PERMASDRA Dynamic Response
The PERMASDRA (Dynamic Response Analysis) module allows for the determination of structural responses in the time or frequency domain.
The solution of the dynamic equation is performed either directly using physical coordinates or in modal coordinates after a transformation into the modal space.
 The response in the time domain (transient response) is determined by an integration of
the equation of motion:
 Absolute transient response with or without rigid body response.
 Direct integration of the equation of motion or integration after a transformation to the modal space. Available solvers are Newmark β and HHT (HilberHughesTaylor)
 nonlinear spring elements,
 nonlinear damper elements, and
 nonlinear control elements.
 The response in the frequency domain (frequency response) is determined by the solution
of the linear complex equation system for each excitation frequency requested:
 Absolute frequency response with or without rigid body response.
 Direct solution of the equation system or solution after a transformation to the modal space.
 Frequency and rotation speed dependent stiffness and damping can be taken into account with CONTROL6 element
 Without running through the transient phenomenon a calculation of the steadystate response can be performed. To achieve that, a number of frequency response analyses are superposed in the time domain. In addition, a static load case can be taken into account. This is facilitated for all periodic excitations with known harmonic composition.
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By specification of a node set the run time and disk space for modal superposition methods can be drastically
reduced when the results are determined for the set members only.
The features below hold for both timehistory and frequency response methods:
 The damping properties may be modeled by one of the following methods:
 material or structural damping for elements,
 global structural damping for Components,
 proportional damping (Rayleigh damping),
 viscous damper elements,
 modal viscous damping,
 modal structural damping,
 modal structural damping,
 direct input of modal damping matrix.
 direct input of damping matrix.

The excitation is defined by static loading cases modulated
by functions of time respectively frequency.
The load definitions may consist of:
 concentrated forces or moments,
 distributed loads (loads applied to lines, surfaces or volumes),
 inertia loads,
 prescribed displacements.

The primary results are:
 displacements,
 velocities and
 accelerations.

Moreover, the following results may be derived:
 reaction forces,
 stresses and stress resultants,
 strain energy,
 kinetic energy,
 specific sound radiation power density.
When modal methods are applied additional functions are available:
Static Mode Shapes can be generated in order to enhance the modal basis of dynamic modes. This has the following two advantages:
 In the low frequency range the results will become essentially more accurate.
 They allow to consider nonstructural degrees of freedom like the internal state variables of control elements.
The static mode shapes can be specified using one of the following cases:
 Directly by nodal displacements,
 By external loads,
 By results from another analysis,
 By natural loads of specified elements (like spring forces),
 Implicitly by internal degrees of freedom of controller elements.
Additional tools are available for the further processing of modal results:
 For the evaluation of a structural response modal participation factors of the primary results can be derived and exported.
 For the evaluation of the contribution of single degrees of freedom to a structural response node participation factors can be derived and exported.
 For a transient response a statistical evaluation of stresses or element forces over the time domain can be performed, which gives the maximal and effective values. These statistical values can be used in durability considerations, for example.