerkin approach. Dynamic responses of forward and backward travelling waves are investigated by analyzing the wave form and the frequency spectrum. Special attention is given to the effects of the weight fraction, dispersion patterns and the geometrical size of GPLs, the external axial load and spinning speeds of the cylindrical shell on the linear and nonlinear free vibrations of the nanocomposite cylindrical shell.

Buckling and free vibration analysis of high speed rotating carbon nanotube reinforced cylindrical piezoelectric shell

• Buckling and vibration behavior of a piezoelectric rotating (CNTRC) shell is investigated. • The generalized differential quadrature method is employed to solve the governing equations. • Both cases of uniform distribution and FG distribution patterns of reinforcements are studied. • Effect of various parameters on critical voltage and natural frequency of piezoelectric rotating CNTRC shell is investigated. In this paper, buckling and free vibration behavior of a piezoelectric rotating cylindrical carbon nanotube-reinforced (CNTRC) shell is investigated. Both cases of uniform distribution (UD) and FG distribution patterns of reinforcements are studied. The accuracy of the presented model is verified with previous studies and also with those obtained by Navier analytical method. The novelty of this study is investigating the effects of critical voltage and CNT reinforcement as well as satisfying various boundary conditions implemented on the piezoelectric rotating cylindrical CNTRC shell. The governing equations and boundary conditions have been developed using Hamilton's principle and are solved with the aid of Navier and generalized differential quadrature (GDQ) methods. In this research, the buckling phenomena in the piezoelectric rotating cylindrical CNTRC shell occur as the natural frequency is equal to zero. The results show that, various types of CNT reinforcement, length to radius ratio, external voltage, angular velocity, initial hoop tension and boundary conditions play important roles on critical voltage and natural frequency of piezoelectric rotating cylindrical CNTRC shell.

Parametric Instability of a Rotating Axially Loaded FG Cylindrical Thin Shell Under Both Axial Disturbances and Thermal Effects

Abstract Parametric instability of a rotating functionally graded (FG) cylindrical thin shell with axial compression under various boundary conditions is studied in this article. In particular, the shell is subjected to both axial periodic displacement disturbances and a thermal environment. The initial hoop tension and Coriolis effects due to rotation are also considered. The coupled dynamic equations of the shell under multiple conditions are formulated based on Love’s thin-shell theory. The instability boundaries of the shell with different boundary conditions considering thermal factors, axial disturbances, and other system parameters are obtained analytically under the case of primary and combination resonance; numerical illustrations are also given. It is found that high temperature weakens the stability of the system, while axial disturbances show stronger influence on the instability regions of the shell compared to other parameters such as thermal factors and the angular rotation velocity.

Nonlinear travelling wave vibrations of a rotating thin cylindrical shell

Nonlinear travelling wave vibrations of a rotating thin cylindrical shell are studied in the paper. Taking into account the effects of centrifugal and Coriolis forces as well as the initial hoop tension due to rotation, governing equations of the nonlinear rotating cylindrical shell with simply supported conditions are derived by using Lagrange equations. The model described by the governing equations is exact, which means no simplification procedures like neglecting all inertia terms on in-plane directions are carried out. Based on the exact model, numerical simulations are carried out to reveal some complex dynamic characteristics of nonlinear travelling wave vibrations, which are different from nonlinear (standing wave) vibrations in generic stationary shells. These results are presented in detail, including amplitude-frequency curves, bifurcation diagrams, time histories, phase portraits, poincaré maps and frequency spectrums.

Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media

This article investigates free vibration of a functionally graded piezomagnetic material cylindrical nanoshell embedded in viscoelastic media under rotational, external electric and magnetic loadings. The governing equations of the nanoshell are derived based on Eringen’s nonlocal theory. It is found that, magnetic and piezoelectric properties of the structure change exponentially along the thickness. The rotational loading is calculated considering initial hoop tension. The results are obtained by applying generalized differential quadrature method to the governing equations and associated boundary conditions. Results also include those achieved for clamped-clamped and simply hinged-hinged boundary conditions. It is found that free vibration characteristics of functionally graded piezomagnetic material cylindrical nanoshell are influenced by several factors including angular velocity, length scale parameter, external voltage, external amperage, functionally graded power index, and viscoelastic media parameters.

Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion

This paper is concerned with free vibration characteristics of the functionally graded graphene reinforced porous nanocomposite cylindrical shell with spinning motion. It is assumed that the graphene platelet (GPL) nanofillers and internal pores are randomly oriented and uniformly dispersed in each concentric cylindrical shell, and both the GPL weight fraction and the porosity coefficient vary continuously along the thickness direction. Effective material properties of the nanocomposite which are position-dependent are derived employing the modified Halpin-Tsai model and the rule of mixture. Three types of the GPL patterns and four types of the porosity distributions are considered. Frequencies of forward and backward travelling waves and critical spinning speeds are derived from the equations of motion which are established based on the first order shear deformation theory and the Hamilton's principle. Detailed parametric studies on dimensionless natural frequencies and critical spinning speeds of the GPL reinforced porous nanocomposite cylindrical shell are carried out, especially, effect of initial hoop tension on vibration characteristics of the spinning cylindrical shell is numerically discussed.

Frequency analysis of rotating truncated conical shells using the Haar wavelet method

• We extend the Haar wavelet method to vibration analysis of rotating conical shells. • We simplify the solution process in this method for non-rotating shells. • Effects of different parameters on the vibration characteristics are investigated. • Critical rotating speed only occurs for the forward wave with mode n = 1. In this study, we present an analysis of the frequency characteristics of rotating truncated conical shells using the Haar wavelet method. Based on the Love first-approximation theory, the governing equations are formulated by considering the effects of centrifugal and Coriolis forces as well as the initial hoop tension due to rotation. The displacement field is expressed as the Haar wavelet series in the axial direction and trigonometric functions in the circumferential direction. By considering the boundary conditions, the eigenvalue equation is obtained to determine the vibration behaviors of rotating conical shells. To validate the current analysis, the results obtained by the proposed method are compared with those reported previously, where the agreement is very good. Finally, we investigate the effects of the geometrical parameters, rotation speed, and boundary conditions on the vibration characteristics of rotating conical shells and the results are presented.