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Effective Mass by Part

This allows for a breakdown of the effective mass of the structure by part where the parts are defined by element lists.

The effective mass for mode i in direction j is defined as

m~ij=({φiT}[m]{uij})2m^\tilde{m}_{ij} = \frac{\left(\left\{\varphi_i^T\right\}[m]\left\{u_{ij}\right\}\right)^2}{\hat{m}}

This gives information about the mass mobilised in a particular direction for a particular mode, but gives no indication as to which part of the structure this is associated with. The effective mass by part modifies this equation to work for the elements, k, in the list so that

m~ij,part=(∑k({φikT}[mk]{ujk}))2m^\tilde{m}_{ij,part} = \frac{\left(\displaystyle\sum_k\left(\left\{\varphi_{ik}^T\right\}[m_k]\left\{u_{jk}\right\}\right)\right)^2}{\hat{m}}

Normally we are interested in the summation over all the modes so we arrive at this value by summing the modal participation factors to report

m~j,part−sum=∑im~ij.part\tilde{m}_{j,part-sum}=\sum_i \tilde{m}_{ij.part}

Definition​

Parts

These are the lists of elements that are to be considered that are to be considered.

Analysis Task

This is the dynamic analysis (modal or Ritz) for which the effective masses are to be calculated.

Target Value

Most seismic code require that a target percentage of the mass is recovered. Values that do not meet the target will be highlighted. This can be compared with either total mass or unrestrained mass.

Include Modal Details

By default only the summation of the effective masses over the modes is reported but mode by mode results can be provided if required.