The Experts below are selected from a list of 291 Experts worldwide ranked by ideXlab platform
Marco Amabili - One of the best experts on this subject based on the ideXlab platform.
-
Nonlinear vibrations of truncated conical Shells considering multiple internal resonances
Nonlinear Dynamics, 2020Co-Authors: Marco Amabili, Prabakaran BalasubramanianAbstract:The geometrically Nonlinear vibration response of truncated thin conical Shells is studied for the first time considering the one-to-one internal resonance, a phenomenon typically observed in symmetric structures such as conical Shells. The Novozhilov Nonlinear Shell Theory, retaining all Nonlinear terms in the in-plane strain–displacement relationships of the three mid-surface displacements, is applied to study Nonlinear vibrations of truncated conical Shells. In-plane inertia is also taken into account, and a relatively large number of generalized coordinates, associated with the global discretization of the Shell, is considered. This gives very accurate numerical solutions for simply supported, truncated thin conical Shells. The effect of an exact one-to-one internal resonance, due to the axial symmetry of conical Shells, is fully considered and the results are presented for different excitation levels. The numerical results show that also an almost exact one-to-one internal resonance with a mode presenting a different number of circumferential waves can also arise, which further complicates the Nonlinear vibrations and leads to 1:1:1:1 internal resonance. The numerical model was augmented with additional generalized coordinates to capture this phenomenon. Pitchfork, Neimark–Sacker and period-doubling bifurcations of the forced vibration responses arising from internal resonances are detected, followed and presented, showing complex Nonlinear dynamics.
-
Nonlinear model of human descending thoracic aortic segments with residual stresses
Biomechanics and modeling in mechanobiology, 2018Co-Authors: Ivan Breslavsky, Marco AmabiliAbstract:The Nonlinear static deformation of human descending thoracic aortic segments is investigated. The aorta segments are modeled as straight axisymmetric circular cylindrical Shells with three hyperelastic anisotropic layers and residual stresses by using an advanced Nonlinear Shell Theory with higher-order thickness deformation not available in commercial finite element codes. The residual stresses are evaluated in the closed configuration in an original way making use of the multiplicative decomposition. The model was initially validated through comparison with published numerical and experimental data for artery and aorta segments. Then, two different cases of healthy thoracic descending aorta segments were numerically simulated. Material data and residual stresses used in the models came from published layer-specific experiments for human aortas. The material model adopted in the study is the mechanically based Gasser-Ogden-Holzapfel, which takes into account collagen fiber dispersion. Numerical results present a difference between systolic and diastolic inner radii close to the data available in literature from in vivo measurements for the corresponding age groups. Constant length of the aortic segment between systolic and diastolic pressures was obtained for the material model that takes the dispersion of the fiber orientations into account.
-
Travelling wave and non-stationary response in Nonlinear vibrations of water-filled circular cylindrical Shells: Experiments and simulations
Journal of Sound and Vibration, 2016Co-Authors: Marco Amabili, Prabakaran Balasubramanian, Giovanni FerrariAbstract:Abstract The Nonlinear vibrations of a water-filled circular cylindrical Shell subjected to radial harmonic excitation in the spectral neighbourhood of the lowest resonances are investigated experimentally and numerically by using a seamless aluminium sample. The experimental boundary conditions are close to simply supported edges. The presence of exact one-to-one internal resonance, giving rise to a travelling wave response around the Shell circumference and non-stationary vibrations, is experimentally observed and the Nonlinear response is numerically reproduced. The travelling wave is measured by means of state-of-the-art laser Doppler vibrometers applied to multiple points on the structure simultaneously. Chaos is detected in the frequency region where the travelling wave response is present. The reduced-order model is based on the Novozhilov Nonlinear Shell Theory retaining in-plane inertia and the Nonlinear equations of motion are numerically studied (i) by using a code based on arclength continuation method that allows bifurcation analysis in case of stationary vibrations, (ii) by a continuation code based on direct integration and Poincare maps that evaluates also the maximum Lyapunov exponent in case of non-stationary vibrations. The comparison of experimental and numerical results is particularly satisfactory.
-
Experimental and numerical study on vibrations and static deflection of a thin hyperelastic plate
Journal of Sound and Vibration, 2016Co-Authors: Marco Amabili, Ivan Breslavsky, Prabakaran Balasubramanian, Giovanni Ferrari, Rinaldo Garziera, Kseniia RiabovaAbstract:Abstract The hyperelastic behavior of a thin square silicone rubber plate has been investigated analytically, numerically and experimentally; the case of small-amplitude vibrations has been considered, as well as the case of large static deflection under aerostatic pressure. The Mooney-Rivlin hyperelastic model has been chosen to describe the material Nonlinear elasticity. The material parameters have been identified by a fitting procedure on the results of a uniaxial traction test. For the analytical model, the equations of motion have been obtained by a unified energy approach, and geometrical Nonlinearities are modeled according to the Novozhilov Nonlinear Shell Theory. A numerical model has also been developed by using a commercial Finite-Element code. In the experiments, the silicone rubber plate has been fixed to a heavy metal frame; a certain in-plane pre-load, applied by stretching the plate, has been given in order to ensure a flatness of the surface. An experimental modal analysis has been conducted; results have been used to identify the applied in-plane loads by optimization procedure with two different models: a numerical and an analytical one. The first four experimental and numerical natural modes and frequencies are in good agreement with the experiments after the pre-load identification. The static deflection has been measured experimentally for different pressures. Results have been compared to those obtained by analytical and numerical models. The static deflections are also satisfactorily compared, up to a deflection 50 times larger than the plate thickness, corresponding to a 30 percent strain.
-
vibration of a square hyperelastic plate around statically pre loaded state
ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2014Co-Authors: Ivan D. Breslavskyi, Mathias Legrand, Marco AmabiliAbstract:Static deflection and free Nonlinear vibrations of thin square plate made of biological material are investigated. The involved physical Nonlinearity is described through Neo-Hookean, Mooney-Rivlin and Ogden hyperelastic laws; geometrical Nonlinearity is modeled by Novozhilov Nonlinear Shell Theory. The problem is solved by sequentially constructing the local models that describe the behavior of plate in the vicinity of a certain static configuration. These models are the systems of ordinary differential equations with quadratic and cubic Nonlinear terms in displacement, which allows application of techniques used in analysis of thin-walled structures of physically linear materials. The comparison of static and dynamic results obtained with different material models is carried out.Copyright © 2014 by ASME
Matthias Heil - One of the best experts on this subject based on the ideXlab platform.
-
Airway closure: surface-tension-driven non-axisymmetric instabilities of liquid-lined elastic rings
Journal of Fluid Mechanics, 2002Co-Authors: Matthias Heil, Joseph P. WhiteAbstract:This paper investigates the stability and large-displacement post-buckling behaviour of liquid-lined elastic rings. The fluid flow and the wall deformation are described by the free-surface Navier–Stokes equations and by geometrically Nonlinear Shell Theory, respectively. The fluid–structure interaction problem is solved numerically by a finite element method. The compressive load on the ring is a combination of the external pressure and the effect of surface tension. Once this combined load exceeds a critical value, the subsequent non-axisymmetric collapse of the ring is controlled by the dynamics of the surface-tension-driven redistribution of fluid in the liquid lining. It is shown that, for sufficiently large surface tension, the ring can undergo a catastrophic collapse which leads to a complete occlusion of its lumen. A novel lubrication Theory model, which ensures exact volume conservation for flows on strongly curved substrates, is developed and found to be capable of accurately describing the motion of the air–liquid interface and the fluid–structure interaction in the large-displacement regime, even in cases where the film thickness is large.The findings have important implications for the occurrence of airway closure in lung diseases (such as oedema) which cause an increase in the thickness of the airways' liquid lining. It is shown that under such conditions, airways can become occluded even if the volume of fluid in their liquid lining is much smaller than that required to occlude them in their axisymmetric state.
-
Minimal liquid bridges in non-axisymmetrically buckled elastic tubes
Journal of Fluid Mechanics, 1999Co-Authors: Matthias HeilAbstract:This study investigates the existence and stability of static liquid bridges in non-axisymmetrically buckled elastic tubes. The liquid bridge which occludes the tube is formed by two menisci which meet the tube wall at a given contact angle along a contact line whose position is initially unknown. Geometrically Nonlinear Shell Theory is used to describe the deformation of the linearly elastic tube wall in response to an external pressure and to the loads due to the surface tension of the liquid bridge. This highly Nonlinear problem is solved numerically by finite element methods.It is found that for a large range of parameters (surface tension, contact angle and external pressure), the compressive forces generated by the liquid bridge are strong enough to hold the tube in a buckled configuration. Typical meniscus shapes in strongly collapsed tubes are shown and the stability of these configurations to quasi-steady perturbations is examined. The minimum volume of fluid required to form an occluding liquid bridge in an elastic tube is found to be substantially smaller than predicted by estimates based on previous axisymmetric models. Finally, the implications of the results for the physiological problem of airway closure are discussed.
-
Stokes flow in collapsible tubes: computation and experiment
Journal of Fluid Mechanics, 1997Co-Authors: Matthias HeilAbstract:We are concerned with the problem of viscous flow in an elastic tube. Elastic tubes collapse (buckle non-axisymmetrically) when the transmural pressure (internal minus external pressure) falls below a critical value. The tube's large deformation during the buckling leads to a strong interaction between the fluid and solid mechanics. In this study, the steady three-dimensional Stokes equations are used to analyse the slow viscous flow in such a tube whose deformation is described by geometrically Nonlinear Shell Theory. Finite element methods are used to solve the large-displacement fluid-structure interaction problem. Typical wall deformations and flow fields in the strongly collapsed tube are shown. Extensive parameter studies illustrate the tube's flow characteristics (e.g. volume flux as a function of the applied pressure drop through the tube) for boundary conditions corresponding to the four fundamental experimental setups
-
LARGE POST-BUCKLING DEFORMATIONS OF CYLINDRICAL ShellS CONVEYING VISCOUS FLOW
Journal of Fluids and Structures, 1996Co-Authors: Matthias Heil, Timothy J. PedleyAbstract:This paper examines the post-buckling deformations of cylindrical Shells conveying viscous fluid . The wall deformation is modelled using geometrically Nonlinear Shell Theory , and lubrication Theory is used to model the fluid flow . The coupled fluid ‐ solid problem is solved using a parallelized FEM technique . It is found that the fluid ‐ solid interaction leads to a violent collapse of the tube such that immediate opposite-wall contact occurs after the buckling if the volume flux is kept constant during buckling . If the pressure drop through the tube is kept constant during the buckling , the fluid ‐ solid coupling slows down the collapse (compared to buckling under a dead load) . The ef fects of various parameters (upstream pressure , axial pre-stretch and the geometry of the tube) on the post-buckling behaviour are examined and the exact geometrically Nonlinear Shell Theory is compared to Sanders’ (1963) moderate rotation Theory . Finally , the implications of the results for previous models which described the wall deformation using so called ‘‘tube laws’’ are discussed .
-
Large Axisymmetric Deformation of a Cylindrical Shell Conveying a Viscous Flow
Journal of Fluids and Structures, 1995Co-Authors: Matthias Heil, Timothy J. PedleyAbstract:Abstract Large axisymmetric deformations of collapsible tubes conveying a viscous flow are examined. Geometrically Nonlinear Lagrangian Shell Theory is used to describe the deformation of the tube. The fluid flow is modelled using lubrication Theory. The coupled fluid-solid problem is solved numerically using an FEM technique. In order to explain the mechanisms involved in the tube deformation, the effects of bending stiffness, wall shear stress and axial pre-stretch are examined in detail. The dependence of the tube resistance on the volume flux is investigated for two different experimental set-ups (constant pressure at either upstream or downstream end of the collapsible tube). Finally, the exact Nonlinear Shell Theory used in this paper is compared to Sanders' moderate rotation Theory and an improvement to his Theory is suggested.
Jie Yang - One of the best experts on this subject based on the ideXlab platform.
-
Harmonic resonances of graphene-reinforced Nonlinear cylindrical Shells: effects of spinning motion and thermal environment
Nonlinear Dynamics, 2019Co-Authors: Youheng Dong, Kang Gao, Jie YangAbstract: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.
-
analytical prediction of the impact response of graphene reinforced spinning cylindrical Shells under axial and thermal loads
Applied Mathematical Modelling, 2019Co-Authors: Youheng Dong, Bo Zhu, Yu Wang, Jie YangAbstract:Abstract 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.
-
Nonlinear free vibrations of spinning functionally graded graphene reinforced cylindrical Shells
2019Co-Authors: Youheng Dong, Shaoyu Zhao, Jie YangAbstract:The graphene nanoplatelet (GPL) is a two-dimensional single layer of carbon atoms with extraordinary mechanical, thermal and electrical properties, and can provide excellent reinforcement effects on the matrix when it disperses at a low concentration. Mechanical behaviors of graphene reinforced nanocomposites structures have attracted tremendous interests due to their potential applications in engineering fields. Nonlinear free vibration behaviors of novel functionally graded nanocomposite spinning cylindrical Shells reinforced with GPLs are studied where the weight fraction of GPLs varies through the thickness direction. Three different GPL distribution patterns are considered. The modified Halpin-Tsai micromechanical model and the extend rule of mixture are employed to determine effective values of position-dependent elastic moduli, mass density and Poisson's ratio. Based on the Donnell's Nonlinear Shell Theory, the Nonlinear partial differential equations of motion for the cylindrical Shell are formulated 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. A set of Nonlinear ordinary differential equations are derived by employing the Galerkin approach. Parametric studies of weight fractions, geometrical sizes and distribution patterns of GPLs, spinning speeds and travelling wave numbers on the linear and Nonlinear natural frequencies for the nanocomposite cylindrical Shell are conducted. Results show that the effective stiffness of the cylindrical Shell can be significantly increased by adding small amounts of graphene into the metal matrix. GPLs with a larger surface area but less single graphene layers are preferred nanofillers as they offer the best structural performance of the nanocomposite cylindrical Shell
-
Nonlinear free vibration of graded graphene reinforced cylindrical Shells: Effects of spinning motion and axial load
Journal of Sound and Vibration, 2018Co-Authors: Youheng Dong, Bo Zhu, Yu Wang, Jie YangAbstract:Abstract 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.
Youheng Dong - One of the best experts on this subject based on the ideXlab platform.
-
Harmonic resonances of graphene-reinforced Nonlinear cylindrical Shells: effects of spinning motion and thermal environment
Nonlinear Dynamics, 2019Co-Authors: Youheng Dong, Kang Gao, Jie YangAbstract: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.
-
analytical prediction of the impact response of graphene reinforced spinning cylindrical Shells under axial and thermal loads
Applied Mathematical Modelling, 2019Co-Authors: Youheng Dong, Bo Zhu, Yu Wang, Jie YangAbstract:Abstract 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.
-
Nonlinear free vibrations of spinning functionally graded graphene reinforced cylindrical Shells
2019Co-Authors: Youheng Dong, Shaoyu Zhao, Jie YangAbstract:The graphene nanoplatelet (GPL) is a two-dimensional single layer of carbon atoms with extraordinary mechanical, thermal and electrical properties, and can provide excellent reinforcement effects on the matrix when it disperses at a low concentration. Mechanical behaviors of graphene reinforced nanocomposites structures have attracted tremendous interests due to their potential applications in engineering fields. Nonlinear free vibration behaviors of novel functionally graded nanocomposite spinning cylindrical Shells reinforced with GPLs are studied where the weight fraction of GPLs varies through the thickness direction. Three different GPL distribution patterns are considered. The modified Halpin-Tsai micromechanical model and the extend rule of mixture are employed to determine effective values of position-dependent elastic moduli, mass density and Poisson's ratio. Based on the Donnell's Nonlinear Shell Theory, the Nonlinear partial differential equations of motion for the cylindrical Shell are formulated 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. A set of Nonlinear ordinary differential equations are derived by employing the Galerkin approach. Parametric studies of weight fractions, geometrical sizes and distribution patterns of GPLs, spinning speeds and travelling wave numbers on the linear and Nonlinear natural frequencies for the nanocomposite cylindrical Shell are conducted. Results show that the effective stiffness of the cylindrical Shell can be significantly increased by adding small amounts of graphene into the metal matrix. GPLs with a larger surface area but less single graphene layers are preferred nanofillers as they offer the best structural performance of the nanocomposite cylindrical Shell
-
Nonlinear free vibration of graded graphene reinforced cylindrical Shells: Effects of spinning motion and axial load
Journal of Sound and Vibration, 2018Co-Authors: Youheng Dong, Bo Zhu, Yu Wang, Jie YangAbstract:Abstract 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.
Q Wang - One of the best experts on this subject based on the ideXlab platform.
-
buckling and vibration analysis of a pressurized cnt reinforced functionally graded truncated conical Shell under an axial compression using hdq method
Computer Methods in Applied Mechanics and Engineering, 2016Co-Authors: M Mehri, Hamed Asadi, Q WangAbstract:Abstract The present research deals with bifurcation and vibration responses of a composite truncated conical Shell with embedded single-walled carbon nanotubes (SWCNTs) subjected to an external pressure and axial compression simultaneously. The distribution of reinforcements through the thickness of the Shell is assumed to be either uniform or functionally graded. The equations of motion are established using Green–Lagrange type Nonlinear kinematics within the framework of Novozhilov Nonlinear Shell Theory. Linear membrane prebuckling analysis is conducted to extract the prebuckling deformations. The stability equations are derived by applying the adjacent equilibrium criterion to the prebuckling state of the conical Shell. A semi-analytical solution on the basis of the trigonometric expansion through the circumferential direction along with the harmonic differential quadrature (HDQ) discretization in the meridional direction is developed. A series of comparison studies are carried out to assure the accuracy and the convergence of the HDQ method. The research indicates that the superb accuracy and efficiency of solutions with few grid points are attributed to the higher-order harmonic approximation function in the HDQ method. Parametric studies are also presented to investigate the influence of boundary conditions, semi-vertex angle of the cone, volume fraction and distribution of CNTs on stability and vibration characteristics of the truncated conical Shell. The results show that both volume fraction and distribution of CNTs play a pivotal role in the natural frequencies, buckling mode and buckling loads of the FG-CNTRC truncated conical Shell.
