Free and forced vibration analysis using the smoothed finite element method (SFEM)

2007 ◽  
Vol 301 (3-5) ◽  
pp. 803-820 ◽  
Author(s):  
K.Y. Dai ◽  
G.R. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Smoothed Finite Element Method ◽  
Forced Vibration Analysis ◽  
Element Method

scholarly journals Forced Vibration Analysis of Laminated Composite Shells Reinforced with Graphene Nanoplatelets Using Finite Element Method

2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Trung Thanh Tran ◽  
Van Ke Tran ◽  
Pham Binh Le ◽  
Van Minh Phung ◽  
Van Thom Do ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Thermal Environments ◽  
Forced Vibration Analysis ◽  
Laminated Composite Shells ◽  
Element Method

This paper carries out forced vibration analysis of graphene nanoplatelet-reinforced composite laminated shells in thermal environments by employing the finite element method (FEM). Material properties including elastic modulus, specific gravity, and Poisson’s ratio are determined according to the Halpin–Tsai model. The first-order shear deformation theory (FSDT), which is based on the 8-node isoparametric element to establish the oscillation equation of shell structure, is employed in this work. We then code the computing program in the MATLAB application and examine the verification of convergence rate and reliability of the program by comparing the data of present work with those of other exact solutions. The effects of both geometric parameters and mechanical properties of materials on the forced vibration of the structure are investigated.

FREE AND FORCED VIBRATION ANALYSIS USING THE n-SIDED POLYGONAL CELL-BASED SMOOTHED FINITE ELEMENT METHOD (nCS-FEM)

2013 ◽  
Vol 10 (01) ◽  
pp. 1340008 ◽  
Author(s):  
T. NGUYEN-THOI ◽  
P. PHUNG-VAN ◽  
T. RABCZUK ◽  
H. NGUYEN-XUAN ◽  
C. LE-VAN
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Forced Vibration ◽  
Solid Mechanics ◽  
Mass Matrix ◽  
Elastic Solid ◽  
Polygonal Cell ◽  
Smoothed Finite Element Method ◽  
Forced Vibration Analysis ◽  
Element Method

A n-sided polygonal cell-based smoothed finite element method (nCS-FEM) was recently proposed to analyze the elastic solid mechanics problems, in which the problem domain can be discretized by a set of polygons with an arbitrary number of sides. In this paper, the nCS-FEM is further extended to the free and forced vibration analyses of two-dimensional (2D) dynamic problems. A simple lump mass matrix is proposed and hence the complicated integrations related to computing the consistent mass matrix can be avoided in the nCS-FEM. Several numerical examples are investigated and the results found of the nCS-FEM agree well with exact solutions and with those of others FEM.

scholarly journals Free and Forced Vibration Analysis in Abaqus Based on the Polygonal Scaled Boundary Finite Element Method

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Nan Ye ◽  
Chao Su ◽  
Yang Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Forced Vibration ◽  
Eigenvalue Decomposition ◽  
Benchmark Problems ◽  
Polygonal Mesh ◽  
Finite Element Software ◽  
Forced Vibration Analysis ◽  
Scaled Boundary Finite Element ◽  
Element Method

The polygonal scaled boundary finite element method (PSBFEM) is a novel approach integrating the standard scaled boundary finite element method and the polygonal mesh technique. In this work, a user-defined element (UEL) for dynamic analysis based on the PSBFEM is developed in the general finite element software ABAQUS. We present the main procedures of interacting with Abaqus, updating AMATRX and RHS, defining the UEL element, and solving the stiffness and mass matrices through eigenvalue decomposition. Several benchmark problems of free and forced vibration are solved to validate the proposed implementation. The results show that the PSBFEM is more accurate than the FEM with mesh refinement. Moreover, the PSBFEM avoids the occurrence of hanging nodes by constructing a polygonal mesh. Thus, the PSBFEM can choose an appropriate mesh resolution for different structures ensuring accuracy and reducing calculation costs.

Torsional Vibration of a Damped Shaft System Using the Analytical-and-Numerical-Combined Method

2001 ◽  
Vol 38 (04) ◽  
pp. 250-260
Author(s):  
Jong-Shyong Wu ◽  
Mang Hsieh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Torsional Vibration ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Combined Method ◽  
Rotating Shaft ◽  
Shaft System ◽  
Element Method

Torsional vibration analysis of the propulsive shaft system of a marine engine—one of the most important tasks in preliminary ship design—is carried out today by either the Holzer method, the transfer matrix method (TMM), or the finite-element method (FEM). Of the three methods, Holzer is the most popular and is adopted by shipyards worldwide. The purpose of this paper is to present an analytical-and-numerical-combined method (ANCM) to improve the drawbacks of existing methods. In comparison with the Holzer method (or TMM), the presented ANCM has the following merits: the mass of the rotating shaft is inherently considered, the damping effect is easily tackled, and the forced vibration responses due to various external excitations are obtained with no difficulty. Since the order of the overall property matrices for the equations of motion derived from the ANCM is usually lower than that derived from the conventional finite-element method (FEM), the CPU time required by the former is usually less than that required by the latter, particularly in the forced vibration analysis. Besides, the sizes (and the total number) of the elements for the FEM have a close relationship with the locations of the disks and the dampers and so does the accuracy of the FEM, but various distributions (or locations) of the disks and the dampers will not create any problems for the ANCM.

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