Clamped Cylindrical Shells of Laminated Composites: Effect of Cutout on Natural Frequency and Mode Shapes (original) (raw)
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2015
Clamped saddle shells made of laminated composite materials in presence of stiffeners and cutouts are analyzed employing the eight-noded curved quadratic isoparametric element for shell with a three noded beam element for stiffener formulation. Free vibration problem of stiffened saddle shells with different size and position of the cutouts with respect to the shell centre are examined to find natural frequency and mode shapes of stiffened shells and arrive at some conclusions useful to the designers. The results are further analyzed to suggest guidelines to select optimum size and position of the cutout with respect to shell centre.
Journal of Mechanical Science and Technology
In order to study the free vibration of simply supported circular cylindrical shells, an exact analytical procedure is developed and discussed in detail. Part I presents a general approach for exact analysis of natural frequencies and mode shapes of circular cylindrical shells. The validity of the exact technique is verified using four different shell theories 1) Soedel, 2) Flugge, 3) Morley-Koiter and 4) Donnell. The exact procedure is compared favorably with experimental results and those obtained using a numerical finite element method. A literature review reveals that beam functions are used extensively as an approximation for simply supported boundary conditions. The accuracy of the resonance frequencies obtained using the approximate method are also investigated by comparing results with those of the exact analysis. Part II presents effects of different parameters on mode shapes and natural frequencies of circular cylindrical shells.
Laminated composite stiffened elliptic paraboloid shell with cutout under clamped condition
International Journal of Advanced Materials Manufacturing and Characterization, 2015
Clamped elliptic paraboloid shells made of laminated composite materials in presence of stiffeners and cutouts are analyzed employing the eight-noded curved quadratic isoparametric element for shell with a three noded beam element for stiffener formulation. Free vibration problem of stiffened shells with different size and position of the cutouts with respect to the shell centre are examined to find natural frequency and mode shapes of stiffened shells and arrive at some conclusions useful to the designers. The results are further analyzed to suggest guidelines to select optimum size and position of the cutout with respect to shell centre.
Composites Part B: Engineering, 2001
The bending, buckling and free vibration problems of non-homogeneous composite laminated cylindrical shells are considered. Hamilton–Reissner's mixed variational principle is used to deduce a consistent first-order theory of composite laminated cylindrical shells with non-homogeneous elastic properties. The governing equations with their required boundary conditions are derived without introducing any shear correction factors. Numerical results for the transverse deflections, stresses, natural frequencies and critical buckling loads are presented to show the advantages of this theory. The influences of the non-homogeneity and thickness ratio on the shell structural response are investigated. The study concludes that the inclusion of the non-homogeneity effect is required, even if it is weak, for predicting the actual structural response of the shells.
Journal of Mechanical Science and Technology
In the second part of this study, the approach developed in Part I is used to analyze parameters which effect the natural frequencies and mode shapes of circular cylindrical shells. Therefore, amplitude ratios are determined analytically for shells of different geometries. The effects of circumferential and longitudinal wave numbers and geometrical parameters are studied on longitudinal, tangential and radial motions. Finally, numerical studies are conducted to investigate the effects of composite laminate parameters on resonance frequencies. Various laminate parameters such as stacking sequence and fiber angle are considered in the study.
Free vibration of composite skewed cylindrical shell panel by finite element method
Journal of Sound and Vibration, 2008
In this paper a composite triangular shallow shell element has been used for free vibration analysis of laminated composite skewed cylindrical shell panels. In the present element first-order shear deformation theory has been incorporated by taking transverse displacement and bending rotations as independent field variables. The interpolation function used to approximate transverse displacement is one order higher than for bending rotations. This has made the element free from locking in shear. Two types of mass lumping schemes have been recommended. In one of the mass lumping scheme the effect of rotary inertia has been incorporated in the element formulations. Free vibration of skewed composite cylindrical shell panels having different thickness to radius ratios (h/R ¼ 0.01-0.2), length to radius ratios (L/R), number of layers and fiber orientation angles have been analyzed following the shallow shell method. The results for few examples obtained in the present analysis have compared with the published results. Some new results of composite skewed cylindrical shell panels have been presented which are expected to be useful to future research in this direction.
Mechanics of Advanced Materials and Structures, 2019
In this paper, the analytical model is established on base of multi-segment partitioning strategy and first-order shear deformation theory. The displacement functions are made up of the Jacobi polynomials along the axial direction and Fourier series along the circumferential direction. In order to obtain continuity conditions and satisfy arbitrary boundary conditions, the penalty method about spring technique is adopted. The solutions about free vibration behaviors of combined composite laminated shell were obtained by approach of Rayleigh-Ritz. The convergence study and numerical verifications are carried out. Results show that the proposed method has a good stable and rapid convergence property.
Materials, 2020
A semi-analytic method is adopted to analyze the free vibration characteristics of the moderately thick composite laminated cylindrical shell with arbitrary classical and elastic boundary conditions. By Hamilton’s principle and first-order shear deformation theory, the governing equation of the composite shell can be established. The displacement variables are transformed into the wave function forms to ensure the correctness of the governing equation. Based on the kinetic relationship between the displacement variables and force resultants, the final equation associated with arbitrary boundary conditions is established. The dichotomy method is conducted to calculate the natural frequencies of the composite shell. For verifying the correctness of the present method, the results by the present method are compared with those in the pieces of literatures with various boundary conditions. Furthermore, some numerical examples are calculated to investigate the effect of several parameters...
MATEC Web of Conferences
In the present work, the natural frequencies of cylindrical and spherical laminated shells with variable stiffness are numerically studied using a shear flexible isogeometric finite element. The kinematics relies on cubic shear deformation theory in which cubic variation is assumed for the surface displacements and a quadratic variation for the traverse displacement along the thickness. A zigzag function, used for the in-plane displacements, accounts for the abrupt discontinuity at the boundaries of the laminae. The Lagrangian equations of motion is deployed to solve the frequencies of curved panels. A detailed parametric analysis examines the influence of fibre centre/edge angles, shell geometric variables, material anisotropy and edge conditions on frequencies and mode shapes.
Free Vibration of Delaminated Composite Shallow Conical Shells
Journal of Solid Mechanics and Materials Engineering, 2011
This paper presents a finite element method to investigate the effects of delamination on free vibration characteristics of graphite-epoxy pretwisted shallow angle-ply composite conical shells. The generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting Coriolis effect for moderate rotational speeds. The theoretical formulation is exercised by using an eight noded isoparametric plate bending element based on Mindlin's theory. Multi-point constraint algorithm is utilized to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The standard eigen value problem is solved by applying the QR iteration algorithm. Finite element codes are developed to obtain numerical results concerning the effect of twist angle, location of delamination and rotational speed on natural frequencies of delaminated angle-ply composite conical shells. The mode shapes are also depicted for a typical laminate configuration. Parametric studies of symmetric and anti-symmetric angle-ply laminates provide the non-dimensional natural frequencies which are the first known results for the type of analyses carried out here.