I'm attempting to figure out how to organise the nonlinear stiffness matrices and entire solution technique utilising the generalised differential quadrature approach. Many research articles cite open literature, however, none of the researchers reveal how to organise nonlinear stiffness with linear stiffness.
You may follow this paper which specifically uses DQM and shows how the matrices are defined.
Nonlinear Free Vibration of Curved Double Walled Carbon Nanotubes Using Differential Quadrature Method | Request PDF (researchgate.net)
However, note that DQM may have convergence problems depending on how you treat the boundary conditions. All the approaches used for treating the BC will result in problems especially for higher modes due to nature of DQM. Therefore, I also suggest other methods for such cases.
Nonlinear free vibration of double walled carbon nanotubes by using describing function method with multiple trial functions | Request PDF (researchgate.net)
This paper is an example of such approach which uses Galerkin's method.
Thank you, Sir, for your response.
I will go through the research articles.
Ahmed Youssef Dear Sir,
Thank you for suggesting me this article to me. But this article is on the free vibration of nanobeams based on various nonlocal theories with an application of DQM.
On the other hand, I'd want to address the problem of nonlinear free vibration of the beam. So, for this, I'm searching for literature that will provide me with a clear grasp of how to deal with the nonlinear components that arise in the equation of motion, as well as the solution technique.