Exact dynamic stiffness matrix of non-symmetric thin-walled curved beams subjected to initial axial force

2005 ◽  
Vol 284 (3-5) ◽  
pp. 851-878 ◽  
Author(s):  
Kim Nam-Il ◽  
Kim Moon-Young
Keyword(s):  
Axial Force ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Curved Beams ◽  
Dynamic Stiffness Matrix ◽  
Thin Walled

Exact dynamic stiffness matrix for a thin-walled beam-column of doubly asymmetric cross-section

2011 ◽  
Vol 38 (2) ◽  
pp. 195-210
Author(s):  
A. Shirmohammadzade ◽  
B. Rafezy ◽  
W.P. Howson
Keyword(s):  
Cross Section ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Dynamic Stiffness Matrix ◽  
Thin Walled

Dynamic stiffness matrix of thin-walled composite I-beam with symmetric and arbitrary laminations

2008 ◽  
Vol 318 (1-2) ◽  
pp. 364-388 ◽  
Author(s):  
Nam-Il Kim ◽  
Dong Ku Shin ◽  
Young-Suk Park
Keyword(s):  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Dynamic Stiffness Matrix ◽  
Thin Walled

scholarly journals Analytical Investigation of the Dynamic Response of a Timoshenko Thin-Walled Beam with Asymmetric Cross Section Under Deterministic Loads

2017 ◽  
Vol 11 (1) ◽  
pp. 802-821
Author(s):  
Elham Ghandi ◽  
Ahmed Ali Akbari Rasa
Keyword(s):  
Differential Equations ◽  
Dynamic Response ◽  
Stiffness Matrix ◽  
Matrix Method ◽  
Nonlinear Eigenvalue Problem ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Dynamic Features ◽  
Dynamic Stiffness Matrix ◽  
Thin Walled

Inroduction: The objective of the present paper is to analyze dynamic response of the Timoshenko thin-walled beam with coupled bending and torsional vibrations under deterministic loads. The governing differential equations were obtained by using Hamilton’s principle. The Timoshenko beam theory was employed and the effects of shear deformations, Rotary inertia and warping stiffness were included in the present formulations. Dynamic features of underlined beam are obtained using free vibration analysis. Methods: For this purpose, the dynamic stiffness matrix method is used. Application of exact dynamic stiffness matrix method on the movement differential equations led to the issue of nonlinear eigenvalue problem that was solved by using Wittrick–Williams algorithm . Differential equations for the displacement response of asymmetric thin-walled Timoshenko beams subjected to deterministic loads are used for extracting orthogonality property of vibrational modes. Results: Finally the numerical results for dynamic response in a sample of mentioned beams is presented. The presented theory is relatively general and can be used for various kinds of deterministic loading in Timoshenko thin-walled beams.

DYNAMIC STIFFNESS MATRIX FOR FLEXURAL-TORSIONAL, LATERAL BUCKLING AND FREE VIBRATION ANALYSES OF MONO-SYMMETRIC THIN-WALLED COMPOSITE BEAMS

2009 ◽  
Vol 09 (03) ◽  
pp. 411-436 ◽  
Author(s):  
NAM-IL KIM ◽  
DONG KU SHIN
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Elastic Strain Energy ◽  
Composite Beams ◽  
Energy Principle ◽  
Dynamic Stiffness Matrix ◽  
Axial Forces ◽  
Thin Walled ◽  
Force Displacement

This paper presents the elastic strain energy, the potential energy with the second order terms of finite rotations, and the kinetic energy with rotary inertia effect for thin-walled composite beams of mono-symmetric cross-section. The equations of motion and force-displacement relationships are derived from the energy principle and explicit expressions for displacement parameters are given based on power series expansions of displacement components. The exact dynamic stiffness matrix is determined using the force-displacement relationships. In addition, the finite element model based on Hermitian interpolation polynomial is developed. In order to verify the accuracy and validity of the formulation, numerical examples are solved and the solutions are compared with results from ABAQUS's shell elements, analytical solutions from previous researchers and the finite element solutions using the Hermitian beam elements. The influence of constant and linearly variable axial forces, fiber orientation, and boundary conditions on the vibration behavior of composite beam are also investigated.

Dynamic stiffness matrix of non-symmetric thin-walled curved beam on Winkler and Pasternak type foundations

2007 ◽  
Vol 38 (3) ◽  
pp. 158-171 ◽  
Author(s):  
Nam-Il Kim ◽  
Chung C. Fu ◽  
Moon-Young Kim
Keyword(s):  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Curved Beam ◽  
Dynamic Stiffness Matrix ◽  
Thin Walled

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

2021 ◽  
pp. 146442072098817
Author(s):  
Md. Imran Ali ◽  
Mohammad Sikandar Azam
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Stiffness Matrix ◽  
Natural Vibration ◽  
Dynamic Stiffness ◽  
Functionally Graded ◽  
Neutral Surface ◽  
Functionally Graded Plate ◽  
Dynamic Stiffness Matrix ◽  
Graded Material

This paper presents the formulation of dynamic stiffness matrix for the natural vibration analysis of porous power-law functionally graded Levy-type plate. In the process of formulating the dynamic stiffness matrix, Kirchhoff-Love plate theory in tandem with the notion of neutral surface has been taken on board. The developed dynamic stiffness matrix, a transcendental function of frequency, has been solved through the Wittrick–Williams algorithm. Hamilton’s principle is used to obtain the equation of motion and associated natural boundary conditions of porous power-law functionally graded plate. The variation across the thickness of the functionally graded plate’s material properties follows the power-law function. During the fabrication process, the microvoids and pores develop in functionally graded material plates. Three types of porosity distributions are considered in this article: even, uneven, and logarithmic. The eigenvalues computed by the dynamic stiffness matrix using Wittrick–Williams algorithm for isotropic, power-law functionally graded, and porous power-law functionally graded plate are juxtaposed with previously referred results, and good agreement is found. The significance of various parameters of plate vis-à-vis aspect ratio ( L/b), boundary conditions, volume fraction index ( p), porosity parameter ( e), and porosity distribution on the eigenvalues of the porous power-law functionally graded plate is examined. The effect of material density ratio and Young’s modulus ratio on the natural vibration of porous power-law functionally graded plate is also explained in this article. The results also prove that the method provided in the present work is highly accurate and computationally efficient and could be confidently used as a reference for further study of porous functionally graded material plate.

Sign in / Sign up

Export Citation Format

Share Document