Cylindrical Spherical Shells Research Articles

Semi-analytical modeling and vibration analysis of joined FGP-GPLRC thin-walled cylindrical-spherical shells with arbitrary boundary conditions

In this paper, the vibration characteristics of the joined thin-walled cylindrical-spherical shells with graphene platelet (GPL) reinforcement in metal foams are investigated based on a relatively novel Gegenbauer-Ritz method. The material properties of the coupled shells are also obtained using the Halpin-Tsai micromechanical modeling. The equations for the mechanical modeling of the coupled shell are given by applying the first-order shear deformation theory (FSDT) and the energy method. In addition, the spring stiffness penalty method is employed to obtain arbitrary boundary conditions at both ends of the shell. The final solution for the coupled shell is obtained by the Gegenbauer-Ritz method. Finally, the results of this paper are compared with the literature results and those obtained by the finite element method (FEM) to prove the accuracy of the approach. On this basis, the effects of arbitrary boundary conditions, GPL distribution modes, porosity distribution patterns, structural openings, and geometrical parameters on the vibration characteristics of the joined cylindrical-spherical shells are discussed.

Analytical study on vibration behaviors of pump-jet–shaft–submarine hull system in wavenumber–frequency​ domain

The pump-jet excitation is transmitted to submarine hull along rotor–shaft system and duct–stator system, which is one of the main causes of structural vibration of the hull. This paper proposes an analytical method for the coupled shaft–submarine hull system. The submarine hull is modeled as a jointed conical-orthogonally stiffened cylindrical–spherical shell coupled with several circular plates. The shaft is modeled with a three-dimensional beam and connected to the hull by bearings. A unified variational modeling procedure is developed to assemble each substructure. The hydrodynamic pressure acting on the rotor and the duct–stator system are respectively considered as single point force and multiple uniformly or non-uniformly spaced point forces acting on the shaft and the conical shell. The vibration displacements are analytically expanded with Fourier series in the circumferential direction. Thus, the wavenumber components that contribute to vibration responses are naturally separated and quantified. The convergence and accuracy of the proposed method are verified by the finite element method. The analytical study on vibration characteristics of the pump-jet–shaft–submarine hull system along distinct vibration transferring paths in circumferential wavenumber–frequency domain is conducted. The results indicate that the rotor excitation can excite more resonance peaks compared to the duct–stator excitation when neglecting the elasticity of the pump-jet propulsor. It mainly owns to the strong circumferential modal coupling and abundant modal contributions when the system is under the rotor excitation. Besides, the non-uniform distribution of external load contributes to the augmentation of resonance peaks compared to the responses under uniform load, which attributes to the participation of extra wavenumber components.

Free vibration of joined cylindrical–hemispherical FGM shells

Free vibration response of a joined shell system including cylindrical and spherical shells is analyzed in this research. It is assumed that the system of joined shell is made from a functionally graded material (FGM). Properties of the shells are assumed to be graded through the thickness. Both shells are unified in thickness. To capture the effects of through-the-thickness shear deformations and rotary inertias, first-order shear deformation theory of shells is used. The Donnell type of kinematic assumptions is adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton’s principle. The resulting system of equations is discretized using the semi-analytical generalized differential quadrature method. Considering the clamped and free boundary conditions for the end of the cylindrical shell and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies of the joined shell. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells, some parametric studies are carried out for the system of combined moderately thick cylindrical–spherical shell system. Novel results are provided for the case of FGM joined shells to explore the influence of power-law index and geometric properties.

Analysis of vibration characteristics of joined cylindrical-spherical shells

In this paper, the free and forced vibration of joined cylindrical-spherical shells (JCSSs) subjected to classical boundary conditions are investigated by a variational method. A JCSSs is divided into its components (i.e., cylindrical and spherical shells) at the cylinder-sphere junction. The interface continuity and geometric boundary conditions are approximately enforced by means of a modified variational principle and least-squares weighted residual method. Donnell shell theory is used to formulate the theoretical model. Double mixed series are adopted as admissible displacement functions for each shell component. In addition, the forced vibration response of the JCSSs is gained through the Newmark-β method. Through the comparison and analysis study, it is obvious that the proposed method has a good stable and rapid convergence property and the results of this paper closely agreed with those obtained by published literatures and the finite element method. The influence of structural parameters and different loading modes on free and forced vibration characteristics of JCSSs are considered.

Free and Forced Vibration Analysis of Ring-Stiffened Conical–Cylindrical–Spherical Shells Through a Semi-Analytic Method

A semi-analytic method is presented to analyze free and forced vibrations of combined conical–cylindrical–spherical shells with ring stiffeners and bulkheads. First, according to locations of discontinuity, the combined shell is divided into one opened spherical shell and a number of conical segments, cylindrical segments, stiffeners, and bulkheads. Meanwhile, a semi-analytic approach is proposed to analyze the opened spherical shell. The opened spherical shell is divided into narrow strips, which are approximately treated as conical shells. Then, Flügge theory is adopted to describe motions of conical and cylindrical segments, and stiffeners with rectangular cross section are modeled as annular plates. Displacement functions of conical segments, cylindrical segments, and annular plates are expanded as power series, wave functions, and Bessel functions, respectively. To analyze arbitrary boundary conditions, artificial springs are employed to restrain displacements at boundaries. Last, continuity and boundary conditions are synthesized to the final governing equation. In vibration characteristics analysis, high accuracy of the present method is first demonstrated by comparing results of the present method with ones in literature and calculated by ansys. Further, axial displacement of boundaries and open angle of spherical shell have significant influence on the first two modes, and forced vibrations are easily affected by bulkheads and external force.

A unified spectro-geometric-Ritz solution for free vibration analysis of conical–cylindrical–spherical shell combination with arbitrary boundary conditions

In the present article, a spectro-geometric-Ritz solution for free vibration analysis of conical–cylindrical–spherical shell combinations with arbitrary boundary conditions is presented. The classical theory of small displacements of thin shells is employed to formulate the theoretical model. The admissible functions of each shell components are described as a combination of a two-dimensional (2-D) Fourier cosine series and auxiliary functions. As an innovative point of this work, the auxiliary functions are introduced to accelerate the convergence of the series representations and eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries and the junction between the shell components. The artificial spring technique is adopted here to model the boundary condition and coupling condition, respectively. All the expansion coefficients are considered as the generalized coordinates and determined by Ritz procedure. Convergence and comparison studies for both open and closed conical–cylindrical–spherical shells with arbitrary boundary conditions are carried out to verify the reliability and accuracy of the present solutions. Some selected mode shapes are illustrated to enhance the understanding of the research topic. It is found the present method exhibits stable and rapid convergence characteristics, and the present results, including the natural frequencies and the mode shapes, agree closely with those solutions obtained from the finite element analyses and results in the literature. The effects of the geometrical dimensions of the shell combinations on the natural frequencies are also investigated.

Vibration analysis of coupled conical-cylindrical-spherical shells using a Fourier spectral element method.

This paper presents a Fourier spectral element method (FSEM) to analyze the free vibration of conical-cylindrical-spherical shells with arbitrary boundary conditions. Cylindrical-conical and cylindrical-spherical shells as special cases are also considered. In this method, each fundamental shell component (i.e., cylindrical, conical, and spherical shells) is divided into appropriate elements. The variational principle in conjunction with first-order shear deformation shell theory is employed to model the shell elements. Since the displacement and rotation components of each element are expressed as a linear superposition of nodeless Fourier sine functions and nodal Lagrangian polynomials, the global equations of the coupled shell structure can be obtained by adopting the assembly procedure. The Fourier sine series in the displacement field is introduced to enhance the accuracy and convergence of the solution. Numerical results show that the FSEM can be effectively applied to vibration analysis of the coupled shell structures. Numerous results for coupled shell structures with general boundary conditions are presented. Furthermore, the effects of geometric parameters and boundary conditions on the frequencies are investigated.

Vibro-acoustic analysis of coupled spherical–cylindrical–spherical shells stiffened by ring and stringer reinforcements

A semi-analytical method is developed to predict the vibration and acoustic responses of submerged coupled spherical–cylindrical–spherical shells stiffened by circumferential rings and longitudinal stringers. The structural model of the coupled stiffened shell is formulated using a modified variational method combined with a multi-segment partitioning technique, whereas a spectral Kirchhoff–Helmholtz integral formulation is employed to model the exterior fluid. The stiffened rings and stringers, which may be few or many in number, non-uniform or uniform in size, and non-uniformly or uniformly spaced, are treated as discrete elements. The displacement and sound pressure variables are expanded in the form of a double mixed series using Fourier series and Chebyshev orthogonal polynomials. This provides a flexible way for the present method to account for the individual contributions of circumferential wave modes to the vibration and acoustic responses of coupled stiffened shells in an analytical manner. The application of the method is illustrated with several numerical examples, and comparisons are made with available solutions obtained from the coupled finite element/boundary element method. The contributions of different circumferential wave modes to the vibration responses, sound power and the directivity of radiated sound pressure for coupled shells bounded by light or heavy fluid are examined. Effects of the rings and stringers on the vibration and acoustic responses of the coupled shells are investigated.

Design methodology for integrating multipath systems (building services)

Purpose – The purpose of this paper is to report on a geometrical integration methodology that can be used to organise some types of these systems. Most multipath delivery systems, such as Building Services (BSs), are arbitrarily distributed with no known solution to reduce the complexity in the way channels are arranged. Design/methodology/approach – Integration for optimal functionality through reduction of geometrical complexity is achieved by understanding the elements of complexity within current practices; identifying commonalities between the various components which can be used for integration; performing an axiomatic design to resolve design complications; adopting theory of inventive problem-solving for methodology and process development towards optimal functionality; and generating a mathematical solution to inform digital modelling of optimal design. The study takes into account thermophysical and electromagnetic interactions between utilities and uses novel mathematical manipulations based on designing a manifold of spherical and cylindrical geometries joined using Bezier surfaces. Findings – Once a solution was reached, computer-aided design (CAD) iterations were undertaken for channelling six BSs into a single unit. The outcome was concentric cylindrical–spherical shells superimposed with spacings of typically few millimetres to deliver/distribute the utilities. It is applied to bring together BSs into a single trunking system at minimal, yet appropriate, proximal distances, and it allows distribution of any number of services in any direction. Physical prototypes were produced and initial testing of their performance (reported elsewhere) has been encouraging. Originality/value – A design methodology for integrating arbitrary distributed paths/conduits. The approach could be incorporated into CAD tools as a design feature to facilitate integration of multipath delivery systems.

A Study on the Free Vibration of the Prestressed Joined Cylindricalspherical Shell Structures

The free vibration characteristics of the prestressed joined spherical–cylindrical shell with free-free boundary conditions are investigated. The Flügge shell theory and Rayleigh-Ritz energy method are applied in order to analyze the free vibration characteristics of the joined shell. In the modal test, the LMS software is used to calculate mode shapes and natural frequencies of the joined shell structure. The natural frequencies and mode shapes are calculated numerically and they are compared with those of the FEM and modal test to confirm the reliability of the analytical solution. The effects of the shallowness and length of the cylindrical shell to the free vibrational behavior of joined shell structure and the effect of internal pressure on the modal charactristics are investigated.

Vibrations characteristics of joined cylindrical-spherical shell with elastic-support boundary conditions

Based on the Reissner-Naghdi’s thin shell theory, this paper concentrates on the free vibration of a joined cylindrical-spherical shell with elastic-support boundary conditions by a domain decomposition method. The joined shell is first separated from the elastic-support boundary and then subdivided into some cylindrical and spherical shell segments along the axis of revolution. The elastic-support boundary is regarded as a combination of distributed linear springs and can be treated as a special interface as well as the interface between two adjacent shell segments. Through the variational operation of the whole energy functional, the discretized equations of motion are derived by the expansions of the displacement field for each shell segment with Fourier series and Chebyshev orthogonal polynomials in the circumferential and longitudinal direction, respectively. To analyze the numerical convergence and precision of the present method, a number of case studies have been conducted and the solutions are compared with those derived by ANSYS and those presented in the previous literature to confirm the reliability and accuracy.

Vibration analysis of ring-stiffened conical–cylindrical–spherical shells based on a modified variational approach

In this paper, free vibration characteristics of conical–cylindrical–spherical shell combinations with ring stiffeners are investigated by using a modified variational method. Reissner–Naghdi's thin shell theory in conjunction with a multilevel partition technique, viz., stiffened shell combination, shell component and shell segment, is employed to formulate the theoretical model. The displacement fields of each shell segment are expressed as a product of orthogonal polynomials along the meridional direction and Fourier series along the circumferential direction. The ring stiffeners in shell combinations are treated as discrete elements. Convergence and comparison studies for both non-stiffened and stiffened conical–cylindrical–spherical shells with different boundary conditions (e.g., free, clamped and elastic supported boundary conditions) are carried out to verify the reliability and accuracy of the present solutions. Some selected mode shapes are illustrated to enhance the understanding of the research topic. It is found the present method exhibits stable and rapid convergence characteristics, and the present results, including the natural frequencies and the mode shapes, agree closely with those solutions obtained from the finite element analyses. The effects of the number and geometric dimensions of ring stiffeners on the natural frequencies of a submarine pressure hull are also investigated.

Vibration characteristics of a spherical–cylindrical–spherical shell by a domain decomposition method

A domain decomposition method is used to analyze the free and forced vibration characteristics of a spherical–cylindrical–spherical shell, based on Reissner–Naghdi's thin shell theory. The joined shell is divided into some cylindrical and spherical shell segments along the meridional (longitudinal) direction. Double mixed series, i.e., Fourier series and Chebyshev polynomials, are employed as the admissible displacement functions to obtain the discretized equation of motion for the joined shell. Numerical comparisons with the results derived by FEM and those available in the previous literature are made to validate the present method. Moreover, the effects of length-to-radius and radius-to-thickness ratios on the natural frequencies are also investigated.

Free Vibration Analysis on Combined Cylindrical-Spherical Shell

Based upon the Reissner-Naghdi-Berry’s shell theory, a domain decomposition method (DDM) is utilized to investigate the vibration characteristics of the combined cylindrical-spherical shell with different boundary conditions. The combined shell was first apart from prescribed-displacement boundary and then divided into some cylindrical and spherical shell subdomains, respectively. The boundary equations were introduced into the energy functional of the combined shell as well as the constraint equations derived from interface continuity conditions between two adjacent shell subdomains. Fourier series and Chebyshev orthogonal polynomials were employed as the admissible displacement functions for each shell subdomain in the circumferential direction and axial direction in order to obtain the discretization equations of motion of the combined shell. Exact free vibration solutions of the combined shell has been performed via the DDM and were compared with those obtained by the finite element software ANSYS to confirm the reliability and accuracy.

Design approach for the integration of services in buildings

This paper describes a novel methodology to group building services into a single trunking system at minimal proximal distances between them. The study focused on solving the geometrical complexity encountered in conventional arrangements of building services, while taking into account thermo-physical and electromagnetic interactions between services together with building regulations. The potential solution for delivery and distribution of building services in any number of directions is an ‘onion layers’ type of design, using novel mathematical manipulations based on manifolds of spherical and cylindrical geometries joined using Bezier surfaces. Computer-aided design iterations were undertaken for channelling six building services into a single unit including water, air, electricity and data. It consists of concentric cylindrical-spherical shells superimposed at few millimetres gaps (channels) for which physical prototypes were produced. Practical application: Successfully integrating building services such as water, air, electricity and data into a single trunking delivery system would offer an important advancement in reducing services installation cost, maintenance and the running cost of a building. Current design tools and techniques do not offer any solution for such integration; hence the current development of a multi-services trunking system. Subject to satisfactory compliance with health and safety requirements, plus maintenance issues, the system is proposed for embedding into building construction walls, panels or for placement into a confined space as a first step towards next generation building service. It is foreseen that many industries and business will be involved in the early stage of this development.

A study on the free vibration of the joined cylindrical–spherical shell structures

The free vibration characteristics of the joined spherical–cylindrical shell with various boundary conditions are investigated. The boundary conditions considered herein are free–free, simply supported–free and clamped–free for the joined cylindrical–spherical shell structures. The Flügge shell theory and Rayleigh’s energy method are applied in order to analyze the free vibration characteristics of the joined shell structure and individual shell components. In the modal test, the I-DEAS test module is used to calculate mode shapes and natural frequencies of the joined shell structure. The natural frequencies and mode shapes are calculated numerically and they are compared with those of the FEM and modal test to confirm the reliability of the analytical solution. The effects of the shallowness of the spherical shell and length of the cylindrical shell to the free vibrational behavior of joined shell structure are investigated.