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.

Modified Interval Perturbation Finite Element Method for a Structural-Acoustic System With Interval Parameters

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
Baizhan Xia ◽  
Dejie Yu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Dynamic Equilibrium ◽  
Dynamic Stiffness ◽  
Response Analysis ◽  
Acoustic System ◽  
Dynamic Stiffness Matrix ◽  
Interval Parameters ◽  
Element Method

For the frequency response analysis of the structural-acoustic system with interval parameters, a modified interval perturbation finite element method (MIPFEM) is proposed. In the proposed method, the interval dynamic equilibrium equation of the uncertain structural-acoustic system is established. The interval structural-acoustic dynamic stiffness matrix and the interval force vector are expanded by using the first-order Taylor series; the inversion of the invertible interval structural-acoustic dynamic stiffness matrix is approximated by employing a modified approximate interval-value Sherman–Morrison–Woodbury formula. The proposed method is implemented at an element-by-element level in the finite element framework. Numerical results on a shell structural-acoustic system with interval parameters verify the accuracy and efficiency of the proposed method.

Frequency domain-based analysis of floor vibrations using the dynamic stiffness matrix method

2018 ◽  
Vol 25 (4) ◽  
pp. 763-776 ◽  
Author(s):  
Tong Guo ◽  
Zhiliang Cao ◽  
Zhiqiang Zhang ◽  
Aiqun Li
Keyword(s):  
Finite Element ◽  
Frequency Domain ◽  
Stiffness Matrix ◽  
Road Traffic ◽  
Dynamic Stiffness ◽  
Design Stage ◽  
Element Analysis ◽  
Frequency Spectra ◽  
Dynamic Stiffness Matrix ◽  
Floor Vibrations

Buildings may experience excessive floor vibrations due to inner excitations such as walking people and running machines, or ground motion caused by the road traffic. Therefore, it is often necessary to evaluate the vibration level at the design stage. In this paper, a frequency domain-based model for predicting vertical vibrations of a building floor is provided, where the floor is simplified as a rectangular plate stiffened by beams in two orthogonal directions, while vertical motion and rotation of the slab–column joints are viewed as the unknown degrees of freedom. The dynamic stiffness matrix of the whole structure is obtained from those of the floor and column elements. To validate the proposed solution, a five-story building was analyzed, and frequency spectra were compared with those from the finite element method. Besides, a prototype building was analyzed and validated based on field measured data. It is found that the proposed solution could predict vibration responses with satisfactory accuracy, and is more computationally efficient than finite element analysis.

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.

Spectral Finite Element Formulation for Nanorods via Nonlocal Continuum Mechanics

2011 ◽  
Vol 78 (6) ◽  
Author(s):  
S. Narendar ◽  
S. Gopalakrishnan
Keyword(s):  
Finite Element ◽  
Continuum Mechanics ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Small Scale ◽  
Element Formulation ◽  
Shape Functions ◽  
Dynamic Stiffness Matrix ◽  
Exact Shape ◽  
Spectral Finite Element

In this article, the Eringen’s nonlocal elasticity theory has been incorporated into classical/local Bernoulli-Euler rod model to capture unique properties of the nanorods under the umbrella of continuum mechanics theory. The spectral finite element (SFE) formulation of nanorods is performed. SFE formulation is carried out and the exact shape functions (frequency dependent) and dynamic stiffness matrix are obtained as function of nonlocal scale parameter. It has been found that the small scale affects the exact shape functions and the elements of the dynamic stiffness matrix. The results presented in this paper can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave dispersion properties of carbon nanotubes.

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