v1.01.338 ZZZZ338 - Validation of the frequency band balancing algorithm

Summary:

This test aims to verify the correct functioning of the frequency band balancing algorithm. of the DEFI_LIST_FREQ operator (EQUI_MODES keyword).

The problem considered in this test consists of an eigenvalue problem. generalized real symmetric standard, with natural frequencies \(f_1 \le \dots \le f_n\). The stiffness and mass matrices for this problem do not match a physical model, but are constructed in such a way as to obtain the natural frequencies \(f_1,\dots,f_n\). To do this, we consider a model composed of \(n\) meshes of type POI1 (modeling DIS_T), whose degrees of freedom DY and DZ are blocked, and whose elementary characteristics are defined so that the assembled stiffness matrix restricted to the degrees of freedom DX is diagonal, of \(2\pi f_1, \dots, 2\pi f_n\) values. Likewise, the associated mass matrix is equal to the identity matrix.

The frequency band balancing algorithm is then used in order to test two cases, namely:

• the case of the specification at the input of the frequency list \(f_1,\dots,f_n\) (« TYPE_SAISIE = “LISTE “``),

• the case of the input specification of assembled stiffness and mass matrices (« TYPE_SAISIE = “MATR_ASSE “ »).

The tested results consist of the frequency bands obtained after balancing, in the two cases mentioned above. In particular, it is verified that the errors in the number of modes per desired band are less than the tolerance in question. It is also verified that the results obtained via a list of input frequencies and via the assembled matrices. are the same.

This documentation is deliberately brief.