Determination of the Boundary Conditions for String Fastening Using Natural Vibration Frequencies in a Medium with a Variable Asymmetric Elasticity Coefficient

2018 ◽  
Vol 59 (4) ◽  
pp. 755-761
Author(s):  
I. M. Utyashev ◽  
A. M. Akhtyamov
2013 ◽  
Vol 57 ◽  
pp. 343-352 ◽  
Author(s):  
Vadims Goremikins ◽  
Karlis Rocens ◽  
Dmitrijs Serdjuks ◽  
Janis Sliseris

2021 ◽  
Vol 11 (4) ◽  
pp. 1482
Author(s):  
Róbert Huňady ◽  
Pavol Lengvarský ◽  
Peter Pavelka ◽  
Adam Kaľavský ◽  
Jakub Mlotek

The paper deals with methods of equivalence of boundary conditions in finite element models that are based on finite element model updating technique. The proposed methods are based on the determination of the stiffness parameters in the section plate or region, where the boundary condition or the removed part of the model is replaced by the bushing connector. Two methods for determining its elastic properties are described. In the first case, the stiffness coefficients are determined by a series of static finite element analyses that are used to obtain the response of the removed part to the six basic types of loads. The second method is a combination of experimental and numerical approaches. The natural frequencies obtained by the measurement are used in finite element (FE) optimization, in which the response of the model is tuned by changing the stiffness coefficients of the bushing. Both methods provide a good estimate of the stiffness at the region where the model is replaced by an equivalent boundary condition. This increases the accuracy of the numerical model and also saves computational time and capacity due to element reduction.


2007 ◽  
Vol 24 (4) ◽  
pp. 1074 ◽  
Author(s):  
Norbert Kerwien ◽  
Thomas Schuster ◽  
Stephan Rafler ◽  
Wolfgang Osten ◽  
Michael Totzeck

The problem involves the determination of a biharmonic generalized plane-stress function satisfying certain boundary conditions. We expand the stress function in a series of non-orthogonal eigenfunctions. Each of these is expanded in a series of orthogonal functions which satisfy a certain fourth-order ordinary differential equation and the boundary conditions implied by the fact that the sides are stress-free. By this method the coefficients involved in the biharmonic stress function corresponding to any arbitrary combination of stress on the end can be obtained directly from two numerical matrices published here The method is illustrated by four examples which cast light on the application of St Venant’s principle to the strip. In a further paper by one of the authors, the method will be applied to the problem of the finite rectangle.


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