Modal Analysis

Modal analysis computes a structure’s natural frequencies and mode shapes. Pynite provides the FEModel3D.analyze_modal() method which assembles the global stiffness and mass matrices, solves the generalized eigenvalue problem, and stores the resulting mode shapes as displacement results in modal load combinations.

How it works

• Assembles the global elastic stiffness matrix [Ke] and mass matrix [M] using the specified mass_combo_name and mass_direction.

• Partitions out supported degrees of freedom before solving to avoid singularities.

• Solves the generalized eigenproblem [Ke]{φ} = λ[M]{φ} where λ = ω². Frequencies are returned in Hz as f = ω / (2π).

• Mode shapes (eigenvectors) are expanded back into the model’s full DOF set and stored in load combinations named Mode 1, Mode 2, etc.

Usage

analyze_modal signature

FEModel3D.analyze_modal(num_modes: int = 12, mass_combo_name: str = 'Combo 1', mass_direction: str = 'Y', gravity: float = 1.0, log=False, check_stability=True)

Parameters

• num_modes: Number of modes to calculate (default: 12).

• mass_combo_name: Name of the load combination used to convert loads to masses. Defaults to 'Combo 1'. If no load combos exist, a default is created automatically.

• mass_direction: Direction to use when converting loads to equivalent mass ('X', 'Y', or 'Z'). Loads applied in this direction will be treated as masses (default: 'Y').

• gravity: Acceleration used when converting loads to mass (default: 1.0).

• log: If True, prints progress messages to the console.

• check_stability: If True, checks the stiffness matrix for unsupported DOFs and will raise an exception if instabilities are found.

Requirements and notes

• SciPy is required for modal analysis. The method uses SciPy’s sparse eigen-solver internally; if SciPy is not installed the method will raise an exception.

• The solver filters modes by solving for a limited number of eigenpairs. Increase num_modes if additional modes are required.

• Ensure materials have density (rho) and/or a suitable mass_combo_name with applied loads so that a nonzero mass matrix is assembled. An exception will be raised if no mass terms are found.

Example

Create a simple model, add mass-producing loads (or define material densities), and run modal analysis:

from Pynite.FEModel3D import FEModel3D

model = FEModel3D()
# add nodes, members, materials, etc.
# ensure material densities or a load combo exists to create mass terms
freqs = model.analyze_modal(num_modes=6, mass_direction='Y', gravity=9.81, log=True)

The returned value is a list (NumPy array) of frequencies in Hz and the mode displacement results are stored in load combinations named Mode 1, Mode 2, etc.

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