Rotating Blade Modal Analysis Model -- 2
Budget: ₹1,500 – ₹12,500 INR
I have derived the governing equations for a rotating, pre-twisted blade treated as a thin shallow shell and now need a full modal vibration study. The formulation already includes the complete mass matrix, the gyroscopic matrix, and separate stiffness contributions for the structural shell, centrifugal stiffening, rotational softening, and an elastic root represented by spring constants. Thickness varies along the span, so any solution must respect the taper, the twist, and the elastic root support while the tip remains free.
Your task is to compute the natural frequencies and mode shapes across a practical range of rotational speeds, capturing the combined influence of centrifugal force, Coriolis coupling, and rotational stiffening. Please work directly from the matrix form I provide, or recreate it in the tool you prefer (MATLAB, Python/Numpy-SciPy, ANSYS APDL, or comparable). Numerical stability and correct treatment of the gyroscopic terms are essential; results should clearly show how the modes split or couple as speed increases.
Deliverables
• Clean, well-commented code or solver input deck that assembles M, G, and the individual stiffness matrices and solves the resulting eigenproblem.
• A concise technical note (PDF or DOCX) listing assumptions, numerical settings, convergence checks, and plotted Campbell diagrams of frequency versus speed.
• Visualisation of at least the first six mode shapes (figures or animations).
• Brief guidance on how I can vary spring stiffness at the root and re-run the study.
I will supply geometry parameters, material data, and the baseline stiffness values once we start.
Your task is to compute the natural frequencies and mode shapes across a practical range of rotational speeds, capturing the combined influence of centrifugal force, Coriolis coupling, and rotational stiffening. Please work directly from the matrix form I provide, or recreate it in the tool you prefer (MATLAB, Python/Numpy-SciPy, ANSYS APDL, or comparable). Numerical stability and correct treatment of the gyroscopic terms are essential; results should clearly show how the modes split or couple as speed increases.
Deliverables
• Clean, well-commented code or solver input deck that assembles M, G, and the individual stiffness matrices and solves the resulting eigenproblem.
• A concise technical note (PDF or DOCX) listing assumptions, numerical settings, convergence checks, and plotted Campbell diagrams of frequency versus speed.
• Visualisation of at least the first six mode shapes (figures or animations).
• Brief guidance on how I can vary spring stiffness at the root and re-run the study.
I will supply geometry parameters, material data, and the baseline stiffness values once we start.