1. Harmonic Analysis Appendix Ten

2. Training Manual General Preprocessing Procedure March 29, 2005 Inventory #002215 A10-2 Background on Harmonic Analysis Separation of real and imaginary terms can be performed for not just the force loading but also the response: If the harmonic loading and response are substituted back in the equation of motion, the following is obtained:

3. Training Manual General Preprocessing Procedure March 29, 2005 Inventory #002215 A10-3 … Loads and Supports (ANSYS) Internally, loads are applied slightly differently than in an equivalent static analysis: –Forces on vertices and edges are applied as real & imaginary nodal loads via F,,FX/FY/FZ,REAL,IMAG –Pressures and Forces on surfaces are applied on surface effect elements SURF154 with KEYOPT(11)=2 For Pressure Load, input is via SF,,PRES,REAL,IMAG For Force Load on surface, input via SFE,,5,PRES,0 for real and SFE,,5,PRES,2 for imaginary components –Given Displacement Support is via D,,UX/UY/UZ,REAL,IMAG –Acceleration, Bearing, and Moment Loads are used as normal: Bearing loads are applied as SFE on face 5 of SURF154. Two sets are created for axial and radial components of bearing load: Axial uses KEYOPT(11)=2, Radial uses KEYOPT(11)=0 Moments on vertices or edges of shells are applied as nodal loads via F,,MX/MY/MZ while moments on surfaces are applied via CONTA174 surface-based constraint (see Ch. 4)

4. Training Manual General Preprocessing Procedure March 29, 2005 Inventory #002215 A10-4 … Mode Superposition Method –The previous two equations can be combined and pre- multiplied by the mode shape {  i } T : –Although outside of the scope of the discussion, the above equation reduces to the following: The resulting equation is uncoupled and is easier to solve The total degrees of freedom are not dictated by the number of nodes in the mesh. Instead, it is determined by the number of modes n used in the equation. The equation is simplified because of the following properties: –Normalization of [M]: –Natural frequency  i for mode i: –Damping ratio  i for mode i:

5. Training Manual General Preprocessing Procedure March 29, 2005 Inventory #002215 A10-5 … Mode Superposition (ANSYS) The ANSYS mode superposition method is run internally: –A modal analysis is run first with Block Lanczos eigenvalue extraction method (MODOPT,LANB,200,FREQB/2,2*FREQE) A maximum of 200 modes between ½ of the beginning frequency FREQB to 2 times the ending frequency FREQE is solved for A load vector is automatically created at this time –A harmonic analysis using mode superposition method (HROPT,MSUP) is then performed Frequency range specified with HARFRQ,FREQB,FREQE If clustering is requested, HROUT,,ON is issued All loads are step-applied in the frequency range (KBC,1) Number of intervals (or cluster number) specified with NSUBST Load vector of 1.0 is issued with LVSCALE,1 OUTRES with nodal and element components used –An expansion pass is also performed for contour results EXPASS,ON and HREXP,ALL are used

6. Training Manual General Preprocessing Procedure March 29, 2005 Inventory #002215 A10-6 … Full Method (ANSYS) Internally, the Full method is used in ANSYS: –Frequency range specified with HARFRQ,FREQB,FREQE –HROPT,FULL is used –Number of intervals specified with NSUBST –Loads are step applied in frequency range with KBC,1 –The equation solver is the default sparse solver. The Details view of the Solution branch has no effect on full harmonic analyses, as no solver command (EQSLV) is issued –OUTRES with nodal and element components used