Three-dimensional vibration analysis of thick functionally graded conical, cylindrical shell and annular plate structures with arbitrary elastic restraints

A numerical solution for vibration analysis of composite laminated conical, cylindrical shell and annular plate structures

Natural frequency analysis of imperfect GNPRN conical shell, cylindrical shell, and annular plate structures resting on Winkler-Pasternak Foundations under arbitrary boundary conditions

A unified Fourier series solution for vibration analysis of FG-CNTRC cylindrical, conical shells and annular plates with arbitrary boundary conditions

Free vibration analysis of laminated closed conical, cylindrical shells and annular plates with a hole using a meshfree method

This article describes the use of fibre reinforced polymer composites to increase the strength of an isotropic metallic cylindrical shell against elephant’s foot buckling. This form of buckling occurs when a cylindrical shell structure is subjected to high internal pressure together with an axial force, such as those that may occur in tanks and silos. It is particularly relevant to tanks under seismic action. Although fibre reinforced polymer composites have been widely applied to different types of structures under several loading conditions, its use to strengthen thin steel cylindrical shells has been very limited. Here, a non-linear elasto-plastic finite element idealisation is used to explore the strengthening effect of a fibre reinforced polymer strip on a thin cylinder. The optimum size and position of the fibre reinforced polymer sheet were obtained and empirically formulated. This study has shown that the strength after repair is sensitive to minor changes in the fibre reinforced polymer parameters so that a close adherence to the optimum parameter values is very desirable.

The cylindrical shell is a widely used structure in engineering practice, and its main form of failure is instability due to buckling. As a classical problem in the field of mechanics, the stability of cylindrical shells has been studied extensively. However, the large difference between the theoretically predicted results of the critical buckling load and the experimental results for the cylindrical shells subjected to uniform axial pressure has contributed to the continuous development of the shell stability theory. This paper briefly reviews the development of the shell stability theory, then presents an overview of the current status and trends of stability research on the stiffened cylindrical shell widely used in cylindrical shell structures in real engineering, and finally presents the difficulties and directions of future stability research on cylindrical shell structures in engineering applications.

Three-dimensional buckling and free vibration analyses of initially stressed functionally graded graphene reinforced composite cylindrical shell

An analysis is carried out of axisymmetric waves propagating along fluid-loaded cylindrical shells within the framework of linear elasticity and classical perfect-slip boundary conditions at the solid–fluid interface. Numerical solutions are obtained for various axisymmetric eigenmodes for a cylindrical shell in vacuum; a cylindrical shell surrounded by a liquid of infinite radial extent; a hypothetical liquid column with both the stress-free and displacement-free boundary conditions; a cylindrical shell with a liquid core; and a cylindrical shell immersed in an infinite liquid. Numerical results are obtained for both the radiating (leaky) and nonradiating eigenmodes of the system by a careful search of the complex eigenfrequencies of the associated boundary value problem. In particular, attenuation of leaky modes due to radiation of energy into the surrounding medium is expressed in terms of the imaginary part of the eigenfrequency. Computational results are presented for the dispersion curves as well as the displacement and stress amplitude component distributions along the radial direction for various propagating modes of the system. Practical benefits from such analyses are discussed.

This paper reinvestigates the classic problem of the dispersion relations of a cylindrical shell by obtaining a complete set of analytical solutions, based on Flügge’s theory, for all orders of circular harmonics, n=0,1,2,…,∞. The traditional numerical root search process, which requires considerable computational effort, is no longer needed. Solutions of the modal patterns (eigenvectors) for all propagating (and nonpropagating) modes are particularly emphasized, because a complete set of properly normalized eigenvectors are crucial for solving the vibration problem of a finite shell under various admissible boundary conditions. The dispersion relations and the associated eigenvectors are also the means by which to construct transfer matrices used to analyze the vibroacoustic transmission in cylindrical shell structures or pipe-hose systems. The eigenvectors obtained from the conventional method in shell analysis are not as conveniently normalized as those commonly used in mathematical physics. The present research proposes a new alternative method to find eigenvectors that are normalized such that their norms equal unity. A parallel display of the dispersion curves and the associated modal patterns has been used in the discussion and shown to provide a more insightful understanding of the wave phenomena in a cylindrical shell.

3D braided composite is gaining popularity over the traditional composite because it has a higher impact resistance, fatigue strength, stiffness in the thickness direction, anti-delamination capability, etc. Based on bridging models, the fibers are considered as transversely isotropic and matrix isotropic. The equivalent material properties of the composites are computed using a volume averaging method (VAM). The four steps 1 × 1 braided technique are introduced to manufacture the 3D braided singly and doubly curved shell panels. The bridging model claimed to be more accurate in predicting mechanical properties and shear modulus in comparison with the other method. In the present study, the free vibration response of 3D braided curved panels is obtained using finite element methods (FEM). A third-order shear deformation (TSDT) with twelve degrees of freedom per node is for the first time employed in 3D braided panels using eight nodded isoparametric formulation. In this theory, the transverse displacement is the function of the thickness coordinate. In reality, the normal stress of the thick shells in the thickness direction can't be neglected. This theory having the capability of predicts the normal stress in the thickness direction. Hence, to predict the accurate results of the 3D braided shell, it has more capability compared to the other shell theory. The free vibration results of the shell panels' viz. cylindrical shells (CYS), elliptical paraboloid shells (EPS), and hyperbolic paraboloid shells (HPS) are computed at a different braided angle, braided volume fraction, aspect ratio, thickness ratio, curvature ratio, and boundary conditions, etc. HIGHLIGHTS The equivalent material properties of the 3D braided composites are calculated using bridging models based on a volume averaging method (VAM). The bridging model claimed to be more accurate in predicting mechanical properties and shear modulus in comparison with the other method. A third-order shear deformation (TSDT) with twelve degrees of freedom per node is for the first time employed in 3D braided panels using eight nodded isoparametric formulation. In this theory, the transverse displacement is the function of the thickness coordinate. To predict the 3D braided shell's accurate results, it has more capability than the other shell theory. The free vibration results of the shell panels' viz. cylindrical shells (CYS), elliptical paraboloid shells (EPS), and hyperbolic paraboloid shells (HPS) are computed at a different braided angle, braided volume fraction, aspect ratio, thickness ratio, curvature ratio, and boundary conditions, etc.

For conducting scientific research at depths in the ocean, deep-sea probes are essential pieces of equipment. The cylindrical shell is the most sensible and rational packaging structure for these detectors. New technical challenges for enhancing the pressure resistance and lightweight design of the pressure-resistant cylindrical shell arise from the need to ensure that the detector packaging structure can withstand the immense water pressure at tens of thousands of meters in the underwater environment, while simultaneously reducing the detector packaging structure’s self-weight. This article examines the detection system’s deep-sea pressure-resistant cylindrical shell. To address the issue of the pressure-resistant shell’s insufficient ability to counteract the overall instability caused by the inability to form unstable half-waves in the radial direction when the ring rib pressure-resistant shell experiences it, a design method for the ribs inside the unequal-stiffness pressure-resistant cylindrical shell is suggested. The shell’s instability pressure increases by 9.65 MPa following the stiffness adjustment. Simultaneously, in order to attain even more lightweight optimization, the optimal inner rib section was obtained by applying the orthogonal topology optimization method, which also reduced the weight by 106.8 g and effectively improved the compression stability of the high-pressure cylindrical shell structure. Based on this, key optimization variables were found by performing sensitivity analysis on the cylindrical shell structure’s parameters. Then, with lightweighting as the primary objective, the high-pressure-resistant cylindrical shell’s optimal structural parameters were found using a multi-objective optimization process using the second-generation fast non-dominated genetic algorithm (NSGA-2). This resulted in a weight reduction of 1.2492 kg, or 17.26% of the original pressure-resistant shell. This has led to the development of a lightweight, highly pressure-resistant method for packaging marine exploration equipment structures.

A modified Fourier–Ritz solution for vibration and damping analysis of sandwich plates with viscoelastic and functionally graded materials

A dynamic model is developed to incorporate a curved beam periodic structure in the transfer path of an internal isolation system to reduce the resultant vibro-acoustic of the receiving cylindrical shell structure in a passive broadband way. The vibration transmission from the multi-connected internal isolation system with/without the curved beam periodic structure is built by the matrix method. The analytical representation of the curved beam is employed to establish the transfer matrix dynamic model of the proposed multi-layer curved beam periodic structure. Both numerical simulations and experimental investigations are carried out. The numerical simulations demonstrate that the resonances of the internal isolation system will magnify the vibro-acoustic responses notably and the designed curved beam periodic structure is an effective band-stop mechanical filter to minimize the vibration transmission and acoustic radiation responses at resonances in the band gap. The experimental results confirm that the normal acceleration responses on both the bases and the surface of the cylindrical shell are reduced in the band gap of the curved beam periodic structure. An average reduction amount of 9∼12 dB on the bases and 2∼3 dB on the shell is obtained. The vibration transmission in the curved beam periodic structure is tested and found to be influenced by the boundary conditions at the input and output ends, which is different from that under the free boundary conditions.

An investigation of the vibration behaviour of carbon-nanotube reinforced composite beams utilizing both traditional and non-traditional boundary conditions is carried out. The Timoshenko formulation is chosen so as to include the effects of deformation of shear and rotary inertia and to obtain the coupled equations of motion which govern vibration of the beam. The Chebyshev collocation method is employed to solve the governing equations to determine the frequencies of the beams with different boundary conditions and compressive loading imposed. Correctness and dependability of the Chebyshev collocation method are validated by comparison with previous results found in the literature for the traditional boundary conditions. Calculations will also be presented for non-traditional (elastic) boundary conditions for different parameters.KeywordsChebyshev collocationTimoshenkoMechanical vibrationCarbon-nanotubeComposite

Cylindrical shell structures are widely used in engineering due to their high strength-to-weight ratio, with applications in automotive, aerospace, and marine. However, these structures are highly susceptible to buckling under axial compression, with experimental studies showing significantly lower load-bearing capabilities than analytical predictions due to their sensitivity to geometric imperfections. This study proposes an AI-driven model to predict the critical buckling loads of cylindrical shells with unknown imperfections, using non-destructive probing test responses and a model trained on simulation data. Finite Element Analysis (FEA) is performed on a model without imperfections to obtain its buckling modes. These modes’ deformations are then scaled and superimposed onto the perfect shape to introduce arbitrary imperfections in samples. Through conducting buckling simulations on a soda-can-size cylindrical shell, a data set comprising over 2,000 imperfect buckling samples was generated, and their load-bearing capacity and effective stiffness was obtained. Furthermore, a lateral probing experiment was simulated on the midpoint of the shell face to obtain the stability landscape in different imperfection conditions. The data was preprocessed, and meaningful features were extracted from it. An innovative network comprising of 2D convolutional neural networks (CNNs) and Extreme Gradient Boosting (XGBoost) models were employed to predict the buckling load and imperfection state of specimens.