Appendix Ten Harmonic Analysis Harmonic Analysis Background on

Appendix Ten Harmonic Analysis

Harmonic Analysis Background on Harmonic Analysis Training Manual • If the harmonic loading and response are substituted back in the equation of motion, the following is obtained: ANSYS Workbench – Simulation • Separation of real and imaginary terms can be performed for not just the force loading but also the response: August 26, 2005 Inventory #002275 A 10 -2

Harmonic Analysis … Loads and Supports (ANSYS) Training Manual – 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 SURF 154 with KEYOPT(11)=2 • For Pressure Load, input is via SF, , PRES, REAL, IMAG • 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 SURF 154. Two sets are created for axial and radial components of bearing load: Axial uses KEYOPT(11)=2, Radial uses KEYOPT(11)=0 ANSYS Workbench – Simulation • Internally, loads are applied slightly differently than in an equivalent static analysis: • Moments on vertices or edges of shells are applied as nodal loads via F, , MX/MY/MZ while moments on surfaces are applied via CONTA 174 surface-based constraint (see Ch. 4) August 26, 2005 Inventory #002275 A 10 -3

Harmonic Analysis … Mode Superposition Method Training Manual – 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]: ANSYS Workbench – Simulation – The previous two equations can be combined and premultiplied by the mode shape {fi}T: – Natural frequency wi for mode i: – Damping ratio xi for mode i: August 26, 2005 Inventory #002275 A 10 -4

Harmonic Analysis … Mode Superposition (ANSYS) Training Manual – 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 ANSYS Workbench – Simulation • The ANSYS mode superposition method is run internally: • 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 A 10 -5

Harmonic Analysis … Full Method (ANSYS) Training Manual – 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 ANSYS Workbench – Simulation • Internally, the Full method is used in ANSYS: August 26, 2005 Inventory #002275 A 10 -6