In a transient dynamic analysis, damping represents the dissipation of energy in the structural system. It also retards the response of the structural system.
CivilFEM allows entering two types of damping in a transient dynamic analysis: modal damping and Rayleigh damping.
During time integration, CivilFEM associates the corresponding damping fraction with each mode. The program bases integration on the usual assumption that the damping matrix of the system is a linear combination of the mass and stiffness matrices, so that damping does not change the modes of the system.
For direct integration damping, the damping matrix can be specified as a linear combination of the mass and stiffness matrices of the system. Damping coefficients can be specified on an element basis.
Numerical damping is used to damp out unwanted high-frequency chatter in the structure. If the time step is decreased (stiffness damping might cause too much damping), use the numerical damping option to make the damping (stiffness) coefficient proportional to the time step. Thus, if the time step decreases, high-frequency response can still be accurately represented. This type of damping is particularly useful in problems where the characteristics of the model and/or the response change strongly during analysis (for example, problems involving opening or closing gaps).
Element damping uses coefficients on the element matrices and is represented by the equation:
Where
is the global damping matrix
is the mass matrix of ith element
is the stiffness matrix of the ith element
is the mass damping coefficient on the ith element
is the usual stiffness damping coefficient on the ith element
is the numerical damping coefficient on the ith element
is the time increment
If the same damping coefficients are used throughout the structure, previous equation is equivalent to Rayleigh damping.
Damping
Damping
Ratio of the damping to the critical damping
Damping = 5 % (default value)
α
α coefficient for Rayleigh damping (coefficient that multiplies the mass matrix)
β
β coefficient for Rayleigh damping (coefficient that multiplies the stiffness matrix)
