Vibrations Of Shells Research Articles

Free vibration analysis of sandwich shells with cutouts: An experimental and numerical study with artificial neural network modelling

This article investigates the free vibration and damping characteristics of cylindrical sandwich shells with cutouts using both experimental and numerical approaches. The effects of cutout shape, size, and position on the dynamic response of cylindrical sandwich shells are explored. Moreover, Artificial Neural Network (ANN) models are constructed to predict the dynamic behavior of the sandwich shell with a cutout. A user-friendly application, Sandwich Shell Vibration Analysis (SSVibA), is developed, incorporating the ANN models to predict the non-dimensionalized natural frequencies and modal loss factors of the sandwich shell under different shell geometries, boundary conditions and cutout configurations. The objective of the present research is to advance the understanding of the dynamic behavior of sandwich structures by integrating experimental investigations, numerical analyses, and ANN modeling.

Vibrations of Plates and Shells with Attached Mass

Vibrations of Plates and Shells with Attached Mass

Free Vibration of Graphene Nanoplatelet-Reinforced Porous Double-Curved Shells of Revolution with a General Radius of Curvature Based on a Semi-Analytical Method

Based on domain decomposition, a semi-analytical method (SAM) is applied to analyze the free vibration of double-curved shells of revolution with a general curvature radius made from graphene nanoplatelet (GPL)-reinforced porous composites. The mechanical properties of the GPL-reinforced composition are assessed with the Halpin–Tsai model. The double-curvature shell of revolution is broken down into segments along its axis in accordance with first-order shear deformation theory (FSDT) and the multi-segment partitioning technique, to derive the shell’s functional energy. At the same time, interfacial potential is used to ensure the continuity of the contact surface between neighboring segments. By applying the least-squares weighted residual method (LWRM) and modified variational principle (MVP) to relax and achieve interface compatibility conditions, a theoretical framework for analyzing vibrations is developed. The displacements and rotations are described through Fourier series and Chebyshev polynomials, accordingly, converting a two-dimensional issue into a suite of decoupled one-dimensional problems. The obtained solutions are contrasted with those achieved using the finite element method (FEM) and other existing results, and the current formulation’s validity and precision are confirmed. Example cases are presented to demonstrate the free vibration of GPL-reinforced porous composite double-curved paraboloidal, elliptical, and hyperbolical shells of revolution. The findings demonstrate that the natural frequency of the shell is related to pore coefficients, porosity, the mass fraction of the GPLs, and the distribution patterns of the GPLs.

Vibration of composite open shell of hydrogen-electric fuselage with rectangular cutout in hygrothermal circumstances: theoretical and experimental research

An effective formulation is performed to approximate calculate the vibration of the typical composite fuselage battery compartment structures of the hydrogen-electric aircraft, which are highly sensitive to hygrothermal circumstances. The strain energy, kinetic energy and hygrothermal potential energy of CLOCSRC are deduced in frame of Donnell's shell assumption and a series of hypothetical elastic springs operating on the edges of divided components are introduced to simulate coupling connection and the elastic supports of the open shell, which contribute to total system energy in the form of elastic spring potential energy. The equations of motion for CLOCSRC subjected to distinct hygrothermal circumstances and arbitrary boundaries are eventually obtained in frame of the Rayleigh-Ritz method by means of the modified orthogonal polynomial as the displacement admissible function. After confirming the convergence and accuracy of the presented formulation by experiment and finite element method, several numerical examples are presented to investigative the effects of geometric parameters, elastic boundaries and hygrothermal circumstances on the vibration of CLOCSRC. Differ from traditional investigation, the present paper offers an effective approach to insight the hygrothermal mechanism of open shell with rectangular cutouts creatively. The relevant investigation demonstrated that the current strategy is beneficial for further research on the vibration characteristics of CLOCSRC.

Nonlinear thermo-mechanical dynamic buckling and vibration of FG-GPLRC circular plates and shallow spherical shells resting on the nonlinear viscoelastic foundation

Nonlinear thermo-mechanical dynamic buckling and vibration of FG-GPLRC circular plates and shallow spherical shells resting on the nonlinear viscoelastic foundation

Periodic and chaotic vibrations of dielectric elastomer spherical shells considering structural damping

Periodic and chaotic vibrations of dielectric elastomer spherical shells considering structural damping

High-dimensional nonlinear flutter suppression of variable thickness porous sandwich conical shells based on nonlinear energy sink

Nonlinear energy sink (NES) is widely applied in engineering field due to the advantages of light weight, high robustness, unidirectional energy transfer, rapid and broadband vibration isolation. In this paper, nonlinear energy sink is utilized to suppress vibration of the variable thickness porous sandwich conical shells for the first time, and the high-dimensional nonlinear flutter suppression characteristics of the system of simply supported variable stiffness truncated porous sandwich conical shell coupled NES under aerodynamic force and thermal stress are investigated. By applying the first-order shear deformation theory (FSDT), Hamilton's principle and Galerkin technique, the high-dimensional nonlinear ordinary differential flutter suppression equations of the system appended with NES are established. The accuracy of the theoretical approach is ensured by the comparison of frequency results, while the NES dissipated kinetic energy ratio and the comparison of NES performance with other suppression systems are presented to prove the effectiveness of NES on nonlinear flutter suppression. The time history diagrams and limit cycle oscillation (LCO) amplitude curves, which reflect the high-dimensional nonlinear flutter suppression effect of NES, are obtained by employing the Runge-Kutta method. The effects of aerodynamic pressure, the parameters and positions of single NES, and the positions of parallel NES and series NES on the high-dimensional nonlinear flutter suppression characteristics of the system attached with NES are discussed in depth. Finally, the optimal high-dimensional nonlinear flutter suppression scheme is arrived.

Analytical solution for strongly nonlinear vibration of a stringer shell

In this paper, a new approach called the global residue harmonic balance technique is applied to construct analytical solutions for nonlinear oscillators that appear in cylindrical shells. Periodic solution is analytically proved, and consequently, the relation between amplitude and frequency is obtained in an analytical form. Numerical and analytical comparisons with the Runge–Kutta method and previously existing homotopy perturbation method (HPM) are given, to show the stability, quality, and efficiency of the present approach. The GRHBM provides an outstanding agreement with the numerical results for different amplitude values, leading to sufficiently accurate solutions for nonlinear oscillators.

Shock Response of Water-Protected Spherical Explosion Containment Vessels

Abstract Explosion containment vessels (ECVs) are important equipment used for underwater explosion experiment research. In this paper, a method is proposed to improve the blast resistance of the ECV by placing it in the water medium. The shock response caused by the underwater explosion in a spherical ECV is studied. The single-layer thin-walled spherical vessel shell submerged in an infinite domain water medium is deduced and simplified as a single-degree-of-freedom elastic vibration system with viscous damping. The underwater explosion shock wave is simplified to an exponential shock loading, and the analytical solutions of the radial shock vibration of the spherical shell are obtained using Duhamel's integrals. Compared with the numerical simulation results, the accuracy of the theoretical model is verified. The study results show that the water medium radiates out vibration energy and plays an important role in eliminating vibration through damping. It is found that the vibration damping ratio can be controlled by adjusting the vessel radius and thickness, so that the vibration of the shell can be controlled within three periods and the impact fatigue can be reduced. In addition, the radiation damping of the water medium greatly reduces the maximum radial displacement of the spherical shell, which significantly improves the blast resistance of the spherical shell.

Cutout effects on the vibration of sandwich auxetic cylindrical shells with an experimental validation

This study investigates the influence of auxetic core layers on the vibrational characteristics of sandwich cylindrical shells with cut-outs. The analysis utilizes the First-order Shear Deformation Theory (FSDT) and analytical techniques. The irregular behavior of auxetic re-entrante honeycomb cells necessitates the exploration of their effects on various systems. Additionally, the proposed method offers advantages over Finite Element Method (FEM). FEM modeling suffers from increased computational time and reduced accuracy with a large number of elements or high aspect ratio elements. These challenges are particularly significant for shells with geometric features of disparate scales, such as large cylinders with tiny cutouts or cutouts with low aspect ratios. However, the present research addresses these challenges by employing a method that integrates five panels with varying dimensions. Consequently, each section can utilize specific Two-Dimensional Generalized Differential Quadrature (2D-GDQ) grid points, tailored to the size of each side, enabling rapid and accurate prediction of displacement and stress parameters, particularly for shorter sides. The proposed method excels at precisely modeling cutouts while preserving their realistic properties. This is achieved by avoiding geometric and material simplifications and by assigning distinct boundary conditions to each region, including critical areas like corners, internal, and external sides. Moreover, Frequency Response Functions (FRFs) obtained from accelerometer and laser signals, alongside vibration-induced sound wave signals captured by electroacoustic microphones, validate the precision of the numerical calculations.

Dynamic examination of closed cylindrical shells utilizing the differential transform method

This article presents an innovative approach using the Differential Transform Method (DTM) to analyze the vibration characteristics of cylindrical shells, integrating Taylor's series with Sander's classical theory. It demonstrates DTM's efficiency, accuracy, and potential as an alternative method. The study introduces a novel application of the DTM in exploring the free vibration of cylindrical shells, detailing a technique to address challenges such as normalization, linear solution methodologies, and parameter derivative modifications. A dimensionless parameter analysis evaluates the impact of length, radius, thickness, and modulus of elasticity. Comparative analysis with Hybrid Finite Element Method (FEM) data and validation against existing literature highlights DTM's precision and reliability. In conclusion, DTM offers a robust solution for the eigenvalue problem in coupled differential equations, providing accurate vibration parameters. Additionally, an important relationship between the modulus of elasticity and frequency in the dimensionless state was obtained.

FEM-BEM analysis of acoustic interaction with submerged thin-shell structures under seabed reflection conditions

The paper introduces a novel method for simulating acoustic–shell interaction subject to seabed reflection. The vibration of thin-shell structure is analyzed using the finite element method (FEM) with Kirchhoff–Love shell elements. Exterior acoustic fields associated with seabed reflection is simulated by the boundary element method (BEM) with half-space fundamental solutions. Then the FEM and BEM are coupled to simulate interaction between acoustics wave and shell vibration in the context of isogeometric analysis. Finally, fast multipole method is formulated for the coupled system to accelerate computation and reduce memory storage. Numerical examples are provided to demonstrate the accuracy of the algorithm.

Structural Study of Four-Layered Cylindrical Shell Comprising Ring Support

In this work, the vibration analysis of a layered, cylinder-shaped shell is undertaken. The structure of the shell layers is composed of functionally graded and isotropic materials. The vibrations of four-layered cylindrical shells with a ring support along the axial direction are investigated in this research. The two internal layers are composed of isotropic materials, and the external two layers are composed of functionally graded materials. The outer functionally graded material layers considered are stainless steel, zirconia, and nickel. The inner two isotropic layers considered are aluminum and stainless steel. The shell frequency equation is acquired by employing the Rayleigh–Ritz method under the shell theory of Sanders. The trigonometric volume fraction law is used to sort the functionally graded material composition of the FGM layers. The natural frequencies are attained under two boundary conditions, namely simply supported–simply supported and clamped–clamped.

An analytical study of thermal environment’s effect on the free vibration of FGM double curved FG shells

The main objectif of this work is to examine the thermal environment’s effect of on the free vibration of double curvature shells made of functionally graded materials. A new mathematical model based on higher order shear deformation theory, is developed to incorporate the influence of dependent and independent thermal stresses, which can be uniform, linear, nonlinear, or sinusoidal on the mechanical properties of the double curvature shell. Two material couples, ( S i 3 N 4 / SUS 304 , ZrO 2 /Ti‐6Al‐4V ) , are considered as progressive materials, accounting for temperature-dependent and temperature-independent heat conduction and material properties in the thickness direction. The temperature field is assumed to be uniform across the shell surface but varies only in the thickness direction. The accuracy of the analytical results is validated by comparing them with existing literature results for functionally graded material (FGM) shells with infinite radii under dependent and independent temperature conditions. The study aims to demonstrate the thermal effects on material composition, as well as various specific geometric shapes such as plates, cylinders, spheres and ellipses and how different temperature laws influence the frequencies of vibrating double curvature FGM shells. Both existing theories accurately predict temperature-independent and temperature-dependent vibration responses of the shells. By verifying and comparing the results with the literature, a better agreement is achieved, thereby paving the way for further research in this field.

Vibrations of viscoelastic FG porous graphene-platelets reinforced doubly-curved shells via experimental characterisation of graphene platelets

This work explores the vibrations of viscoelastic functionally-graded (FG) porous graphene-platelets reinforced doubly-curved shallow shells via experimental characterisations of graphene platelets. In particular, the effects of ultrasonication time of graphene platelets, on the vibrations of graphene-platelets reinforced shells, are studied. This is of interest because graphene platelets are often ultrasonicated in solvents to achieve better dispersions during the fabrication of graphene-platelets/epoxy composite structures. In this study, geometric characteristics of the graphene platelets under different sonication times are quantitatively and qualitatively analysed through experimental characterisation techniques, including a laser diffraction particle size analyser, a scanning electron microscopy (SEM), and a scanning force microscopy (SFM). The geometric characteristics of graphene platelets are considered in the effective material properties using a micromechanics model of Halpin-Tsai. Different FG distributions of graphene platelets and closed-cell porosity are modelled. The Kelvin-Voigt viscoelastic model is used to consider the internal friction-induced energy dissipation for the polymeric composite shell. Hamilton’s variational principle and an assumed mode method are used to derive and solve the equations of motion, respectively, for the vibrations of the doubly-curved shells. The effects of graphene platelets sonication time, in combination with the effects of graphene platelets weight fraction, porosity coefficient, FG distributions, shell thickness ratio, and shell curvature radii, are scrutinised. The results show that increasing ultrasonication time reduces the shell’s out-of-plane dimensionless fundamental frequency as a result of the reduction in graphene platelets aspect ratio.

Vibration control of thin shallow paraboloidal shells with light-activated shape memory polymers

With the applications of thin-walled paraboloidal shell structure in aviation, aerospace and communication systems, smart-structure based active vibration control becomes essential to improve the performance of thin-walled parabolic structures. Light-activated shape memory polymer (LaSMP) is a novel actuator material that exhibits dynamic Young's modulus and strain properties under ultraviolet (UV) light exposures, which can be used for non-contact vibration control. This study focuses on investigating the vibration control performance of a shallow parabolic thin shell, with simply supported boundary conditions, with laminated LaSMP patches. Based on the LaSMP strain model, the vibration control effect of LaSMP patch on the thin shell is discussed. A finite element model of the simply supported parabolic thin shell is developed to obtain the natural frequencies. The modal expansion method is employed to investigate the vibration control of the shallow parabolic thin shell laminated with LaSMPs, and independent modal responses are calculated. According to the different control mode, the effects of LaSMP actuators on vibration control of shallow paraboloid shell are studied in three cases with varying actuation position and coverage area of LaSMP actuators. The results indicate that LaSMP can control the vibration of the thin shell by reducing the vibration amplitude and the final vibration control effect is determined by the mode shape, the initial LaSMP strain, and the location and area covered by LaSMP actuators. By establishing the model between the LaSMP actuator force and the attenuations in modal amplitude, this study provides an analytical tool for the application of LaSMPs in vibration control of flexible structures.

Vibration and damping analyses of sandwich cylindrical and conical shells using meshfree method

Vibration and damping analyses of sandwich cylindrical and conical shells using meshfree method

Vibration damping method of cantilever structure considering redundant constraint of monocrystalline blade casting mold shell

Excessive vibrations of the mold shell during the manufacturing process of monocrystalline blades lead to dendirite and frekle defects in directional solidification. The dynamics of the casting lifting device-mold shell system is analysed theoretically to reveal the influence of key parameters such as excitation force, damping and stiffness on the monocrystalline blade casting. The effect of redundant constraint onto the system is analysed via the developed vibration model. A lifting device-mold shell system test bench is developed, a slide-support arm device is designed to provide redundant constraint. A self-developed high-precision sensor is used to test the vibration signals, and the effectiveness of the damping method is verified. The experimental results show that the redundant constraint can reduce the undesired vibration of mold shell by more than 77 %, which ensures the casting quality of monocrystalline blades. The proposed vibration damping method can provide a reference for the vibration damping of the cantilever machine.

Prediction of Time Domain Vibro-Acoustic Response of Conical Shells using Jacobi–Ritz Boundary Element Method

Considering the lack of studies on the transient vibro-acoustic properties of conical shell structures, a Jacobi–Ritz boundary element method for forced vibro-acoustic behaviors of structure is proposed based on the Newmark-β integral method and the Kirchhoff time domain boundary integral equation. Based on the idea of the differential element method and the first-order shear deformation theory (FSDT), the vibro-acoustic model of conical shells is established. The axial and circumferential displacement tolerance functions are expressed using Jacobi polynomials and the Fourier series. The time domain response of the forced vibration of conical shells is calculated based on the Rayleigh–Ritz method and Newmark-β integral method. On this basis, the time domain response of radiated noise is solved based on the Kirchhoff integral equation, and the acoustic radiation characteristics of conical shells from forced vibration are analyzed. Compared with the coupled FEM/BEM method, the numerical results demonstrate the high accuracy and great reliability of this method. Furthermore, the semi-vertex angle, load characteristics, and boundary conditions related to the vibro-acoustic response of conical shells are examined.

Advanced Thick FGM Plates-Cylindrical Shells in Linear Unsteady Supersonic Flow

Introduction:: Thick functionally graded (FG) plates-cylindrical shells with third-order shear deformation theory (TSDT) of displacement models under thermal vibration in linear unsteady supersonic flow are investigated by using the generalized differential quadrature (GDQ) method. Method:: The nonlinear coefficient term of TSDT models and the advanced nonlinear shear correction coefficient expression are used to study the thermal vibration of thick FG plates and cylindrical shells in linear unsteady supersonic flow. At the intersection of FG plates-cylindrical shells, the displacements, stress resultants, and moment resultants could be reasonably assumed in the continuity condition for the differential volume in linear unsteady supersonic flow, respectively. Result:: The dynamic equilibrium differential equations of thick FG plates and cylindrical shells in linear unsteady supersonic flow, respectively in terms of partial derivatives of displacements and shear rotations subjected to partial derivatives of thermal loads, mechanical loads consist of the linear supersonic aerodynamic pressure and inertia terms can be presented. Two parametric effects including environment temperature and functionally graded material (FGM) power law index on the thermal stress and center displacement of thick FG plates-cylindrical shells in linear unsteady supersonic flow are investigated. Conclusion:: The linear unsteady supersonic flow over the outer surface of thick FG platescylindrical shells provides the additional aerodynamic effect on the values of displacements and stresses.