A New Consistent Mass Matrix for Timoshenko's Flexural Model

2009 ◽  
Author(s):  
J.E. Laier ◽  
C.C. Noronha
Keyword(s):  
Mass Matrix ◽  
Consistent Mass Matrix

scholarly journals Modeling Structural Dynamics Using FE-Meshfree QUAD4 Element with Radial-Polynomial Basis Functions

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2288
Author(s):  
Hongming Luo ◽  
Guanhua Sun
Keyword(s):  
Structural Dynamics ◽  
Interpolation Method ◽  
Mass Matrix ◽  
Time Integration ◽  
Partition Of Unity ◽  
Implicit Time ◽  
Lumped Mass ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Consistent Mass Matrix

The PU (partition-of-unity) based FE-RPIM QUAD4 (4-node quadrilateral) element was proposed for statics problems. In this element, hybrid shape functions are constructed through multiplying QUAD4 shape function with radial point interpolation method (RPIM). In the present work, the FE-RPIM QUAD4 element is further applied for structural dynamics. Numerical examples regarding to free and forced vibration analyses are presented. The numerical results show that: (1) If CMM (consistent mass matrix) is employed, the FE-RPIM QUAD4 element has better performance than QUAD4 element under both regular and distorted meshes; (2) The DLMM (diagonally lumped mass matrix) can supersede the CMM in the context of the FE-RPIM QUAD4 element even for the scheme of implicit time integration.

Consistent mass matrix in fluid sloshing problems

AIAA Journal ◽  
1976 ◽  
Vol 14 (2) ◽  
pp. 245-247 ◽  
Author(s):  
Grant P. Steven
Keyword(s):  
Mass Matrix ◽  
Fluid Sloshing ◽  
Consistent Mass Matrix

Finite Element Modeling of Dynamic Behavior of Some Basic Structural Members

1992 ◽  
Vol 114 (1) ◽  
pp. 3-9 ◽  
Author(s):  
R. C. Engels
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Finite Element Modeling ◽  
Mass Matrix ◽  
Matrix Approach ◽  
Structural Members ◽  
Shape Functions ◽  
Generalized Coordinates ◽  
Stiffness Matrices ◽  
Consistent Mass Matrix

A method is described to model the dynamics of finite elements. The assumed modes method is used to show how static shape functions approximate the element mass distribution. The deterioration of the modal content of a model can be linked to the neglect of interface restrained assumed modes. Restoration of a few of these modes leads to higher accuracy with fewer generalized coordinates compared to the standard consistent mass matrix approach. Also, no need exists for subdivision of basic elements such as rods and beams. The mass and stiffness matrices for several basic elements are derived and used in demonstration problems.

Finite Element Analysis of Vibrating Frequency for Skew Slab Bridge Based on Finite Strip Thought

2010 ◽  
Vol 163-167 ◽  
pp. 1121-1127
Author(s):  
Mei Liang Yang ◽  
Gui Yun Xia ◽  
Jian Ren Zhang
Keyword(s):  
Mass Matrix ◽  
Maximum Error ◽  
Euler Beam ◽  
Element Analysis ◽  
Finite Strip ◽  
System A ◽  
Specification Method ◽  
Mesh Density ◽  
Cartesian Coordinate ◽  
Consistent Mass Matrix

Based on the finite strip thought and displacement interpolation function of Bernoulli-Euler beam element, using the transformation relationship between skew coordinate and Cartesian coordinate system, a new kind of thin parallel slab element was established, element stiffness matrix and consistent mass matrix were derived. The vibrating frequency of simply supported skewed slab was calculated. Computing results were compared with theoretical results and Ansys results. The maximum error was 2.68%. Changing the mesh density of skew slab, the convergence of present element was tested. Examples show that this element has the features of high precision and strong convergence. At last, the vibrating frequency coefficients of skew slab bridge with different ratios of span to width were provided, which can be adopted to compute the vehicle’s impact factor of skew slab bridge by specification method.

Frequency-Dependent Element Mass Matrices

1992 ◽  
Vol 59 (1) ◽  
pp. 136-139 ◽  
Author(s):  
N. J. Fergusson ◽  
W. D. Pilkey
Keyword(s):  
Stiffness Matrix ◽  
Shape Function ◽  
Mass Matrix ◽  
Power Series Expansion ◽  
Shape Functions ◽  
Frequency Dependent ◽  
Mass Matrices ◽  
The Matrix ◽  
Matrix Expansion ◽  
Consistent Mass Matrix

This paper considers some of the theoretical aspects of the formulation of frequency-dependent structural matrices. Two types of mass matrices are examined, the consistent mass matrix found by integrating frequency-dependent shape functions, and the mixed mass matrix found by integrating a frequency-dependent shape function against a static shape function. The coefficients in the power series expansion for the consistent mass matrix are found to be determinable from those in the expansion for the mixed mass matrix by multiplication by the appropriate constant. Both of the mass matrices are related in a similar manner to the coefficients in the frequency-dependent stiffness matrix expansion. A formulation is derived which allows one to calculate, using a shape function truncated at a given order, the mass matrix expansion truncated at twice that order. That is the terms for either of the two mass matrix expansions of order 2n are shown to be expressible using shape functions terms of order n. Finally, the terms in the matrix expansions are given by formulas which depend only on the values of the shape function terms at the boundary.

A Strain Energy Comparison of Discrete Modeling for Vibrating Continuous Systems

1972 ◽  
Vol 94 (1) ◽  
pp. 23-30
Author(s):  
S. K. Tolani ◽  
R. D. Rocke
Keyword(s):  
Strain Energy ◽  
Mass Matrix ◽  
Free Vibrations ◽  
Continuous Systems ◽  
Euler Beam ◽  
Closed Form Solutions ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Vibration Problems ◽  
Consistent Mass Matrix

Lumped parameter models commonly used to describe continuous one-dimensional and Bernoulli-Euler beam vibration problems have been compared on the basis of maximum system strain energy. The consistent mass matrix approach has been included in the comparison. Standard matrix techniques have been employed to mathematically obtain desired solutions. Closed form solutions and solutions via the models to the system strain energy were obtained for all systems in three dynamic states: Free vibrations, constant base acceleration, and half sine base acceleration. Behavior of the strain energy errors, in general, were found to be similar to those of the frequency root errors.

scholarly journals Free vibration of prestress Timoshenko beams resting on elastic foundation

2007 ◽  
Vol 29 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Nguyen Dinh Kien
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Axial Force ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Element Formulation ◽  
Timoshenko Beams ◽  
Various Boundary Conditions ◽  
Consistent Mass Matrix

This paper presents a finite element formulation for investigating the free vibration of uniform Timoshenko beams resting on a Winkler-type elastic foundation and prestressing by axial force. Taking the effect of prestress, foundation support and shear deformation into account, a stiffness matrix for Timoshenko-type beam element is formulated using the energy method. The element consistent mass matrix is obtained from the kinetic energy using simple linear shape functions. Employing the formulated element, the natural frequencies of the beams having various boundary conditions are determined for different values of the axial force and foundation stiffness. The vibration Characteristics of the beams partially supported on the foundation are also studied and highlighted. Specially, the effects of shear deformation on the vibration frequencies of prestress beams fully and partially supported on the elastic foundation are investigated in detail.

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