Dynamic Responses of Beam With Sloping Support Traversed by a Moving Mass

2010 ◽  
Author(s):  
Guolai Yang ◽  
James Yang ◽  
Chen Qiang ◽  
Jianli Ge ◽  
Qiang Chen
Keyword(s):  
Structural Design ◽  
Stiffness Matrix ◽  
Mass Matrix ◽  
Inertial Force ◽  
Variable Cross Section ◽  
Dynamic Responses ◽  
Moving Mass ◽  
Variable Cross ◽  
Matrix Stiffness ◽  
Damping Matrix

This paper contributes to investigation on vibration analysis for cradle subjected to the moving barrel. The tipping part of the gun is simplified by a beam with sloping support traversed by a moving mass. The cradle structure is modeled by Euler-Bernoulli variable cross-section beam and the elevating strut is modeled by elastic supporting rod. The beam and supporting rod are discretized into finite elements, and then the main mass matrix, stiffness matrix, and damping matrix can be formulated. Gravity and inertial force are described by external nodal load vectors. The time-varying additional mass matrix, stiffness matrix, and damping matrix are derived. Numerical computation is conducted to analyze the effect of the barrel velocity on dynamic response of system, which can provide theoretical foundation to structural design of such system.

scholarly journals Solution of discrete oscillating system on personal computer

1993 ◽  
Vol 15 (2) ◽  
pp. 37-41
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Methods ◽  
Personal Computer ◽  
Stiffness Matrix ◽  
Discrete System ◽  
Mass Matrix ◽  
Equation Of Motion ◽  
Parameters Optimization ◽  
Personal Computers ◽  
Matrix Stiffness ◽  
Damping Matrix

The article is devoted an algorithm for deriving mass matrix, stiffness matrix and damping matrix for oscillating discrete system. The algorithm is common setting equation of motion. This technique enables solving different problems of oscillating system, especially a problem of parameters optimization, by numerical methods. Comparison of different methods realized on personal computers was done.

Study on Kinetic Energy for Saving Materials with Analysis of Lumped Mass Matrix of Variable Cross-Section Beam Element

2013 ◽  
Vol 675 ◽  
pp. 158-161
Author(s):  
Lv Zhou Ma ◽  
Jian Liu ◽  
Yu Qin Yan ◽  
Xun Lin Diao
Keyword(s):  
Kinetic Energy ◽  
Cross Section ◽  
Mass Matrix ◽  
Nonlinear Problems ◽  
Variable Cross Section ◽  
Beam Element ◽  
Variable Cross ◽  
Lumped Mass ◽  
Geometrical Nonlinear ◽  
Properties Of Materials

Based on positional finite element method (FEM), a new, simple and accurate lumped mass matrix to solve dynamic geometrical nonlinear problems of materials applied to variable cross-section beam element has been proposed. According to Hamilton theory and the concept of Kinetic energy, concentrate the beam element mass to the two nodes in certain proportion, the lumped mass matrix is deduced. The lumped mass matrix is diagonal matrix and its calculated quantity is less than using consistent mass matrix about properties of materials under the same calculation precision.

Reckoning for Element Characteristics Matrix of Space Timoshenko-Beam Based on Energy Variational Principle

2011 ◽  
Vol 66-68 ◽  
pp. 1356-1361
Author(s):  
Wen Jun Pan ◽  
Zhi Wu Wei
Keyword(s):  
Variational Principle ◽  
Timoshenko Beam ◽  
Stiffness Matrix ◽  
Mass Matrix ◽  
Research Work ◽  
Energy Functional ◽  
Displacement Function ◽  
Matrix Stiffness ◽  
Stiffness Matrices

To analyze and calculate the element characteristics matrices of space Timoshenko-beam, research work were carried out on the basis of energy variational principle. Displacement function for the space Timoshenko-beam were put forward, the expressions for element mass matrix, stiffness matrix and load array were deduced by energy functional extremum, and the explicit forms of element mass and stiffness matrices were integrated finally. Results show that the element mass and stiffness matrices computed by this method are consistent with those in related references. It has a good theoretical and practical value in the calculation for characteristics matrices of other elements.

Study on Flexible Spin-Up Maneuver with Variable Cross-Section Based on Positional FEM

2014 ◽  
Vol 670-671 ◽  
pp. 834-837
Author(s):  
Lv Zhou Ma ◽  
Yu Qin Yan ◽  
Xun Lin Diao ◽  
Jian Liu
Keyword(s):  
Cross Section ◽  
Mass Matrix ◽  
Variable Cross Section ◽  
Beam Element ◽  
Variable Cross ◽  
Lumped Mass ◽  
Nonlinear Fem ◽  
Calculation Results ◽  
Properties Of Materials ◽  
Consistent Mass Matrix

Based on positional finite element method (FEM) and MATLAB platform, program VBEP (Variable cross-section Beam Element based on Positional FEM) is compiled. Flexible spin-up maneuver is calculated. The calculation results show that positional FEM uses fewer elements and gains higher calculation precision and efficiency when compared with traditional nonlinear FEM, and that calculated quantity using lumped mass matrix is less than using consistent mass matrix about properties of materials under the same calculation precision.

scholarly journals Static, Vibration, and Transient Dynamic Analyses by Beam Element with Adaptive Displacement Interpolation Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-25
Author(s):  
Shuang Li ◽  
Jinjun Hu ◽  
Changhai Zhai ◽  
Lili Xie
Keyword(s):  
Cross Section ◽  
Material Properties ◽  
Polynomial Interpolation ◽  
Mass Matrix ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Lumped Mass ◽  
Beam Elements ◽  
Dynamic Analyses ◽  
Interpolation Functions

An approach to analyzing structures by using beam elements is developed with adaptive displacement interpolation functions. First, the element stiffness matrix and equivalent nodal loads are derived on the basis of the equilibrium between nodal forces and section forces rather than the compatibility between nodal deformations and section deformations, which avoids discretization errors caused by the limitation of conventional polynomial interpolation functions. Then, six adaptive element displacement interpolation functions are derived and extended to include several cases, such as beams with variable cross-section, variable material properties, and many different steps in cross-section and/or material properties. To make the element usable in dynamic analyses, consistent mass matrix (CMM) and diagonally lumped mass matrix (LMM) are constructed using the presented adaptive displacement interpolation functions. All these features have made the element elegant, which is tested with a number of simple static, vibration, and dynamic examples to show its accuracy.

scholarly journals Dynamic Analysis of a Timoshenko Beam Subjected to an Accelerating Mass Using Spectral Element Method

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Guangsong Chen ◽  
Linfang Qian ◽  
Qiang Yin
Keyword(s):  
Timoshenko Beam ◽  
Spectral Element Method ◽  
Mass Matrix ◽  
Tangential Force ◽  
Inertial Force ◽  
Spectral Element ◽  
Dynamic Responses ◽  
Mass System ◽  
Integration Rule ◽  
Element Method

This paper presents formulations for a Timoshenko beam subjected to an accelerating mass using spectral element method in time domain (TSEM). Vertical displacement and bending rotation of the beam were interpolated by Lagrange polynomials supported on the Gauss-Lobatto-Legendre (GLL) points. By using GLL integration rule, the mass matrix was diagonal and the dynamic responses can be obtained efficiently and accurately. The results were compared with those obtained in the literature to verify the correctness. The variation of the vibration frequencies of the Timoshenko and moving mass system was researched. The effects of inertial force, centrifugal force, Coriolis force, and tangential force on a Timoshenko beam subjected to an accelerating mass were investigated.

Dynamical Stress Distribution Analysis of a Non-Uniform Cross-Section Beam Under Moving Mass

2006 ◽  
Author(s):  
M. T. Ahmadian ◽  
E. Esmailzadeh ◽  
M. Asgari
Keyword(s):  
Stress Distribution ◽  
Cross Section ◽  
Natural Frequencies ◽  
Moving Load ◽  
Variable Cross Section ◽  
Moving Mass ◽  
Variable Cross ◽  
Distribution Analysis ◽  
Concentrated Force ◽  
Direct Integration Method

One of the engineers concern in designing bridges and structures under moving load is the uniformity of stress distribution. In this paper the analysis of a variable cross-section beam subjected to a moving concentrated force and mass is investigated. Finite element method with cubic Hermitian interpolation functions is used to model the structure based on Euler-Bernoulli beam and Wilson-Θ direct integration method is implemented to solve time dependent equations. Effects of cross-section area variation, boundary conditions, and moving mass inertia on the deflection, natural frequencies and longitudinal stresses of beam are investigated. Results indicates using a beam of parabolically varying thickness with constant mass can decrease maximum deflection and stresses along the beam while increasing natural frequencies of the beam. The effect of moving mass inertia of moving load is found to be significant at high velocity.

KED Modeling of PLS Mechanism

2012 ◽  
Vol 268-270 ◽  
pp. 1319-1326 ◽  
Author(s):  
Yong Peng ◽  
Xiao Xu Bai
Keyword(s):  
Time Domain ◽  
Stiffness Matrix ◽  
Mass Matrix ◽  
Mechanical Vibration ◽  
Beam Element ◽  
Matrix Versus ◽  
Damping Matrix ◽  
Lagrange’S Equation ◽  
The Time Domain ◽  
Final System

For the super-size and large flexibility of Pipe Lay-down System, considering the influence on the mechanism from elastic deformation and mechanical vibration during the movements, the kineto-elastodynamics model is established by using the KED theory which is based on the analysis of kinematics. The PLS mechanism is divided into several finite elements. Dynamic equations of beam element are established in the local coordinate by using Lagrange’s equation. In the process of changing from local coordinate into global coordinate, no longer considering the instantaneous structure assumes. In consideration of the first and second derivative of the coordinate transformation matrix versus time are not zero. The mass matrix, damping matrix and stiffness matrix of the final system kinematic differential equation are the function of time. It realizes the continuity of variable in the time domain. Derivation of the results in this paper lays a foundation for the next more accurate and efficient methods being applied to solve the KED equation of PLS mechanism.

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