Harmonic Analysis

1. Appendix Ten Harmonic Analysis

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: August 26, 2005 Inventory #002275 A10-2

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) August 26, 2005 Inventory #002275 A10-3

4. … Mode Superposition Method • The previous two equations can be combined and pre-multiplied by the mode shape {fi}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 modesn used in the equation. • The equation is simplified because of the following properties: • Normalization of [M]: • Natural frequency wi for mode i: • Damping ratio xi for mode i: August 26, 2005 Inventory #002275 A10-4

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 August 26, 2005 Inventory #002275 A10-5

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 August 26, 2005 Inventory #002275 A10-6