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How to define modal strain energy?

How to define modal strain energy?

How to define modal strain energy?

When we define modal strain energy, is it done separately for translational and rotational modal displacements?
I am looking on a paper where they use Modal Strain Energy Criterion in FEM crack detection in beams. They use an expression like: MSEij=1/2*PhiTij*Ki*Phiij, where:
PhiTij refers to vector corresponding mode shape of ith element in jth mode shape
Ki is the stiffness matrix of ith element

Moreover, I am interested in the dimension of the vector Phi. If we look at one 1D element where we neglect axial deformations, we have translational and rotational DOF, so Ki is 4by4. Is vector Phi 4by1? Should I separate modal displacements related to translational and rotational DOF, so at the end Phi would be 2by1? But then I cannot write the expression for MSE because the dimensions of matrices don't agree.

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