Dynamic-stiffness matrix of unbounded soil by finite-element multi-cell cloning

1994 ◽  
Vol 31 (4) ◽  
pp. 191
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Cell Cloning ◽  
Dynamic Stiffness Matrix

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.

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.

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.

The Dynamic Stiffness Method for Linear Rotor-Bearing Systems

1996 ◽  
Vol 118 (3) ◽  
pp. 332-339 ◽  
Author(s):  
F. A. Raffa ◽  
F. Vatta
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Matrix Analysis ◽  
Theoretical Formulation ◽  
Dynamic Stiffness Matrix ◽  
Rotor Systems ◽  
Stiffness Method ◽  
Dynamic Stiffness Method ◽  
Rotor Bearing

The behavior of linear rotor-bearing systems is investigated by using the exact approach of the dynamic stiffness method, which entails the use of continuous rather than lumped models. In particular, the theoretical formulation for rotor systems with anisotropic bearings is developed by utilizing the complex representation of all the involved variables. The proposed formulation eventually leads to the 8 × 8 complex dynamic stiffness matrix of the rotating Timoshenko beam; this matrix proves to be related, by a simple rule, to the 4 × 4 dynamic stiffness matrix, which describes rotor systems with isotropic bearings. The method is first applied to the critical speeds evaluation of a simple rotor system with rigid supports; for this case, the exact results of the dynamic stiffness approach are compared to the usual convergence procedure of the finite element method. Successively, the steady-state unbalance response of two rotor systems with anisotropic supports is analyzed; for these examples, the dynamic stiffness results compare favorably with the results of the finite element and the transfer matrix analysis performed by other authors.

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.

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