Static analysis of thin-walled space frame structures with arbitrary closed cross-sections using transfer matrix method

2018 ◽  
Vol 123 ◽  
pp. 255-269 ◽  
Author(s):  
Haolong Zhong ◽  
Zijian Liu ◽  
Huan Qin ◽  
Yu Liu
Keyword(s):  
Static Analysis ◽  
Transfer Matrix ◽  
Cross Sections ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Frame Structures ◽  
Space Frame ◽  
Thin Walled

Extension of the Transfer Matrix Method for Rotordynamic Analysis to Include a Direct Representation of Conical Sections and Trunnions

1980 ◽  
Vol 102 (1) ◽  
pp. 122-129 ◽  
Author(s):  
M. S. Darlow ◽  
B. T. Murphy ◽  
J. A. Elder ◽  
G. N. Sandor
Keyword(s):  
Transfer Matrix ◽  
Cross Sections ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Critical Speed ◽  
Axial Direction ◽  
Matrix Analysis ◽  
Beam Elements ◽  
Conical Section ◽  
Rotor Model

The transfer matrix method for rotordynamic analysis (alternately known as the HMP or LMP method) has enjoyed wide popularity due to its flexibility and ease of application. A number of computer programs are generally available which use this method in various forms to perform undamped critical speed, unbalance response, damped critical speed and stability analyses. For all of these analyses, the assembly of the transfer matrices from the rotor model is essentially the same. In all cases, the rotor model must be composed entirely of cylindrical beam elements. There are two situations when this limitation is not desirable. The first situation is when the rotor being modelled has one or more sections whose cross sections vary continually in the axial direction. The most common of these sections is the conical section. Presently, a conical section must be modelled as a series of “steps” of cylindrical sections. This adversely affects both the simplicity and accuracy of the rotor model. The second situation when current transfer matrix techniques are not accurate is when the rotor being modelled has one or more sections that do not behave as beam elements. The most common example is a trunnion which behaves as a plate. This paper describes the analytical basis and the method of application for direct representation of conical sections and trunnions for a transfer matrix analysis. Analytical results are currently being generated to demonstrate the need for and advantages of these modelling procedures.

Simplified Calculation of the Eccentric Press Stiffness

2014 ◽  
Vol 613 ◽  
pp. 402-407
Author(s):  
Peter Demeč ◽  
Dominika Palaščáková
Keyword(s):  
Transfer Matrix ◽  
Cross Sections ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Mechanical Systems ◽  
Matrix Form ◽  
Entire Length ◽  
The Press ◽  
The Cross ◽  
Simplified Calculation

The article deals with the simplified calculation of the stiffness of the eccentric press frame. The described method applies to the solving of problem a mathematical identification of condition parameters in the press frame the transfer matrix method (TMM), which is in essence a matrix form of initial parameters method. This method is suitable for mechanical systems with continuously distributed mass in space while the cross-sections along the entire length of the system are not constant.

Free vibration analysis of axial-loaded beams with variable cross sections and multiple concentrated elements

2021 ◽  
pp. 107754632110128
Author(s):  
Yunxing Du ◽  
Peng Cheng ◽  
Fen Zhou
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Cross Sections ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Free Vibration Analysis ◽  
Frequency Equation ◽  
Variable Cross ◽  
Bending Vibrations ◽  
Euler Bernoulli Beam

A transfer matrix method is used to study free vibration characteristics of an axial-loaded Euler–Bernoulli beam with variable cross sections and multiple concentrated elements in the article. The differential equation for bending vibrations of the beam element is solved by the Frobenius method, and the solution is in power series form. Then, the transfer matrix method is applied to establish the state vector equation for both ends of the beam. Combined with boundary conditions, the frequency equation is obtained and expressed in a two-order determinant. The numerical results in this article are compared with those of the finite element method, which illustrates the accuracy of the method we proposed. The influence of the size of each concentrated elements and axial force on the natural frequency coefficients and the influence of the concentrated elements on the first critical buckling load are discussed.

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