6.8. Performing a Multi-Point Response Spectrum (MPRS) Analysis

The procedure for a MPRS analysis consists of six steps:

  1. Build the model.

  2. Obtain the modal solution.

  3. Obtain the spectrum solution.

  4. Combine the modes.

  5. Review the results.

The first two steps for an MPRS analysis are the same as the steps described for a modal analysis. The procedure for the remaining three steps is explained below.

 

6.8.1. Step 3: Obtain the Spectrum Solution

In this step, the program uses mode shapes extracted by the modal solution to calculate the MPRS solution. The following requirements apply:

  • The mode shape file (Jobname.mode) must be available. The left mode shape file (Jobname.lmode) must also be available when the modal solution is obtained with the unsymmetric eigensolver.

  • The database must contain the same model from which the modal solution was obtained.

  • The Jobname.full, .esav, and .emat files must be available for the participation factors calculation.

  • The results file (Jobname.rst) must be available for writing the static solutions (base excitation) and missing mass solutions.

Note:  If the MPRS analysis is not performed in the same directory as the modal analysis, remote modal files usage must be activated (MODDIR). In this case, the MPRS information is stored in the Jobname.prs file and the MPRS results file only contains the static solutions for base excitation and missing mass responses (if any). The modal analysis files in the modal analysis directory are not modified. Also, if element results calculation based on element modal results is activated (Elcalc = YES on the SPOPT command), the MPRS results file only contains MPRS results.

  1. Enter SOLUTION (/SOLU).

  2. Define the analysis type and analysis options. For spectrum type (SPOPT), select Multi-Point Response Spectrum (MPRS).

  3. Specify the damping (Dynamics Options).

    The forms of damping available are listed in Table 6.10: Damping (Dynamic Options). If you specify more than one form of damping, Mechanical APDL calculates an effective damping ratio at each frequency. The spectral value at this effective damping ratio is then calculated by log-log interpolation of the spectral curves. If no damping is specified, the spectral curve with the lowest damping is used. For more information about different forms of damping, see Damping in Transient Dynamic Analysis.

    Table 6.10: Damping (Dynamic Options)

    Beta (Stiffness) Damping BETAD This option results in a frequency-dependent damping ratio.
    Alpha (Mass) Damping ALPHAD This option results in a frequency-dependent damping ratio.
    Damping Ratio DMPRAT This option specifies a damping ratio to be used at all frequencies.
    Modal Damping MDAMP This option results in a frequency-dependent damping ratio.
    Material-dependent Damping RatioMP,DMPRAvailable in specific conditions (see Note below).

    Note:  Material-dependent damping ratio (MP,DMPR) is available only if specified in the modal analysis where an effective damping ratio is calculated based on the elements' strain energies. You must request that element results be calculated in the modal expansion (Elcalc = YES on the MXPAND command).

  4. Specify load step options. The following options are available:

    • Spectrum Data

      • Type of input spectrum (SPUNIT)

      • The input spectrum type can be displacement, velocity, force, pressure, or acceleration. The type of excitation (base excitation or a nodal excitation) is specified in steps 4 and 5 of this procedure. If a pressure spectrum is to be applied, the pressures should be applied in the modal analysis.

      • Spectrum value-versus-frequency table

      Define the points of each spectrum curve. You can define a family of spectrum curves; each curve is associated with a damping ratio. The following commands apply: SPFREQ, SPVAL, SPDAMP, SPGRAPH.

      You can issue SPTOPT followed by STAT to list the tables, and SPGRAPH to display them.

    • Missing mass and rigid responses

      • Missing Mass Effect (MMASS)

      The missing mass effect reduces the error caused when the higher modes are neglected in the analysis.

      If rigid responses are included, the combination of modal responses with frequencies in the higher end of the spectrum frequency range will be more accurate.

      • Residual Vector (RESVEC)

        Just like the missing mass response, the residual vectors reduce the error caused when the higher modes are neglected in the analysis.

        Unlike the missing mass response, the residual vector is calculated in the modal analysis and is considered as an additional mode. Hence, it is combined as such, and coupling may exist between the residual vector and the modes depending on the mode combination method.

        A frequency is associated with the residual vector. The input spectrum for this frequency should correspond to the Zero Period Acceleration value. The frequency is also used for the calculation of the velocity and acceleration solutions.

  5. Apply the excitation.

    • For base excitation, use the UX, UY, UZ and the ROTX, ROTY, ROTZ labels on the D (or DK, or DL, or DA) command. A value of 0.0 (or blank) removes a specification. Values other than 1.0 scale the participation factors.

    • For uniform base motion using the SED command, specify SEDX, SEDY, or SEDZ. A value of 0.0 (or blank) removes a specification.

    • For nodal excitation, use the FX, FY, FZ on the F (or FK) command. A value of 0.0 (or blank) removes a specification. Values other than 1.0 scale the participation factors.

    • For pressure excitation (where the pressure distribution was provided in the modal analysis), bring in the load vectors from the modal analysis (LVSCALE). You can use the scale factor to scale the participation factors.

      Note:  You can apply base excitations only at nodes that were constrained in the modal analysis. If you applied the constraints using solid model constraints (DK), you must use the same solid model commands in defining the MPRS excitation. Any loads applied during the preceding modal analysis must be removed by deleting or zeroing them.

  6. Begin participation factor calculations for the above MPRS excitation (PFACT).

    Use the TBLNO field to indicate which spectrum table to use, and Excit to specify whether the calculations are for a base or nodal excitation.

    Note:  Since PFACT is an action command, similar to a SOLVE, all commands relative to points 3 - 5 above must be issued before this command.

    If you need to apply multiple MPRS excitations on the same model, repeat steps 4, 5, and 6 above for each additional spectrum table.

 

6.8.2. Step 5: Combine the Modes

This step is the same as step3 described in Performing a Single-Point Response Spectrum (SPRS) Analysis; however, the absolute sum method (AbsSumKey=yes on the SRSS command) acts as an additional combination method.

Note:  You can run multiple MPRS analyses without performing the modal analysis each time. To do so, you must activate the modeReuseKey on the SPOPT command after the first MPRS analysis and for each subsequent one so that the database as well as the necessary files are ready for the new analysis.

 

6.8.3. Step 6: Review the Results

This step is the same as step 6 described in Performing a Single-Point Response Spectrum (SPRS) Analysis.

Intermediate results from a MPRS analysis are written to the structural results file, Jobname.rst. When modal remote file usage is not activated (MODDIR), they consist of the following quantities:

  1. Expanded mode shapes from the modal analysis (loadstep 1)

  2. Static solutions for base excitation (PFACT,,BASE) (loadstep 2)

  3. Missing mass responses if requested (MMASS) (loadstep 3)

 

6.8.4. Example: Multi-Point Response Spectrum (MPRS) Analysis

In this example problem, you determine the seismic response of a three-beam frame using Mechanical APDL commands.

 

6.8.4.1. Problem Description

A three-beam frame is subjected to vertical motion of both supports. The motion is defined in terms of seismic acceleration response spectra. A multi-point response spectrum analysis is performed to determine the nodal displacements.

 

6.8.4.2. Problem Specifications

The following material properties are used for this problem:

Young’s modulus = 1e7 psi
Density = 3e-4 lb/in3

The following geometric properties are used for this problem:

Cross-sectional area = .1 in2
Area moment of inertia = .001 in4
Beam height = .1 in
Beam length = 100 in
 

6.8.4.3. Problem Sketch

Figure 6.3: Three-Beam Frame

Three-Beam Frame

 

6.8.4.4. Command Listing

Items prefaced by an exclamation point (!) are comments.

/prep7
et,1,188
keyopt,1,3,3
sectype,1,beam,rect
secdata,0.1,1
!r,1,.1,.001,.1
mp,ex,1,1e7
mp,nuxy,1,.3
mp,dens,1,.0003
k,1
k,2,   ,100
k,3,100,100
k,4,100
l,1,2
l,2,3
l,3,4
esize,,10
lmesh,all
d,all,uz,0
d,all,rotx,0
d,all,roty,0
d,node(0,0,0),all
d,node(100,0,0),all
fini

/solu
antype,modal
modop,lanb,2            ! Lanczos eigensolver, request 2 modes
mxpand,2                ! Expand 2 modes
solve
fini

/solu
antype,spectrum         ! Spectrum analysis
spopt,mprs,,no          ! Multi-point response (use all extracted modes by default)
!spopt,mprs,,yes        ! Alternative option

!********** Spectrum #1 **********
spunit,1,accg           ! Define the type of 1st spectrum (acceleration) 
spfreq,1,1.0,100.0      ! Define the frequency range [1,100]Hz of 1st spectrum
spval,1,,1.0,1.0	! Define acceleration values of 1st spectrum
d,node(0,0,0),uy,1.0    ! Define constraint
pfact,1                 ! Calculate participation factors of 1st spectrum
                        ! (base excitation by default)

!********** Spectrum #2 **********
spunit,2,accg           ! Define the type of 2nd spectrum (acceleration)
spfreq,2,1.0,100.0      ! Define the frequency range [1,100]Hz of 2nd spectrum
spval,2,,0.8,0.8        ! Define acceleration values of 2nd spectrum
d,node(0,0,0),uy,0      ! Remove previous constraint
d,node(100,0,0),uy,1.0  ! Define new constraint
pfact,2                 ! Calculate participation factors of 2nd spectrum
                        ! (base excitation by default)
srss                    ! Combine using SRSS (displacement solution by default)
solve
fini

/post1
/inp,,mcom              ! Input the mode combination file to perform the 
                        ! combination of displacement solutions, if Elcalc=no in SPOPT
!set,last               ! If Elcalc=yes on SPOPT, issue this command instead of /inp,,mcom 
prns,u,y                ! Printout displacement uy
finish