# What are the state outputs from the Reduced Order Flexible Solid in Simulink?

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Zhengyou on 19 Apr 2024
Edited: Himanshu on 2 May 2024
I'm using the Reduced Order Flexible Solid in Simulink for my project. To put the question in a more general context, lets say I have n interfaces on the solid and I want to keep m fixed-interface modes then in total I have 6*n + m degrees of freedom. To reconstruct the full solution, I need to know the solutions of the 6*n interface dofs and the m fixed-interface modal dofs. The solutions of the 6*n dofs can be obtained easliy, but those of the m fixed-interface modal dofs can not.
I checked the state outputs from the Reduced Order Flexible Solid and there are 6*n+m-6 state outputs. My questions are:
1. What are the 6*n+m-6 states? Are they the non-rigid dofs?
2. If so, what eigenvalue analysis routine is used to obtain the rigid modes and the non-rigid modes,and more importantly how are the modes scaled?
Knowning the answers to the above questions would help me reconstruct the solutions of the m fixed-interface modal dofs.
Thank you very much!
Zheng-You Zhang

Himanshu on 2 May 2024
Edited: Himanshu on 2 May 2024
Hey Zhengyou,
As per my understanding, your queries revolve around the compostion of the (6n + m - 6) states and understanding the type of eigenvalue analysis used to distinguish between rigid and non-rigid modes within the context of Reduced Order Flexible Solid block inmulink.
State Outputs (6*n + m - 6):
The state outputs you've described as being 6*n + m - 6 in number represent the dynamic states of the system that are used to describe its motion fully, excluding the rigid body modes. Here's a breakdown:
• Rigid Body Modes: In a fully unconstrained body in 3D space, there are 6 rigid body modes (3 translational, 3 rotational), which do not contribute to the deformation of the body. These modes are typically not included in the reduced-order model since they do not represent deformations.
• Non-Rigid Modes: The remaining modes (both from the interface DOFs and the fixed-interface modal DOFs) represent the deformable behavior of the solid. These are the modes of interest when analyzing vibrations and deformations.
Eigenvalue Analysis:
• Routine Used: The specific eigenvalue analysis routine used can vary based on the software implementation and the options selected by the user. Common routines involve solving the generalized eigenvalue problem derived from the solid's mass and stiffness matrices.
• Rigid vs. Non-Rigid Modes: The eigenvalue analysis separates out the rigid body modes (associated with zero or near-zero eigenvalues) from the non-rigid (elastic deformation) modes. The rigid body modes are typically not of interest in a reduced-order model focused on deformation analysis.
• Mode Scaling: The modes can be scaled in various ways, often normalized to have a unit modal mass or to ensure the mode shapes have a certain magnitude at a specific point. The scaling is crucial for interpreting the mode shapes and for subsequent analysis, such as modal superposition.
Hope this helps!