A beam on elastic foundation is fully described in "Continuous Vibration" by Rao. In the attached article by Chang-New Chen, there are a number of test cases. In this paper, only one beam "simply support" is compared with exact solution.
The other test cases including fixed-fixed beam and cantilever are not compared with exact solution.
Does anyone know that vibration of a beam on elastic foundation have exact solution for various type of boundary condition?
It depends on what foundation model you are going to use, e.g, if you use Winkle's model, you can have exact solutions.
Many thanks dear Jianqiao Ye. Does a beam on Winkler foundation have exact solution for fixed-fixed beam, cantilever, simply support ,...
Many thanks for your time and patience.
would please kindly address the web link for some typical boundary conditions for beam on a Winkler foundation?
is there anyone who can kindly provide me with some references about beam on Winkler foundation with boundary conditions such as : fixed-fixed, fixed-free, simply support at both ends.
Many thanks in advance.
in Journal of Sound and Vibration you may find a lot
http://www.sciencedirect.com/science?_ob=ArticleListURL&_method=list&_ArticleListID=-514339532&_sort=r&_st=13&view=c&_acct=C000228598&_version=1&_urlVersion=0&_userid=10&md5=207112c322f1882dbc0fea10781460b1&searchtype=a
Here it is the exact solution (dynamic stiffness matrix) for a Timoshenko beam-column with generalized end conditions resting on a two parameter elastic foundation:
https://www.researchgate.net/publication/229433274_Dynamic_Stiffness_Matrix_and_Load_Vector_of_Timoshenko_Beam-Column_with_Generalized_End_Conditions?ev=prf_pub
Article Dynamic Stiffness Matrix and Load Vector of Timoshenko Beam-...
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