Solution for free vibration of spatial curved beams

2019 ◽  
Vol 37 (5) ◽  
pp. 1597-1616 ◽  
Author(s):  
Guangxin Wang ◽  
Lili Zhu ◽  
Ken Higuchi ◽  
Wenzhong Fan ◽  
Linjie Li
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Cross Section ◽  
Circular Cross Section ◽  
Accurate Solution ◽  
Vibration Response ◽  
Curved Beams ◽  
Content Type ◽  
Variable Curvature ◽  
Free Vibration Response

Purpose The purpose of this paper is to propose and analyze the free vibration response of the spatial curved beams with variable curvature, torsion and cross section, in which all the effects of rotary inertia, shear and axial deformations can be considered. Design/methodology/approach The governing equations for free vibration response of the spatial curved beams are derived in matrix formats, considering the variable curvature, torsion and cross section. Frobenius’ scheme and the dynamic stiffness method are applied to solve these equations. A computer program is coded in Mathematica according to the proposed method. Findings To assess the validity of the proposed solution, a convergence study is carried out on a cylindrical helical spring with a variable circular cross section, and a comparison is made with the finite element method (FEM) results in ABAQUS. Further, the present model is used for reciprocal spiral rods with variable circular cross section in different boundary conditions, and the comparison with FEM results shows that only a limited number of terms in the results provide a relatively accurate solution. Originality/value The numerical results show that only a limited number of terms are needed in series solutions and in the Taylor expansion series to ensure an accurate solution. In addition, with a simple modification, the present formulation is easy to extend to analyze a more complicated model by combining with finite element solutions or analyze the transient responses and stochastic responses of spatial curved beams by Laplace transformation or Fourier transformation.

Vibration Analysis of Thick Arbitrarily Laminated Plates of Various Shapes and Edge Conditions

2011 ◽  
Vol 471-472 ◽  
pp. 1177-1183
Author(s):  
Tasneem Pervez ◽  
F.K.S. Al-Jahwari ◽  
Abdennour Seibi
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Laminated Plates ◽  
Vibration Response ◽  
Element Formulation ◽  
Edge Conditions ◽  
Shear Deformation Theories ◽  
Free Vibration Response

Free vibration analysis of arbitrarily laminated plates of quad, penta and hexagonal shapes, which have combinations of clamped, simply supported and free edge conditions is performed. The finite element formulation is based on first and higher order shear deformation theories to study the free vibration response of thick laminated composite plates. A finite element code is developed incorporating shear deformation theories using an 8-noded serendipity element. The effect of plate shape, arbitrary lamination and different edge conditions on natural frequencies and mode shapes are investigated. A systematic study is carried out to determine the influence of material orthotropy and aspect ratio on free vibration response. For various cases, the comparisons of results from present study showed good agreement with those published in the literature.

FREE VIBRATION RESPONSE OF SHEAR-FLEXIBLE MODERATELY-THICK ORTHOTROPIC CYLINDRICAL SHELLS

2006 ◽  
Vol 06 (01) ◽  
pp. 121-138 ◽  
Author(s):  
Z. I. SAKKA ◽  
J. A. ABDALLA ◽  
H. R. H. KABIR
Keyword(s):  
Finite Element ◽  
Fourier Series ◽  
Analytical Solution ◽  
Free Vibration ◽  
Orthotropic Cylindrical Shell ◽  
Shell Element ◽  
Vibration Response ◽  
Fourier Series Expansion ◽  
Mode Shapes ◽  
Free Vibration Response

The free vibration response of shear-flexible moderately-thick orthotropic cylindrical shell panels, with fixed edges, is investigated using an analytical approach. The governing partial differential equations are developed based on Sander's kinematics and are solved using generalized Navier's with a boundary continuous double Fourier series expansion. The frequencies and mode shapes from the analytical solution for various parametric ratios, including degree of orthotropy (stiffness ratio), radius-to-segment ratio and segment-to-thickness ratio are compared with the finite element solutions that are based on an eight-node 48 degrees of freedom shell element. The rate of convergence of the analytical solution method with respect to the number of Fourier series terms, for various parametric ratios, is presented. The results of the analytical solution are very comparable to that of the finite element solution. It is clear that the presented analytical solution can be used as a benchmark to calibrate and validate numerical and finite element solutions that usually involve approximation to shell theories.

Finite Element Technique for the Curved Beam Analysis: In-Plate Vibration of Curved Beam With Varying Cross Section

1991 ◽  
Author(s):  
Michihiko Tanaka ◽  
Motoki Kobayashi
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Cross Section ◽  
Element Formulation ◽  
Curved Beam ◽  
Curved Beams ◽  
Finite Element Technique ◽  
Beam Analysis ◽  
Power Series Expansions ◽  
Element Technique

Abstract The purpose of this paper is to present details of an algorithm for performing the numerical analysis of in-plane free vibration problem of curved beam by using the finite element technique. Although the finite element techniques for the straight or flat structures such as rods, beams and plates are well established, the finite element formulation for curved beam has not yet been completely discussed because of analytical complexity of the beam. The analysis of curved beam is reduced to the coupled problems of the axial and the transverse components of forces, bending moments, displacements and slopes in the beam. Sabir and Ashwell have discussed the vibrations of a ring by using the shape functions (interpolation functions) based on simple strain functions[1]. The discrete element displacement method was applied to the vibrations of shallow curved beam by Dawe[2]. Suzuki et al have presented the power series expansions method for solving free vibration of curved beams[3]. Irie et al have used spline functions to analyse the in-plane vibration of the varying cross section beams supported at one end[4].

Determination of collapse moment of different angled pipe bends with initial geometric imperfection subjected to in-plane bending moments

2021 ◽  
pp. 095440622199640
Author(s):  
Manish Kumar ◽  
Pronab Roy ◽  
Kallol Khan
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Circular Cross Section ◽  
Initial Imperfection ◽  
Bend Angle ◽  
Bending Moments ◽  
Element Analysis ◽  
Geometric Imperfection ◽  
Initial Geometric Imperfection

From the recent literature, it is revealed that pipe bend geometry deviates from the circular cross-section due to pipe bending process for any bend angle, and this deviation in the cross-section is defined as the initial geometric imperfection. This paper focuses on the determination of collapse moment of different angled pipe bends incorporated with initial geometric imperfection subjected to in-plane closing and opening bending moments. The three-dimensional finite element analysis is accounted for geometric as well as material nonlinearities. Python scripting is implemented for modeling the pipe bends with initial geometry imperfection. The twice-elastic-slope method is adopted to determine the collapse moments. From the results, it is observed that initial imperfection has significant impact on the collapse moment of pipe bends. It can be concluded that the effect of initial imperfection decreases with the decrease in bend angle from 150∘ to 45∘. Based on the finite element results, a simple collapse moment equation is proposed to predict the collapse moment for more accurate cross-section of the different angled pipe bends.

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