11.1. State-Space Matrices Based on Modal Analysis

The SPMWRITE command can be used to export state-space matrices based on a modal analysis when:

Prior to calculating the state-space matrices, you need to perform a modal analysis using the LANB, LANPCG, SNODE, or SUBSP eigensolver (MODOPT command). When obtaining the modal solution, consider the following:

State-space matrices are calculated in postprocessing using the file Jobname.MODE. They are written to the file Jobname.SPM using the requested format (FileFormat on the SPMWRITE command).

11.1.1. Examples of SPMWRITE Command Usage

This section describes how to use SPMWRITE to export state-space matrices based on two sets of model criteria.

  1. The first set of model criteria for export to Simplorer are as follows:

    • 10 modes are taken into account.

    • There are 2 inputs specified in the array parameter ‘inputTab’.

    • The inputs labels are defined in the character array parameter ‘inputLab’.

    • There is 1 output specified in the array parameter ‘outputTab’.

    • The output label is defined in the character array parameter ‘outputLab’.

    • The initial condition is calculated from the first load vector.

    • Velocity and acceleration results are not included.

    • The SML format for Simplorer is used to printout the state-space matrices.

    If your model can be described by this first set of criteria, issue the following to export the state-space matrices:

    ! ** inputs definition
    *dim,inputTab,,2,2
    *dim,inputLab,CHAR,2
    inputTab(1,1) = 413          ! node 413
    inputTab(1,2) = 1            ! ux
    inputLab(1) = ‘n413_ux’
    inputTab(2,1) = node(50e-2,0,45e-2)   ! node @(.5,0,.45)
    inputTab(2,2) = 4                     ! rotx
    inputLab(2) = ‘n01_rotx’
    
    ! ** outputs definition
    *dim,outputTab,,1,2
    *dim,outputLab,CHAR,1
    outputTab(1,1) = 1022         ! node 1022
    outputTab(1,2) = 1            ! ux
    outputLab(1) = ‘n1022_ux’
    
    spmwrite,modal,10,inputTab,inputLab,outputTab,outputLab,1
    
  2. The second set of model criteria are as follows:

    • All modes are taken into account.

    • The inputs are based on all existing load vectors from the modal analysis.

    • The outputs are equal to the inputs.

    • There is no initial condition.

    • Velocity and acceleration results are not included.

    • The dense format is used to printout the state-space matrices.

    If your model can be described by this second set of criteria, issue the following to export the state-space matrices:

    spmwrite,modal, ,, ,, ,, ,0

11.1.2. Example of Reduced Model Generation in ANSYS and Usage in Simplorer

11.1.2.1. Problem Description

The model in this example is a basic representation of a disk drive suspension as described in Hatch[1]. It is a clamped-free beam with a mass and spring at tip. The mass represents the recording head. The reduced model is generated in ANSYS and imported into Simplorer where global half-sine acceleration is applied in a transient analysis.

11.1.2.2. Problem Specifications

Material

Young Modulus: 190e+6 mN/mm2

Density: 7.83e-6 kg/mm3

Poisson ratio: 0.293

Beam

Length: 20 mm

Area: 0.15 mm2

Cross section inertia IYY: 0.05 mm4

Cross Section inertia IZZ: 0.00007031 mm4

Spring

Stiffness: 1.e+7 N/mm

Mass at tip

Mass: 1.e-6 kg

11.1.2.3. Input File for the Analysis

Use the input below to generate the state-space matrices file (file.spm) based on the first 3 modes plus the residual vector.

/title, Beam on Shaker (ACEL) - SPMWRITE 3 modes + resvec
/prep7

! ** Parameters
num_elem = 16
nummodes = 2*num_elem

! ** Material
ex,1,190e6	
dens,1,7.83e-6	
nuxy,1,0.293         

! ** Properties
r,1,0.15,0.05,0.00007031,0.075,0.2	
r,2,1000000				
r,3,0.00002349,0.00002349,0.00002349		

! Nodes
n,1,0,0,0			
n,num_elem+1,20,0,0		
fill,1,num_elem+1		
n,num_elem+2,20,0,-3		
nall

! ** Beam
et,1,4  
type,1
mat,1
real,1
e,1,2
egen,num_elem,1,-1

! ** Spring
et,2,14	
type,2
real,2
e,num_elem+1,num_elem+2

! ** Mass
et,3,21	
type,3
real,3
e,num_elem+1

! ** Constraints
d,1,all,0	
d,num_elem+2,all,0
nsel,s,node,,2,num_elem+1
d,all,ux
d,all,uy
d,all,rotx
d,all,rotz
nsel,all
fini

! ** Modal analysis 
/solu					
antype,modal
modopt,lanb,3			! << 3 modes
mxpand,3
resvec,on				! << residual vector
acel,,,1.0				! << load vector definition
dmprat,0.02			! << modal damping
solve 
fini

/post1
/eshape,1
! ** Definition of the output
*dim,output,,1,2
output(1,1) = num_elem+1		! << node at tip
output(1,2) = 3					! << UZ
*dim,outputLab,CHAR,1
outputLab(1) = 'UZtip'

! ** Write SPM file: input = load vector
spmwrite, modal, ,,, output, outputLab
*list,,spm
fini

The state-space matrices file can be imported in Simplorer using: Simplorer Circuit > SubCircuit > Add Mechanical Component

A transient analysis is performed in Simplorer for the 3 following reduced models:

  • All 32 modes are used.

  • First 3 modes are used.

  • First 3 modes plus residual vector are used (ANSYS input is listed above).

The schematic of the simulation is shown on the figure below:

Figure 11.1:  Simulation Schematic

Simulation Schematic

A zoom on the graph showing the evolution of the spring force is given below:

Figure 11.2:  Evolution of Spring Force

Evolution of Spring Force

The reduced model based on the first 3 modes (red curve) is not accurate. When the residual vector is included (purple curve), the spring force is similar to the reference given by the 32 modes reduced model (dotted curve).


Release 16.2 - © SAS IP, Inc. All rights reserved.