Free vibration of composite and sandwich laminates with a higher-order facet shell element

2004 ◽  
Vol 65 (3-4) ◽  
pp. 405-418 ◽  
Author(s):  
Rakesh Kumar Khare ◽  
Tarun Kant ◽  
Ajay Kumar Garg
Keyword(s):  
Free Vibration ◽  
Shell Element ◽  
Higher Order

Free Vibration of Moderately Thick Conical Shells Using a Higher Order Shear Deformable Theory

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
R. D. Firouz-Abadi ◽  
M. Rahmanian ◽  
M. Amabili
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Arbitrary Boundary ◽  
Conical Shells ◽  
First Time ◽  
Circumferential Wave ◽  
Shear Deformable

The present study considers the free vibration analysis of moderately thick conical shells based on the Novozhilov theory. The higher order governing equations of motion and the associate boundary conditions are obtained for the first time. Using the Frobenius method, exact base solutions are obtained in the form of power series via general recursive relations which can be applied for any arbitrary boundary conditions. The obtained results are compared with the literature and very good agreement (up to 4%) is achieved. A comprehensive parametric study is performed to provide an insight into the variation of the natural frequencies with respect to thickness, semivertex angle, circumferential wave numbers for clamped (C), and simply supported (SS) boundary conditions.

Free vibration characteristics of delaminated composite pretwisted stiffened cylindrical shell

2017 ◽  
Vol 232 (4) ◽  
pp. 595-611 ◽  
Author(s):  
Mrutyunjay Rout ◽  
Sasank Shekhara Hota ◽  
Amit Karmakar
Keyword(s):  
Free Vibration ◽  
Dynamic Equilibrium ◽  
Twist Angle ◽  
Cylindrical Shells ◽  
Shell Element ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Iteration Algorithm ◽  
Lagrange’S Equation ◽  
Benchmark Solutions

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.

An hp-version adaptive finite element algorithm for eigensolutions of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yongliang Wang ◽  
Jianhui Wang
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Cylindrical Shells ◽  
Higher Order ◽  
Wave Number ◽  
Adaptive Finite Element ◽  
Content Type ◽  
Circular Cylindrical Shells ◽  
Geometrical Factors ◽  
Circumferential Wave

PurposeThis study presents a novel hp-version adaptive finite element method (FEM) to investigate the high-precision eigensolutions of the free vibration of moderately thick circular cylindrical shells, involving the issues of variable geometrical factors, such as the thickness, circumferential wave number, radius and length.Design/methodology/approachAn hp-version adaptive finite element (FE) algorithm is proposed for determining the eigensolutions of the free vibration of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation. This algorithm first develops the established h-version mesh refinement method for detecting the non-uniform distributed optimised meshes, where the error estimation and element subdivision approaches based on the superconvergent patch recovery displacement method are introduced to obtain high-precision solutions. The errors in the vibration mode solutions in the global space domain are homogenised and approximately the same. Subsequently, on the refined meshes, the algorithm uses higher-order shape functions for the interpolation of trial displacement functions to reduce the errors quickly, until the solution meets a pre-specified error tolerance condition. In this algorithm, the non-uniform mesh generation and higher-order interpolation of shape functions are suitable for addressing the problem of complex frequencies and modes caused by variable structural geometries.FindingsNumerical results are presented for moderately thick circular cylindrical shells with different geometrical factors (circumferential wave number, thickness-to-radius ratio, thickness-to-length ratio) to demonstrate the effectiveness, accuracy and reliability of the proposed method. The hp-version refinement uses fewer optimised meshes than h-version mesh refinement, and only one-step interpolation of the higher-order shape function yields the eigensolutions satisfying the accuracy requirement.Originality/valueThe proposed combination of methodologies provides a complete hp-version adaptive FEM for analysing the free vibration of moderately thick circular cylindrical shells. This algorithm can be extended to general eigenproblems and geometric forms of structures to solve for the frequency and mode quickly and efficiently.

Free-Vibration of Rotating Composite Beams Incorporating Higher-Order Transverse Shear Effects

2001 ◽  
Author(s):  
N. K. Chandiramani ◽  
L. I. Librescu ◽  
C. D. Shete
Keyword(s):  
Free Vibration ◽  
Transverse Shear ◽  
Present Model ◽  
Structural Model ◽  
Laminated Composite ◽  
Higher Order ◽  
Rotating Blade ◽  
Box Beam ◽  
Shear Effects ◽  
Transverse Shear Effects

Abstract The free vibration behavior of a rotating blade modeled as a laminated composite hollow (single celled) box beam is studied. The geometrically nonlinear structural model developed herein incorporates a number of non-classical effects such as anisotropy, heterogeneity, transverse shear flexibility, and warping inhibition. The centrifugal and Coriolis force field effects are also included. The main focus here being the refinement of the existing model, the traction-free boundary conditions are satisfied here in contrast to the existing model. The resulting linearized equations and numerical results based on them are presented. Results obtained for the present higher-order shearable model are compared with those of the existing first-order shearable and the non-shearable models. Tailoring studies using the present model reveal an enhancement of eigenfrequency characteristics.

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