Free vibration analysis of pretwisted delaminated composite stiffened shallow shells: A finite element approach

2017 ◽  
Vol 36 (8) ◽  
pp. 619-636 ◽  
Author(s):  
Mrutyunjay Rout ◽  
Tanmoy Bandyopadhyay ◽  
Amit Karmakar
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Dynamic Equilibrium ◽  
Twist Angle ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Shell Element ◽  
Mode Shapes ◽  
Shallow Shells

This paper presents the effect of stiffeners on the free vibration response of delaminated composite shallow cylindrical shells employing the finite element method. An eight-noded isoparametric shell element based on the first-order shear deformation theory is combined with a three-noded isoparametric curved beam element in the present formulation. The stiffeners follow the nodal lines of the shell wherein the stiffness and mass of the stiffeners are lumped at the corresponding nodal points of the shell elements considering curvature and eccentricity. The generalized dynamic equilibrium equation is derived from Lagrange’s equation of motion, wherein Coriolis effect for moderate rotational speeds is neglected. The multi-point constraint algorithm has been used to model delamination at the desired locations wherein the compatibility of deformation and equilibrium of stress resultants are ensured at the delamination crack front. Numerical results are presented for cantilevered long, intermediate and short cylindrical shells as defined by Aas-Jakobsen’s parameters, and the influence of important parameters like location of delamination, twist angle, rotational speed, number of layers and eccentricity of the stiffeners is studied. The mode shapes for a typical composite un-stiffened and stiffened long cylindrical shell at different rotational speeds and twist angles are also presented.

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.

scholarly journals On the Finite Element Model of Rotating Functionally Graded Graphene Beams Resting on Elastic Foundation

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Nguyen Van Dung ◽  
Nguyen Chi Tho ◽  
Nguyen Manh Ha ◽  
Vu Trong Hieu
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Mechanical Response ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Engineering Practice

Rotating structures can be easily encountered in engineering practice such as turbines, helicopter propellers, railroad tracks in turning positions, and so on. In such cases, it can be seen as a moving beam that rotates around a fixed axis. These structures commonly operate in hot weather; as a result, the arising temperature significantly changes their mechanical response, so studying the mechanical behavior of these structures in a temperature environment has great implications for design and use in practice. This work is the first exploration using the new shear deformation theory-type hyperbolic sine functions to carry out the free vibration analysis of the rotating functionally graded graphene beam resting on the elastic foundation taking into account the effects of both temperature and the initial geometrical imperfection. Equations for determining the fundamental frequencies as well as the vibration mode shapes of the beam are established, as mentioned, by the finite element method. The beam material is reinforced with graphene platelets (GPLs) with three types of GPL distribution ratios. The numerical results show numerous new points that have not been published before, especially the influence of the rotational speed, temperature, and material distribution on the free vibration response of the structure.

scholarly journals Effect of Location of Delamination on Free Vibration of Cross-Ply Conical Shells

2012 ◽  
Vol 19 (4) ◽  
pp. 679-692 ◽  
Author(s):  
Sudip Dey ◽  
Amit Karmakar
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Twist Angle ◽  
Structural Instability ◽  
Numerical Results ◽  
Mode Shapes ◽  
Iteration Algorithm ◽  
Conical Shells

Location of delamination is a triggering parameter for structural instability of laminated composites. In this paper, a finite element method is employed to determine the effects of location of delamination on free vibration characteristics of graphite-epoxy cross-ply composite pre-twisted shallow conical shells. The generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting Coriolis effect for moderate rotational speeds. The 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 the numerical results concerning the effects of location of delamination, twist angle and rotational speed on the natural frequencies of cross-ply composite shallow conical shells. The mode shapes are also depicted for a typical laminate configuration. Numerical results obtained from parametric studies of both symmetric and anti-symmetric cross-ply laminates are the first known non-dimensional natural frequencies for the type of analyses carried out here.

Free vibration response of carbon nanotube reinforced pretwisted conical shell under thermal environment

2019 ◽  
Vol 234 (3) ◽  
pp. 770-783 ◽  
Author(s):  
Pabitra Maji ◽  
Mrutyunjay Rout ◽  
Amit Karmakar
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Conical Shell ◽  
Dynamic Equilibrium ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Mode Shapes

Finite element procedure is employed to analyze the free vibration characteristics of rotating functionally graded carbon nanotubes reinforced composite conical shell with pretwist under the thermal environment. In this paper, four types of carbon nanotube grading are considered, wherein the distribution of carbon nanotubes are made through the thickness direction of the conical shell. An eight-noded isoparametric shell element is used in the present formulation to model the panel based on the first-order shear deformation theory. For moderate rotational speeds, the generalized dynamic equilibrium equation is derived from Lagrange’s equation of motion, neglecting the Coriolis effect. The finite element code is developed to investigate the effect of twist angle, temperature, aspect ratio, and rotational speed on natural frequencies. The mode shapes of a carbon nanotube reinforced functionally graded conical shell at different twist angles and rotational speeds are also presented.

scholarly journals Dynamic Response of Shear-Flexible Cylindrical Isotropic Shells with Clamped Edges

2006 ◽  
Vol 13 (2) ◽  
pp. 103-116 ◽  
Author(s):  
Zafer I. Sakka ◽  
Jamal A. Abdalla ◽  
H.R.H. Kabir
Keyword(s):  
Free Vibration ◽  
Cylindrical Shells ◽  
Shell Element ◽  
Double Fourier Series ◽  
Analytical Investigation ◽  
Fourier Series Expansion ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Bench Mark ◽  
Approximate Methods

It is fundamental to obtain the natural frequencies and the corresponding mode shapes for cylindrical shells in order to determine their response to different dynamic loading. In this paper an analytical investigation to the free vibration response of moderately-thick shear flexible isotropic cylindrical shells with all edges clamped is presented. The Sander’s kinematic relations for moderately thick cylindrical shell panels are utilized to develop the governing partial differential equations in conjunction with the boundary conditions. A recently developed generalized Navier’s approach, based on a boundary continuous double Fourier series expansion, is used as a solution methodology. A parametric study is presented with respect to various thicknesses, length and radius of curvature of the shell panel. The convergence of the solution method is established numerically for various parametric properties. The present results are compared with the results obtained from finite element method using a four-node isoparametric shell element. The results thus presented should serve as bench-mark solutions for future comparisons with numerical and approximate methods for calculation of free vibration parameters of moderately-thick isotropic cylindrical shells.

Free vibration analysis of a rectangular plate carrying multiple various concentrated elements

2003 ◽  
Vol 217 (2) ◽  
pp. 171-183 ◽  
Author(s):  
J-S Wu ◽  
H-M Chou ◽  
D-W Chen
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Normal Mode ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Equation Of Motion ◽  
Mode Shapes

The dynamic characteristic of a uniform rectangular plate with four boundary conditions and carrying three kinds of multiple concentrated element (rigidly attached point masses, linear springs and elastically mounted point masses) was investigated. Firstly, the closed-form solutions for the natural frequencies and the corresponding normal mode shapes of a rectangular ‘bare’ (or ‘unconstrained’) plate (without any attachments) with the specified boundary conditions were determined analytically. Next, by using these natural frequencies and normal mode shapes incorporated with the expansion theory, the equation of motion of the ‘constrained’ plate (carrying the three kinds of multiple concentrated element) were derived. Finally, numerical methods were used to solve this equation of motion to give the natural frequencies and mode shapes of the ‘constrained’ plate. To confirm the reliability of previous free vibration analysis results, a finite element analysis was also conducted. It was found that the results obtained from the above-mentioned two approaches were in good agreement. Compared with the conventional finite element method (FEM), the approach employed in this paper has the advantages of saving computing time and achieving better accuracy, as can be seen from the existing literature.

Multistage Coupling of Eight Mistuned Bladed Disk on a Solid Shaft: Part 1—Free Vibration Analysis

2012 ◽  
Author(s):  
Romuald Rzadkowski ◽  
Artur Maurin
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
Rotor Blades ◽  
Mode Shapes ◽  
Bladed Disk ◽  
Centrifugal Stiffening

Considered here was the effect of multistage coupling on the dynamics of a rotor consisting of eight mistuned bladed discs on a solid shaft. Each bladed disc had a different number of rotor blades. Free vibrations were examined using finite element representations of rotating single blades, bladed discs, and the entire rotor. In this study the global rotating mode shapes of eight flexible mistuned bladed discs on shaft assemblies were calculated, taking into account rotational effects such as centrifugal stiffening. The thus obtained natural frequencies of the blade, shaft, bladed disc and entire shaft with discs were carefully examined to discover resonance conditions and coupling effects. This study found that mistuned systems cause far more intensive multistage coupling than tuned ones. The greater the mistuning, the more intense the multistage coupling.

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