CAE Fidesys 9.0 Documentation

Damping

The damping matrix [C] in the most general form has the form:

where α is a constant multiplier to the mass matrix,

β is a constant multiplier to the stiffness matrix,

β_j is a constant factor to the stiffness matrix, depending on the material,

β_c is a variable multiplier to the stiffness matrix (applicable in harmonic analysis, used to ensure the constancy of the degree of damping ζ, regardless of the frequency ω):

where ζ is the constant damping ratio. According to the presented expression, ζ must be equal to n/2.

where n is the loss factor;

f is the frequency, in harmonic analysis it varies in the interval from the initial (f_b) to the final (f_e).

[C_ζ]- frequency-dependent damping matrix; [C_ζ] can be expressed in terms of ζ_r - the degree of damping for the rth own fashion, but never calculated explicitly.

ζ - constant degree of damping

[C_k] is the damping matrix of the kth element (N_ele - the number of elements having their own damping matrix).

In Fidesys, the damping matrix [C] in the most general form has the form (Fidesys Theory Reference):

where α is α - damping of the mass matrix;

β - damping of the stiffness matrix;

ξ - structural damping;

α_j^m is the damping coefficient of the mass matrix material;

β_j^m is the damping coefficient of the stiffness matrix j-th material;

ξ_j^m - structural damping of the j-th material;

C_k - element damping matrix;

N_m - the number of materials with a given damping;

N_e - the number of elements with the specified damping.