Our research is turing to nonlinear vibrations of plates and solids of acosutic wave device strcutures. It is high frequency vibration, and associated phononmena can only be considered with nonlinear analysis.
Please share your experiences and publications on nonlinear Rayleigh-Ritz method with us.
Joint work on the problem is possible for co-authored publications.
Dear Ji Wang,
Very interesting method!
I didn't use this method, but I know that the that Ritz–Rayleigh approach offering several significant benefits over commonly used matrix methods. This approach widely used for calculation of guided and surface waves propagating in an arbitrary direction through a thin structure or half-space of any symmetry class.
The most important advantage of the Ritz–Rayleigh method is the transformation of the problem into an eigenvalue problem through a specifically tailored functional basis, like the Legendre polynomial method.
Dear professor Ji Wang
RR method can be used vastly when it is difficult to obtain analytical solution. One of the key benefits of this approach is its capability to be used for variety of boundary conditions.
For the nonlinear vibration it is used to transfer the space-time problem to the time problem. I mean, after applying this method the vibration problem converts to the a 1dof system, which is just time-dependent (mD[X,2]+cD[X,1]+kX=f). now you can implement a variety of methods for this current problem, namely, multiple scale, straight forward expansion, harmonic balance, etc.
Hope it helps
All the best
Mahdi
Very interesting topic Ji Wang , but if I may ask: what is it that you're really after?
Do you want to design a novel experimental equipment? Do you want to analyse an existing setup?
R-R is a method and is applicable to a very large class of engineering problems involving eigen-values (e.g. natural frequencies) and eigen-functions (e.g. mode forms).
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