Journal articles: 'Shells (Engineering) Vibration'

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Zhao, Ming Hui. "Vibration Analysis of a Shell Structure by Finite Element Method." Advanced Materials Research 591-593 (November 2012): 1929–33. http://dx.doi.org/10.4028/www.scientific.net/amr.591-593.1929.

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Plate-shell structures, especially cylindrical shells and spherical shells, are widely used in engineering fields, such as aircraft and tanks, missiles, submarines, ships, hydraulic pumps, infusion pipelines and gas pipelines, and so on. These structures are usually in a fluid medium, which are related to the structure fluid-solid coupling and acoustic radiation field. As many experiments show that enclosed air in a thin walled structure, just like the violin, affects some modes of vibration significantly, air coupling between vibrating sides of the structure cannot be neglected. In order to explore the sound pressure distribution of vibrational frequencies, this paper, considering the material anisotropy, analyzes a typical complex shell structure of the violin by finite element method, including acoustic-structure coupling analysis and post-processing, especially sound pressure vibration frequency extraction. Finally, we get the conclusion that the distribution of sound pressure vibration frequency is similar to the normal distribution.

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Khatri, K. N. "Vibration Control of Conical Shells Using Viscoelastic Materials." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 206, no. 3 (May 1992): 167–78. http://dx.doi.org/10.1243/pime_proc_1992_206_113_02.

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The vibration and damping analysis of multi-layered conical shells incorporating layers of viscoelastic materials in addition to elastic ones, the former causing dissipation of vibratory energy, is the subject matter of this paper. The analysis given herein uses Hamilton's variational principle for deriving equations of motion of a general multi-layered conical shell. In view of the correspondence principle of linear viscoelasticity which is valid for harmonic vibrations, the solution is obtained by replacing the moduli of viscoelastic layers by complex moduli. An approximate solution for axisymmetric vibrations of multi-layered conical shells with two end conditions—simply supported edges and clamped edges—is obtained by utilizing the Galerkin procedure. The damping effectiveness in terms of the system loss factor for all families of modes of vibrations for three-, five- and seven-layered shells is evaluated and its variation with geometrical parameters is investigated.

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Qatu, Mohamad S. "Recent research advances in the dynamic behavior of shells: 1989-2000, Part 1: Laminated composite shells." Applied Mechanics Reviews 55, no. 4 (July 1, 2002): 325–50. http://dx.doi.org/10.1115/1.1483079.

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Laminated composite shells are increasingly being used in various engineering applications including aerospace, mechanical, marine, and automotive engineering. With the increasing awareness of and sensitivity to structural noise and vibration, research covering the dynamic behavior of composite shells has received considerable attention. The purpose of this article is to review most of the recent research done in this field. Review of the literature on the dynamic behavior of homogeneous shells is covered in Part 2 of this article to be published in the September 2002 issue of AMR. Research on shell dynamics is found to be mainly free vibration analyses. The review is conducted with emphasis given to the theory being applied (thin, thick, 3D, nonlinear, …), the analysis method (exact, Ritz, finite elements, …), complicating effects (initial stress, imperfection, added masses and springs, elastic supports, rotating shells, and others), and the various shell geometries that were subject to vibration research (cylindrical, conical, spherical, and others). There are 374 references cited in this review article.

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Ribeiro, Pedro. "Linear modes of vibration of cylindrical shells in composite laminates reinforced by curvilinear fibres." Journal of Vibration and Control 22, no. 20 (August 9, 2016): 4141–58. http://dx.doi.org/10.1177/1077546315571661.

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Modes of vibration of thin cylindrical shells made up of layers with curvilinear fibres (variable stiffness composite laminates (VSCL) shells) are investigated in the linear regime. A p-version finite element type formulation is developed for that purpose; in the absence of data on vibrations of cylindrical VSCL shells, the formulation is verified by comparisons with published data on laminated shells reinforced by straight fibres and on VSCL plates. Parametric studies are performed, in order to investigate how curvilinear fibre paths can influence the modes of vibration. It is found that curvilinear fibre paths can have a very large effect, larger than on plates, on the natural frequencies and natural mode shapes of vibration of cylindrical shells. Factors that strongly influence the modes of vibration of VSCL shells are found; these include the fibre orientation at boundaries and in relation to principal normal sections.

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XIANG, Y., C. W. LIM, and S. KITIPORNCHAI. "AXISYMMETRIC VIBRATION OF CYLINDRICAL SHELLS WITH INTERMEDIATE RING SUPPORTS." International Journal of Structural Stability and Dynamics 03, no. 01 (March 2003): 35–53. http://dx.doi.org/10.1142/s021945540300080x.

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This paper treats the axisymmetric vibration of thin circular cylindrical shells with intermediate ring supports based on the Goldenveizer–Novozhilov thin shell theory. An analytical method is proposed, and new exact solutions are presented to study the axisymmetric vibration characteristics of the ring supported cylindrical shells. In the proposed method, the state-space technique is employed to derive a homogenous differential equation system for a shell segment, and a domain decomposition approach is developed to cater for the continuity requirements between shell segments. Exact frequency parameters are presented for circular cylindrical shells that have multiple intermediate ring supports and various combinations of end support conditions. These exact vibration frequencies may serve as important benchmarks against which researchers can validate their numerical methods for such circular cylindrical shell problems.

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Kang, Jae-Hoon. "3D Vibration Analysis of Combined Shells of Revolution." International Journal of Structural Stability and Dynamics 19, no. 02 (February 2019): 1950005. http://dx.doi.org/10.1142/s0219455419500056.

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A three-dimensional (3D) method of analysis is presented for determining the natural frequencies and the mode shapes of combined hemispherical–cylindrical shells of revolution with and without a top opening by the Ritz method. Instead of mathematically two-dimensional (2D) conventional thin shell theories or higher-order thick shell theories, the present method is based upon the 3D dynamic equations of elasticity. Mathematically, minimal or orthonormal Legendre polynomials are used as admissible functions in place of ordinary simple algebraic polynomials which are usually applied in the Ritz method. The analysis is based upon the circular cylindrical coordinates instead of the shell coordinates which are normal and tangent to the shell mid-surface. Strain and kinetic energies of the combined shell of revolution with and without a top opening are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the Legendre polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies. Numerical results are presented for the combined shells of revolution with or without a top opening, which are completely free and fixed at the bottom of the combined shells. The frequencies from the present 3D Ritz method are compared with those from 2D thin shell theories by previous researchers. The present analysis is applicable to very thick shells as well as very thin shells.

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Qatu, Mohamad S. "Vibration of Homogeneous and Composite Thick Barrel Shells." Journal of Vibration and Control 10, no. 3 (March 2004): 319–41. http://dx.doi.org/10.1177/1077546304031845.

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This paper presents a vibration analysis for homogeneous and laminated composite deep, thick barrel shells using recently derived equations of elastic deformation. Assuming a first-order linear displacement field, the equations include accurate force and moment resultants, in which the stresses over the thickness of the shell are integrated exactly on a trapezoidal-like cross-section of a shell element. Exact solutions were obtained for thick barrel, open and closed, shells having shear diaphragm boundary conditions and cross-ply lamination sequence. The results were compared with previously obtained results where various other thick shell theories were used. The effects of various parameters including radii of curvature on shell frequencies are studied.

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Sarkheil, Saeed, Mahmud S. Foumani, and Hossein M. Navazi. "Free vibration of bi-material cylindrical shells." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 15 (August 9, 2016): 2637–49. http://dx.doi.org/10.1177/0954406215602037.

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Based on the Sanders thin shell theory, this paper presents an exact solution for the vibration of circular cylindrical shell made of two different materials. The shell is sub-divided into two segments and the state-space technique is employed to derive the homogenous differential equations. Then continuity conditions are applied where the material of the cylindrical shell changes. Shells with various combinations of end boundary conditions are analyzed by the proposed method. Finally, solving different examples, the effect of geometric parameters as well as BCs on the vibration of the bi-material shell is studied.

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Patil, Subhash R., H. N. Narasimha Murthy, G. S. Srivatsa, Viketh S. Yandigeri, Ramanraj K., Basavaraja Meti, Gangadhar Angadi, and D. V. N. Harish. "Study of Vibration Behaviour of Stiffened Polymer Composite Shells for Underwater Structural Applications." Defence Science Journal 70, no. 3 (April 24, 2020): 342–50. http://dx.doi.org/10.14429/dsj.70.14703.

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This paper presents vibration behavior of ring stiffened polymer composite thick shells used for underwater structures. Filament wound shells stiffened with internal and external rings and with hemispherical ends were tested for vibration in air and water in free-free boundary condition using roving hammer and fixed response method. Modal testing of the shells was performed under hydrostatic loading in a custom designed buckling tester for determining natural frequency at higher sea depths. Accelerometer was mounted on the inner surface of the shell. It was excited using a plumbob, rope and pulley arrangement. Experimental results were validated by modal analysis using Hyperworks and ANSYS. Vibration behavior in water was simulated by Fluid structure interaction approach. Experimental first natural frequency in water was lesser than that in air. With increase in hydrostatic pressure, the shell showed moderate variation in natural frequency. The experimental and numerical results of natural frequency and mode shapes were in good agreement with each other. Natural frequencies were lower in long and thick shells.

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Ko, Soo-Min, and Jae-Hoon Kang. "Vibration of Hemispherical-Cylindrical-Hemispherical Shells and Complete Hollow Spherical Shells with Variable Thickness." International Journal of Structural Stability and Dynamics 19, no. 03 (March 2019): 1950018. http://dx.doi.org/10.1142/s0219455419500184.

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The natural frequencies and mode shapes of enclosed shell typed structures with variable thickness (hemispherical-cylindrical-hemispherical shells and complete hollow spherical shells) are determined by the Ritz method using a three-dimensional (3D) analysis. However, in the conventional shell analysis, mathematically two-dimensional (2D) thin shell theories or higher order thick shell theories are often employed, which adopt limiting assumptions about the displacement variation through the shell thickness. While most researchers have adopted the 3D shell coordinates that are normal and tangential to the shell mid-surface, the present analysis is based upon the circular cylindrical coordinates. By the Ritz method, the Legendre polynomials, which are mathematically orthonormal and minimal, are used as the admissible functions, instead of the ordinary algebraic polynomials. The strain and kinetic energies of the combined shell structures are formulated, and upper bound solutions of the frequencies are obtained by minimizing the solution for frequencies. As the degree of the Legendre polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies. The frequencies from the present 3D method are compared with those from other 3D approach and 2D thin and thick shell theories existing in the literature. The present 3D analysis is applicable to both very thick shells and very thin shells.

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Li, Bing Ru, Yue Peng Jiang, Xuan Yin Wang, and Hui Liang Ge. "Vibro-Acoustics Characteristics of Non-Uniform Ring Stiffened Cylindrical Shells Using Wave Propagation Approach." Advanced Materials Research 655-657 (January 2013): 562–67. http://dx.doi.org/10.4028/www.scientific.net/amr.655-657.562.

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Based on Donnell’s thin shell theory and basic equations, the wave propagation method is discussed here in detail, which is used to investigate the vibration and sound radiation characteristics of non-uniform ring stiffened cylindrical shells under various boundary conditions. The structure damp effects of cylindrical shells are investigated and the ring ribs were considered very narrow, and the rib forces are considered in radial direction. The conclusion are drawn that with the structural loss factor changing large, the whole pressure level are changed little, but the peak of resonance are slacking down obviously; The shell’s resonance frequency can be changed with irregular ring stiffened cylindrical shell .The work will give some guidelines for noise reduction of this kind of shell.

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Ghasemi, Ahmad Reza, and Mohammad Meskini. "Free vibration analysis of porous laminated rotating circular cylindrical shells." Journal of Vibration and Control 25, no. 18 (June 18, 2019): 2494–508. http://dx.doi.org/10.1177/1077546319858227.

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In this research, investigations are presented of the free vibration of porous laminated rotating circular cylindrical shells based on Love’s shell theory with simply supported boundary conditions. The equilibrium equations for circular cylindrical shells are obtained using Hamilton’s principle. Also, Navier’s solution is used to solve the equations of the cylindrical shell due to the simply supported boundary conditions. The results are compared with previous results of other researchers. The numerical result of this study indicates that with increase of the porosity coefficient the nondimensional backward and forward frequency decreased. Then the results of the free vibration of rotating cylindrical shells are presented in terms of the effects of porous coefficients, porous type, length to radius ratio, rotating speed, and axial and circumferential wave numbers.

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Anwar, Rabia, Madiha Ghamkhar, Muhammad Imran Khan, Rabia Safdar, Muhammad Zafar Iqbal, Wasim Jamshed, Esra Karatas Akgül, and M. Prakash. "Frequency Analysis for Functionally Graded Material Cylindrical Shells: A Significant Case Study." Mathematical Problems in Engineering 2021 (November 5, 2021): 1–10. http://dx.doi.org/10.1155/2021/4843321.

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Cylindrical shells play an important role for the construction of functionally graded materials (FGMs). Functionally graded materials are valuable in order to develop durable materials. They are made of two or more materials such as nickel, stainless steel, zirconia, and alumina. They are extremely beneficial for the manufacturing of structural elements. Functionally graded materials are broadly used in several fields such as chemistry, biomedicine, optics, and electronics. In the present research, vibrations of natural frequencies are investigated for different layered cylindrical shells, those constructed from FGMs. The behavior of shell vibration is based on different parameters of geometrical material. The problem of the shell is expressed from the constitutive relations of strain and stress with displacement, as well as it is adopted from Love’s shell theory. Vibrations of natural frequencies (NFs) are calculated for simply supported-simply supported (SS-SS) and clamped-free (C-F) edge conditions. The Rayleigh–Ritz technique is employed to obtain the shell frequency equation. The shell equation is solved by MATLAB software.

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Wang, Xian-Zhong, Quan-Zhou Jiang, Ye-Ping Xiong, and Xin Gu. "Experimental studies on the vibro-acoustic behavior of a stiffened submerged conical-cylindrical shell subjected to force and acoustic excitation." Journal of Low Frequency Noise, Vibration and Active Control 39, no. 2 (May 9, 2019): 280–96. http://dx.doi.org/10.1177/1461348419844648.

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An experimental model was made to investigate the influence of force and acoustic excitation on the vibration and underwater sound radiation of the stiffened conical-cylindrical shell. Meanwhile, a coupled precise transfer matrix method and wave superposition method was also proposed to analyze vibro-acoustic responses of combined shells. To test accuracy of the present method, vibration and acoustic results of combined shells are firstly examined. As expected, results of present method are in excellent agreement with the ones in literature and model test. The experimental results show that free vibrations of the experimental test are consistent with the literature data and the present method’s results. Forced vibration and acoustic test results are also well agreed with the numerical results from the coupled precise transfer matrix method/wave superposition method. The comparisons show that the coupled precise transfer matrix method/wave superposition method is reliable and credible to solve the vibro-acoustic response of combined shells. The analysis shows that the acoustic excitation is the key factor for radiated noise in low-frequency range. However, the radiated noise resulted from force excitation is dominant in mid-high frequency band.

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Melaibari, Ammar, Ahmed Amine Daikh, Muhammad Basha, Ahmed Wagih, Ramzi Othman, Khalid H. Almitani, Mostafa A. Hamed, Alaa Abdelrahman, and Mohamed A. Eltaher. "A Dynamic Analysis of Randomly Oriented Functionally Graded Carbon Nanotubes/Fiber-Reinforced Composite Laminated Shells with Different Geometries." Mathematics 10, no. 3 (January 27, 2022): 408. http://dx.doi.org/10.3390/math10030408.

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The present study demonstrates the free vibration behavior of composite laminated shells reinforced by both randomly oriented single-walled carbon nanotubes (SWCNTs) and functionally graded fibers. The shell structures with different principal radii of curvature are considered, such as cylindrical, spherical, elliptical–paraboloid shell, hyperbolic–paraboloid shell, and plate. The volume fraction of the fibers has a linear variation along the shell thickness from layer to layer, while the volume fraction of CNTs is constant in all shell layers and uniformly distributed. The fiber-reinforced elements are distributed with three functions which are V-distribution, O-distribution, and X-distribution in addition to the uniform distribution. A numerical analysis was carried out systematically to validate the proposed solution. A new analytical solution is presented based on the Galerkin approach for shells and is exploited to illustrate the influence of some factors on the free vibration behavior of CNTs/fibe-reinforced composite (CNTs/F-RC) laminated shells, including the distributions and volume fractions, various boundary conditions, and geometrical properties of the reinforcement materials. The proposed solution is shown to be an effective theoretical tool to analyze the free vibration response of shells.

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Roots, Larissa. "Non-Axisymmetric Vibrations of Stepped Cylindrical Shells Containing Cracks." Advanced Materials Research 934 (May 2014): 136–42. http://dx.doi.org/10.4028/www.scientific.net/amr.934.136.

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Based on the Donnell’s approximations of the thin shell theory, this paper presents solutions for the problem of free non-axisymmetric vibration of stepped circular cylindrical shells with cracks. The shell under consideration is sub-divided into multiple segments separated by the locations of thickness variations. It is assumed that at thejth step there exists a circumferential surface crack with uniform depthcj. The influence of circular cracks with constant depth on the vibration of the shell is prescribed with the aid of a matrix of local flexibility. The latter is related to the coefficient of the stress intensity known in the linear fracture mechanics. Numerical results are obtained for cylindrical shells of stepped thickness containing cracks at re-entrant corners of steps. Shells with various combinations of boundary conditions can be analyzed by the proposed method. Furthermore, the influences of the shell thicknesses, locations of step-wise variations of the thickness and other parameters on the natural frequencies are examined. The results can be used for the approximate evaluation of dynamic parameters of cylindrical shells with cracks and flaws.

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BRISCHETTO, SALVATORE. "AN EXACT 3D SOLUTION FOR FREE VIBRATIONS OF MULTILAYERED CROSS-PLY COMPOSITE AND SANDWICH PLATES AND SHELLS." International Journal of Applied Mechanics 06, no. 06 (December 2014): 1450076. http://dx.doi.org/10.1142/s1758825114500768.

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A 3D free vibration analysis of multilayered structures is proposed. An exact solution is developed for the differential equations of equilibrium written in general orthogonal curvilinear coordinates. The equations consider a geometry for shells without simplifications and allow the analysis of spherical shell panels, cylindrical shell panels, cylindrical closed shells and plates. The method is based on a layer-wise approach, the continuity of displacements and transverse shear/normal stresses is imposed at the interfaces between the layers of the structures. Results are given for multilayered composite and sandwich plates and shells. A free vibration analysis is proposed for a number of vibration modes, thickness ratios, imposed wave numbers, geometries and multilayer configurations embedding isotropic and orthotropic composite materials. These results can also be used as reference solutions for plate and shell 2D models developed for the analysis of multilayered structures.

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Ghasemi, Ahmad Reza, and Masood Mohandes. "Free vibration analysis of rotating fiber–metal laminate circular cylindrical shells." Journal of Sandwich Structures & Materials 21, no. 3 (May 22, 2017): 1009–31. http://dx.doi.org/10.1177/1099636217706912.

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In this article, free vibration of rotating fiber–metal laminate thin circular cylindrical shells has been analyzed. Strain–displacement relations have been obtained based on Love’s first approximation shell theory. The variations of frequencies of the fiber–metal laminate cylindrical shell with rotational speeds for different axial and circumferential wave numbers, L/R ratios, metal thicknesses and volume fractions of metal have been presented. Also, free vibrations of the rotating fiber–metal laminate shell have been studied for carbon/epoxy, glass/epoxy and aramid/epoxy composite materials combining thin aluminum layers. The results showed that with increasing rotating speed, the gap between backward and forward waves frequencies increased.

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Oh, J., M. Ruzzene, and A. Baz. "Passive Control of the Vibration and Sound Radiation from Submerged Shells." Journal of Vibration and Control 8, no. 4 (April 2002): 425–45. http://dx.doi.org/10.1177/107754602023689.

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Vibration and noise radiation from fluid-loaded cylindrical shells are controlled using multiple stiffeners and Passive Constrained Layer Damping treatment. Dynamic and fluid finite element models are developed to study the fundamental phenomena governing the interaction between the stiffened shell, with and without damping, and the fluid domain surrounding it. The models are used to predict the response of the shell and to evaluate the effect of the stiffening rings and damping treatment on both the structural vibration and noise radiation in the fluid domain. The prediction of the models are validated experimentally and against the predictions of a commercial FE software package (ANSYS). It is shown that stiffening of the shell reduces the amplitude of the vibration and noise radiation, particularly for high order lobar modes. The attenuation of the shell response and sound radiation can be significantly increased through the application of Passive Constrained Layer Damping treatment on the inner surface of the stiffening rings. The numerical and experimental validations demonstrate the accuracy of the developed models and emphasize its potential extension to the application of smart materials for active control of vibration and noise radiation from fluid-loaded shells.

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Chen, Xudong, and Kangsheng Ye. "Free Vibration Analysis for Shells of Revolution Using an Exact Dynamic Stiffness Method." Mathematical Problems in Engineering 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/4513520.

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An exact generalised formulation for the free vibration of shells of revolution with general shaped meridians and arbitrary boundary conditions is introduced. Starting from the basic shell theories, the vibration governing equations are obtained in the Hamilton form, from which dynamic stiffness is computed using the ordinary differential equations solver COLSYS. Natural frequencies and modes are determined by employing the Wittrick-Williams (W-W) algorithm in conjunction with the recursive Newton’s method, thus expanding the applications of the abovementioned techniques from one-dimensional skeletal structures to two-dimensional shells of revolution. A solution for solving the number of clamped-end frequenciesJ0in the W-W algorithm is presented for both uniform and nonuniform shell segment members. Based on these theories, a FORTRAN program is written. Numerical examples on circular cylindrical shells, hyperboloidal cooling tower shells, and spherical shells are given, and error analysis is performed. The convergence of the proposed method onJ0is verified, and comparisons with frequencies from existing literature show that the dynamic stiffness method is robust, reliable, and accurate.

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Yang, Zhong, and Jing Cao. "Vibration Reduction Analysis of Reticulated Shell." Advanced Materials Research 243-249 (May 2011): 1062–66. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.1062.

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Reticulated shell is one type of the common spatial structure form. This paper proposes a vibration reduction method by supplementing viscous dampers in the reticulated shell. It analyzes the seismic performance on the optimum partial double-layer reticulated shell with dampers by ANSYS soft, gains the stress in the members and the nodal displacements, and compares the dynamic responses between the normal and vibration reduction structure. By means of different parameters, the rules of vibration reduction effect in the reticulated shell with viscous dampers are acquired. It is shown through the calculation that the method developed in this paper is efficient for the dynamic analysis of the reticulated shells.

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Kang, Jae-Hoon. "Vibration Analysis of Complete Conical Shells with Variable Thickness." International Journal of Structural Stability and Dynamics 14, no. 04 (April 2, 2014): 1450001. http://dx.doi.org/10.1142/s0219455414500011.

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A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies of complete (not truncated) conical shells with linearly varying thickness. The complete conical shells free or clamped at the bottom edge with a free vertex are investigated. Unlike conventional shell theories, which are mathematically 2D, the present method is based upon the 3D dynamic equations of elasticity. Displacement components ur, uθ and uz in the radial, circumferential and axial directions, respectively, are taken to be periodic in θ and in time, and expressed by algebraic polynomials in the r- and z-directions. Potential (strain) and kinetic energies of the complete conical shell are formulated. The Ritz method is used to solve the eigenvalue problem, yielding the upper bound values of the frequencies by minimization. As the degree of the polynomials is increased, frequencies converge to the exact values, with four-digit exactitude demonstrated for the first five frequencies. The frequencies from the present 3D method are compared with those from other 3D approaches and 2D shell theory by previous researchers.

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Kang, Jae-Hoon, and Arthur W. Leissa. "Three-Dimensional Vibration Analysis of Thick, Complete Conical Shells." Journal of Applied Mechanics 71, no. 4 (July 1, 2004): 502–7. http://dx.doi.org/10.1115/1.1767843.

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A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution. Unlike conventional shell theories, which are mathematically two-dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components ur,uz, and uθ in the radial, axial, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the r and z-directions. Potential (strain) and kinetic energies of the conical shells are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the conical shells. Novel numerical results are presented for thick, complete conical shells of revolution based upon the 3D theory. Comparisons are also made between the frequencies from the present 3D Ritz method and a 2D thin shell theory.

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RAHMAN, T., E. L. JANSEN, and P. TISO. "A FINITE ELEMENT-BASED PERTURBATION METHOD FOR NONLINEAR FREE VIBRATION ANALYSIS OF COMPOSITE CYLINDRICAL SHELLS." International Journal of Structural Stability and Dynamics 11, no. 04 (August 2011): 717–34. http://dx.doi.org/10.1142/s0219455411004312.

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In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation and is subsequently converted to a finite element notation. After the determination of the linear natural frequency and corresponding vibration mode, the perturbation approach yields the initial curvature of the amplitude–frequency relation with a modest additional computational cost. The implementation of the perturbation approach in a general purpose finite element code using a laminated curved shell element is described. The effectiveness of the approach is illustrated by application to single-mode and coupled-mode nonlinear vibration analyses of cylindrical shells. Results for isotropic and composite cylindrical shells are presented and compared with results obtained via alternative approaches.

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Jam, J., M. Zadeh, H. Taghavian, and B. Eftari. "Vibration Analysis of Grid-Stiffened Circular Cylindrical Shells with Full Free Edges." Polish Maritime Research 18, no. 4 (January 1, 2011): 23–27. http://dx.doi.org/10.2478/v10012-011-0022-y.

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Vibration Analysis of Grid-Stiffened Circular Cylindrical Shells with Full Free Edges Free vibration of grid stiffened circular cylindrical shells is investigated based on the first Love's approximation theory using Galerkin method. Full free edges are considered for boundary conditions. An equivalent stiffness model (ESM) is used to develop the analytical solution of the grid stiffened circular cylindrical shell. The effect of helical stiffeners orientation and some of the geometric parameters of the structure have been shown. The accuracy of the analysis has been examined by comparing results with those available in the literature and finite element approach.

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Naeem, Muhmmad Nawaz, Shazia Kanwal, Abdul Ghafar Shah, Shahid Hussain Arshad, and Tahir Mahmood. "Vibration Characteristics of Ring-Stiffened Functionally Graded Circular Cylindrical Shells." ISRN Mechanical Engineering 2012 (October 15, 2012): 1–13. http://dx.doi.org/10.5402/2012/232498.

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The vibration characteristics of ring stiffened cylindrical shells are analyzed. These shells are assumed to be structured from functionally graded materials (FGM) and are stiffened with isotropic rings. The problem is formulated by coupling the expressions for strain and kinetic energies of a circular cylindrical shell with those for rings. The Lagrangian function is framed by taking difference of strain and kinetic energies. The Rayleigh-Ritz approach is employed to obtain shell dynamical equations. The axial model dependence is approximated by characteristic beam functions that satisfy the boundary conditions. The validity and efficiency of the present technique are verified by comparisons of present results with the previous ones determined by other researchers.

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Sahoo, S., and D. Chakravorty. "FiniteElement Vibration Characteristics of Composite Hypar Shallow Shells with Various Edge Supports." Journal of Vibration and Control 11, no. 10 (October 2005): 1291–309. http://dx.doi.org/10.1177/1077546305057260.

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A review of the literature reveals that information regarding fundamental frequencies and mode shapes of shallow laminated composite hypar shells with practical civil engineering boundary conditions is not available. The present investigation aims to fill this gap by applying an eight-noded isoparametric shell element as the tool. Numerical experiments are carried out for different parametric variations including boundary conditions and stacking orders to obtain the fundamental frequencies and mode shapes. Some of the results are used for validating the correctness of the present approach by comparing with the existing benchmark, while the other results are studied meticulously to extract a set of meaningful conclusions regarding the free vibration characteristics of composite shallow hypar shells.

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Mohandes, Masood, Ahmad Reza Ghasemi, Mohsen Irani-Rahagi, Keivan Torabi, and Fathollah Taheri-Behrooz. "Development of beam modal function for free vibration analysis of FML circular cylindrical shells." Journal of Vibration and Control 24, no. 14 (March 21, 2017): 3026–35. http://dx.doi.org/10.1177/1077546317698619.

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The free vibration of fiber–metal laminate (FML) thin circular cylindrical shells with different boundary conditions has been studied in this research. Strain–displacement relations have been obtained according to Love’s first approximation shell theory. To satisfy the governing equations of motion, a beam modal function model has been used. The effects of different FML parameters such as material properties lay-up, volume fraction of metal, fiber orientation, and axial and circumferential wavenumbers on the vibration of the shell have been studied. The frequencies of shells have been calculated for carbon/epoxy and glass/epoxy as composites and for aluminum as metal. The results demonstrate that the influences of FML lay-up and volume fraction of composite on the frequencies of the shell are remarkable.

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Dai, Lu, Tie Jun Yang, Yao Sun, and Ji Xin Liu. "Influence of Boundary Conditions on the Active Control of Vibration and Sound Radiation for a Circular Cylindrical Shell." Applied Mechanics and Materials 66-68 (July 2011): 1270–77. http://dx.doi.org/10.4028/www.scientific.net/amm.66-68.1270.

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Vibration and acoustic radiation of circular cylindrical shells are hot topics in the structural engineering field. However for a long period, this sort of problems is only limit to classical homogeneous boundary conditions. In this paper, the vibration of a circular cylindrical shell with elastic boundary supports is studied using modified Fourier series method, and the far-field pressure for a baffled shell is calculated by Helmholtz integral equation. Active control of vibration and acoustic radiation are carried out by minimizing structural kinetic energy and radiated acoustic power respectively. The influence of boundary conditions on the active control is investigated throughout several numerical examples. It is shown that the active control of vibration and acoustic for an elastically restrained shell can exhibit unexpected and complicated behaviors.

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30

Singh, Anand V. "Random vibration of cylindrical shells." AIAA Journal 25, no. 12 (December 1987): 1641–43. http://dx.doi.org/10.2514/3.9841.

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Guo, Xiangying, Dameng Liu, Wei Zhang, Lin Sun, and Shuping Chen. "Nonlinear Dynamic Analysis of Macrofiber Composites Laminated Shells." Advances in Materials Science and Engineering 2017 (2017): 1–17. http://dx.doi.org/10.1155/2017/4073591.

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This work presents the nonlinear dynamical analysis of a multilayer d31 piezoelectric macrofiber composite (MFC) laminated shell. The effects of transverse excitations and piezoelectric properties on the dynamic stability of the structure are studied. Firstly, the nonlinear dynamic models of the MFC laminated shell are established. Based on known selected geometrical and material properties of its constituents, the electric field of MFC is presented. The vibration mode-shape functions are obtained according to the boundary conditions, and then the Galerkin method is employed to transform partial differential equations into two nonlinear ordinary differential equations. Next, the effects of the transverse excitations on the nonlinear vibration of MFC laminated shells are analyzed in numerical simulation and moderating effects of piezoelectric coefficients on the stability of the system are also presented here. Bifurcation diagram, two-dimensional and three-dimensional phase portraits, waveforms phases, and Poincare diagrams are shown to find different kinds of periodic and chaotic motions of MFC shells. The results indicate that piezoelectric parameters have strong effects on the vibration control of the MFC laminated shell.

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32

Miramini, Seyed Mohammad, and Abdolreza Ohadi. "Three-Dimensional Vibration of Fluid-Conveying Laminated Composite Cylindrical Shells with Piezoelectric Layers." International Journal of Structural Stability and Dynamics 19, no. 03 (March 2019): 1950026. http://dx.doi.org/10.1142/s0219455419500263.

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Cylindrical shells containing flowing fluid have wide applications in various industries. They can be enhanced as smart structures through inclusion of piezoelectric layers, of which the dynamic behavior, however, has not been fully understood. In this paper, the vibration and dynamic analysis of a laminated composite hollow cylinder with piezoelectric layers, subjected to an internal incompressible fluid flow is investigated. It is assumed that the shell is simply supported and the fluid is inviscid and irrotational. The differential equations of the elastic layers, piezoelectric layers, and flowing fluid are derived by the three-dimensional (3D) theory of elasticity, theory of piezoelectricity, and potential flow theory, respectively. A well-known recursive method is applied and extended for the first time to solve the fluid-conveying pipes using 3D theory. This approach makes it possible for the solutions to converge to the exact ones with reasonable computational cost. After validating the results against those available in the literature, the vibrational behavior of the system is examined for various cases with the effect of each parameter investigated. Also, the influence of fluid on the vibration and stability of the shell has been analyzed. The present method can be used to analyze and design hybrid shells conveying fluid with high accuracy and low computational cost.

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33

Kamaloo, Abbas, Mohsen Jabbari, Mehdi Yarmohammad Tooski, and Mehrdad Javadi. "Nonlinear free vibration analysis of delaminated composite circular cylindrical shells." Journal of Vibration and Control 26, no. 19-20 (January 30, 2020): 1697–707. http://dx.doi.org/10.1177/1077546320902556.

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This study aims to present an analysis of nonlinear free vibrations of simply supported laminated composite circular cylindrical shells with throughout circumference delamination. Governing equations of motion are derived by applying energy methods; using Galerkin’s method reduced the nonlinear partial differential equations to a system of coupled nonlinear ordinary differential equations, which are subsequently solved using a numerical method. This research examines the effects of delamination on the oscillatory motion of delaminated composite circular cylindrical shells and then the effects of increase in delamination length, shell middle surface radius, number of layers, and orthotropy as changes in material properties on the nonlinearity of these types of shells. The results show that delamination leads to a decrease in frequency of oscillations and displacement. An increase in delamination length, shell middle surface radius, and orthotropy of layers decreases nonlinearity and displacement, whereas an increase in the number of layers increases nonlinearity and displacement. It is also observed that an increase in the circumferential wave number can decrease the effect of delamination.

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34

Bakhtiari, Mehrdad, Aouni A. Lakis, and Youcef Kerboua. "Nonlinear Vibration of Truncated Conical Shells: Donnell, Sanders and Nemeth Theories." International Journal of Nonlinear Sciences and Numerical Simulation 21, no. 1 (February 25, 2020): 83–97. http://dx.doi.org/10.1515/ijnsns-2018-0377.

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AbstractNonlinear free vibration of truncated conical shells has been investigated for three different shell theories; Donnell, Sanders and Nemeth to investigate the effect of their simplifying assumptions. The displacement field of a finite element model that was obtained from the exact solution of equilibrium equations of Sander’s improved first-approximation theory is used to define the nonlinear strain energy of conical shells. Employing generalized coordinates method the equations of motion are derived and subsequently the amplitude equation of nonlinear vibration of conical shells was developed. The amplitude equation is solved for multiple cases of isotropic materials. Linear and nonlinear free vibration results are validated against the existing studies in scientific literature and demonstrate good accordance. The validated model is used to investigate effects of different parameters including circumferential mode number, cone-half angle, length to radius ratio, thickness to radius ratio and boundary conditions for the nonlinear vibration of conical shells.

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35

Tong, L. "Free Vibration of Axially Loaded Laminated Conical Shells." Journal of Applied Mechanics 66, no. 3 (September 1, 1999): 758–63. http://dx.doi.org/10.1115/1.2791722.

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Analytical solutions for the three displacements are obtained, in the form of power series, directly from the three governing equations for free vibration of laminated conical shells under axial load. Numerical results are presented for free vibration of axially loaded laminated conical shells with different geometric parameters and under two types of boundary conditions. It is found that an axial tension increases the frequencies while an axial compression decreases the frequencies. For the shells studied, the effect of axial load on the lowest frequency of the shell is found to be not sensitive to change in semivertex angle when the applied axial load is kept as a constant fraction of the critical buckling load. However, the axial load effect becomes very sensitive to variation in semivertex angle when a constant axial load is applied.

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36

Birman, V. "Extension of Vlasov’s Semi-membrane Theory to Reinforced Composite Shells." Journal of Applied Mechanics 59, no. 2 (June 1, 1992): 462–64. http://dx.doi.org/10.1115/1.2899547.

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Governing equations for the statics and dynamics of reinforced composite shells are developed based on Vlasov’s semi-membrane shell theory. These equations have closed-form solutions illustrated for buckling and free vibration problems. The buckling solution converges to the known result for unstiffened isotropic shells.

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37

Yu, Hao. "Vibration Character Analysis and Calculation for Hemispherical Resonator Gyro." Applied Mechanics and Materials 271-272 (December 2012): 1224–28. http://dx.doi.org/10.4028/www.scientific.net/amm.271-272.1224.

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Hemispherical Resonator Gyro is rotation-sensing instrument and has the merits of reliability and longevity etc. The precision of HRG is depended on the vibration character of hemispherical shells. Using the semi-analytic method, this paper discussed vibration character of hemispherical shell resonator and derived an algorithm of semi-analytic spherical elements. The method applies displacement function with toroidal analysis and axial discrete, so original two dimension problem is reduced to one dimension problem. The new method is very much simplified and can efficiently calculate the correlative physical character of hemispherical shell resonator, so it has high practical value for engineering application.

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Yang, Fuchun, Xiaofeng Jiang, and Fuxin Du. "Vibration of rotating circular cylindrical shells with distributed springs." Journal of Mechanics 37 (2021): 346–58. http://dx.doi.org/10.1093/jom/ufab008.

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Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

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Hussain, Muzamal, Muhammad Nawaz Naeem, and Mohammad Reza Isvandzibaei. "Effect of Winkler and Pasternak elastic foundation on the vibration of rotating functionally graded material cylindrical shell." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 24 (January 22, 2018): 4564–77. http://dx.doi.org/10.1177/0954406217753459.

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In this paper, vibration characteristics of rotating functionally graded cylindrical shell resting on Winkler and Pasternak elastic foundations have been investigated. These shells are fabricated from functionally graded materials. Shell dynamical equations are derived by using the Hamilton variational principle and the Langrangian functional framed from the shell strain and kinetic energy expressions. Elastic foundations, namely Winkler and Pasternak moduli are inducted in the tangential direction of the shell. The rotational motions of the shells are due to the Coriolis and centrifugal acceleration as well as the hoop tension produced in the rotating case. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in rotating functionally graded cylindrical shell. The complex exponential functions, with the axial modal numbers that depend on the boundary conditions stated at edges of a cylindrical shell, have been used to compute the axial modal dependence. In our new investigation, frequency spectra are obtained for circumferential wave number, length-to-radius ratio, height-to-radius ratio with simply supported–simply supported and clamped–clamped boundary conditions without elastic foundation. Also, the effect of elastic foundation on the rotating cylindrical shells is examined with the simply supported–simply supported edge. To check the validity of the present method, the fundamental natural frequencies of non-rotating isotropic and functionally graded cylindrical shells are compared with the open literature. Also, a comparison is made for infinitely long rotating with the earlier published paper.

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Rout, Mrutyunjay, Sasank Shekhara Hota, and Amit Karmakar. "Free vibration characteristics of delaminated composite pretwisted stiffened cylindrical shell." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 4 (January 10, 2017): 595–611. http://dx.doi.org/10.1177/0954406216686389.

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Effects of delamination on free vibration characteristics of laminated stiffened cylindrical shells with pretwist are analyzed by finite element method. The investigation is carried out using an eight-noded quadratic isoparametric shell element, which incorporates the transverse shear deformation and rotary inertia along with a three-noded beam element for the stiffener. The multipoint constraint algorithm has been included to guarantee the compatibility of deformation, equilibrium of resultant forces, and moments at delamination crack tip. The general dynamic equilibrium equation is derived from Lagrange’s equation of motion for moderate rotational speeds for which the Coriolis effect is neglected. The standard eigenvalue problem is solved utilizing QR iteration algorithm. The accuracy of the present formulation is validated with benchmark solutions is available in the literature. The present work concerns about the effects of delamination, fiber orientation, twist angle, stiffener depth-to-shell thickness ratio, and rotational speed on the fundamental frequency of shallow cylindrical shells with stiffener. Representative mode shapes for some typical case of the stiffened shell for different twist angles and rotational speeds are also presented.

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41

Kamaloo, Abbas, Mohsen Jabbari, Mehdi Yarmohammad Tooski, and Mehrdad Javadi. "Nonlinear Free Vibrations Analysis of Delaminated Composite Conical Shells." International Journal of Structural Stability and Dynamics 20, no. 01 (November 29, 2019): 2050010. http://dx.doi.org/10.1142/s0219455420500108.

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This paper examines the nonlinear free vibration of laminated composite conical shells throughout the circumferential delamination. First, based on the energy method, the governing equation of motion for the shell was derived. To simplify the analysis, the nonlinear partial differential equations were reduced into a system of coupled ordinary differential equations using Galerkin’s method. Consequently, the results were obtained by the numerical methods. Finally, the effects of delamination, variations in the delamination length, conical shells characteristics, materials property and circumferential wave number on the nonlinear response of delaminated composite conical shells were examined. The results show that the presence of delamination leads to increase in the amplitude of oscillations for the shells. Besides, the increase in the delamination length and decrease of the circumferential wave number, number of layers, and half vertex angle of the cone and orthotropy bring about a decrease in the nonlinearity of delaminated composite conical shells. However, an increase of the middle surface radius of the shell leads to a reduction of the nonlinearity as well as an increase of the amplitude.

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42

Wang, Zhi Wei, Yan Fu Wang, and Bai Qin. "Analysis of Fiberglass Winding Angle on Natural Frequency of Cylindrical Shell with Symmetric Boundary Conditions." Advanced Materials Research 765-767 (September 2013): 106–9. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.106.

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In order to obtain approximate solution of natural frequencies for the free vibration of anisotropic circular cylindrical shells made of GFRP (glass fiber-reinforced plastic) with symmetric boundary conditions, Loves theory and energy method are used. Computation results show that the fundamental natural frequency comes from different vibration modes while the winding angle varies, the effect of number of axial half waves is stronger than number of circumferential waves on natural frequency of free vibration of anisotropic circular cylindrical shell.

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Wattanasakulpong, Nuttawit, Sacharuck Pornpeerakeat, and Arisara Chaikittiratana. "Chebyshev Collocation Solutions for Vibration Analysis of Circular Cylindrical Shells with Arbitrary Boundary Conditions." International Journal of Structural Stability and Dynamics 17, no. 02 (March 2017): 1750020. http://dx.doi.org/10.1142/s0219455417500201.

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This paper applies the Chebyshev collocation method to finding accurate solutions of natural frequencies for circular cylindrical shells. The shells with different boundary conditions are considered in the parametric study. By using the method to solve the coupled differential equations of motion governing the vibration of the shell, numerical results are obtained from the algebraic eigenvalue equation using the Chebyshev differentiation matrices. And the results satisfy both the geometric and force boundary conditions. Based on the numerical examples, the proposed method shows its capacity and reliability in predicting accurate frequency results for circular cylindrical shells with various boundary conditions as compared to some exact solutions available in the literature.

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Li, Xue-Qin, Guang-Chen Bai, Lu-Kai Song, and Wei Zhang. "Nonlinear Vibration Analysis for Stiffened Cylindrical Shells Subjected to Electromagnetic Environment." Shock and Vibration 2021 (July 19, 2021): 1–26. http://dx.doi.org/10.1155/2021/9983459.

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The nonlinear vibration behaviors of stiffened cylindrical shells under electromagnetic excitations, transverse excitations, and in-plane excitations are studied for the first time in this paper. Given the first-order shear deformation theory and Hamilton principle, the nonlinear partial differential governing equations of motion are derived with considering the von Karman geometric nonlinearity. By employing the Galerkin discretization procedure, the partial differential equations are diverted to a set of coupled nonlinear ordinary differential equations of motion. Based on the case of 1 : 2 internal resonance and principal resonance-1/2 subharmonic parametric resonance, the multiscale method of perturbation analysis is employed to precisely acquire the four-dimensional nonlinear averaged equations. From the resonant response analysis and nonlinear dynamic simulation, we discovered that the unstable regions of stiffened cylindrical shells can be narrowed by decreasing the external excitation or increasing the magnetic intensity, and their working frequency range can be expanded by reducing the in-plane excitation. Moreover, the different nonlinear dynamic responses of the stiffened cylindrical shell are acquired by controlling stiffener number, stiffener size, and aspect ratio. The presented approach in this paper can provide an eﬃcient analytical framework for nonlinear dynamics theories of stiffened cylindrical shells and will shed light on complex structure design in vibration test engineering.

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45

Zhou, Qi Zheng, De Shi Wang, and Sheng Yao Gao. "Acoustic and Vibration Characteristics of Stiffened Finite Cylindrical Shells in Water under Multiple Axial-Excitations." Advanced Materials Research 662 (February 2013): 721–25. http://dx.doi.org/10.4028/www.scientific.net/amr.662.721.

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A research on the vibration and acoustic radiation of stiffened finite cylindrical shells in water under a multiple axial-excitations driven was presented. The vibro-acoustic coupling equations of shell under multiple axial-excitations based on Flügge thin shell theory were established. The displacements, surface acoustic pressure and stiffener impedances were expressed in terms of the numbers of normal modals and modes, and considering multiple excitations, the forces were expressed in terms of the numbers of normal modals and modes. Then analytical solution was derived for the vibration and sound radiation from the stiffened shell under multiple excitations. Based on the analytical solution, the influences of excitations’ positions to the vibration and acoustic radiation were investigated. The results show that for double excitations, at high frequencies, the distance between excitations was more large, the average velocity was more low. The results could be used to control the underwater vehicle’s vibration and acoustic radiation.

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Kayran, A., and J. R. Vinson. "The Effect of Transverse Shear Deformation on the Natural Frequencies of Layered Composite Paraboloidal Shells." Journal of Vibration and Acoustics 112, no. 4 (October 1, 1990): 429–39. http://dx.doi.org/10.1115/1.2930125.

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An analysis is presented for the study of the effect of transverse shear deformation on the natural frequencies of layered composite paraboloidal shells. The applicability of linear shell theory due to Reissner is assumed and governing equations are solved for the natural frequencies using the transfer matrix approach. The results of the present analysis are compared with the results for paraboloidal shells reported in the literature and good agreement is found. Transverse shear deformation effects are carried out separately for axisymmetric torsional vibration modes, axisymmetric bending-extensional vibration modes and nonsymmetric vibration modes. The variation of the effect of transverse shear deformation with respect to different rim boundary conditions, geometry of the paraboloid, material type (isotropic-orthotropic), lamination arrangement and particular meridional and circumferential vibration modes is investigated.

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Li, Pengcheng, and Lei Wang. "Nonlinear Stability Behavior of Cable-Stiffened Single-Layer Latticed Shells Under Earthquakes." International Journal of Structural Stability and Dynamics 18, no. 10 (October 2018): 1850117. http://dx.doi.org/10.1142/s0219455418501171.

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A cable-stiffened single-layer latticed shell is an efficient and lightweight structural system in the category of spatial structures. In the past, much emphasis was placed on determining the static stability behavior of this structural system. Relatively little research was attempted on the seismic behavior of cable-stiffened single-layer latticed shells. The article aims to investigate numerically the seismic behavior of this structural system and to compare the behavior of the cable-stiffened single-layer latticed shell with that of the conventional unstiffened shell. The natural vibration characteristics, including the vibration modes and natural frequencies, were examined initially by modal analysis. Subsequently, a time-history analysis was conducted to analyze the nonlinear behavior of the cable-stiffened single-layer latticed shell under the El Centro earthquake. It was demonstrated that the seismic behavior of single-layer latticed shells can be greatly enhanced by the cable-stiffening system. In addition, the effects of pretension in cables, cross-sectional area, and other parameters relating to the seismic behavior of the cable-stiffened latticed shell have also been investigated.

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Mohammadrezazadeh, Shahin, and Ali Asghar Jafari. "The influences of magnetostrictive layers on active vibration control of laminated composite rotating cylindrical shells based on first-order shear deformation theory." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 13 (February 24, 2019): 4606–19. http://dx.doi.org/10.1177/0954406219830439.

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

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Li, H., and Z. B. Chen. "Torsional Sensors for Conical Shell in Torsional Vibrations." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, no. 11 (March 19, 2010): 2382–89. http://dx.doi.org/10.1243/09544062jmes1940.

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This paper presents shear piezoelectric sensors for conical shell sensing. The piezoelectric patch is polarized in the longitudinal direction of conical shell structure. The electrodes are fixed at the sides parallel to the directions of polarization. Sensors in this arrangement are only sensitive to the in-plane shear strains. Both sensing equations and modal signals are derived based on the thin-shell assumption and piezoelectric effect. Numerical results are presented for free torsional vibrations of frustum shell of revolution with clamped-free boundary, and the effects of sensor length on the output are evaluated. The amplitudes of the output signal of the sensors are lower than that of modal ones, but they are all share the same trends. The amplitudes depend on the deformation of the shell and the length of the sensor. The results indicate the optimal locations of the piezoelectric sensor for sensing the torsional vibration of clamped-free shell. The output signals of the sensor can be used as the control input for later active vibration control. The sensing equations are applicable to sense shear strains and torsion of other type shells by replacing the strain equation.

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Olaosebikan, Lekan. "Vibration analysis of elastic spherical shells." International Journal of Engineering Science 24, no. 10 (January 1986): 1637–54. http://dx.doi.org/10.1016/0020-7225(86)90138-2.

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Journal articles on the topic 'Shells (Engineering) Vibration'

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