Appendix Five Modal Analysis Modal Analysis Basics of

Appendix Five Modal Analysis

Modal Analysis Basics of Free Vibration Analysis Training Manual – Free Vibration analysis does not consider the response of the structure under dynamic loads but just solves for the natural frequencies. A free vibration analysis is usually the first step before solving more complicated dynamic problems. • A free vibration analysis is a subset of the general equation of motion: ANSYS Workbench – Simulation • A free vibration analysis (a. k. a. modal or normal modes analysis) is performed to obtain the natural frequencies and mode shapes of a structure August 26, 2005 Inventory #002275 A 5 -2

Modal Analysis Basics of Free Vibration Analysis Training Manual where fi is the mode shape (eigenvector) and wi is the natural circular frequency for mode i. • By substituting this value in the earlier equation, the following is obtained: ANSYS Workbench – Simulation • In free vibration analysis, the structure is assumed to be linear, so the response is assumed to be harmonic: Noting that the solution fi =0 is trivial, wi is solved for: August 26, 2005 Inventory #002275 A 5 -3

Modal Analysis … Requesting Results Training Manual – If Frequency Finder branch is present, ANTYPE, MODAL is set – The number of modes is set with the nmodes argument, and the beginning and ending search frequencies are specified with freqb and freqe of the MODOPT, , nmodes, freqb, freqe command – All modes are expanded via the MXPAND command. To save disk space and calculation times, the element solution option of MXPAND is not turned on unless stress or strain results are requested. ANSYS Workbench – Simulation • The corresponding ANSYS commands for the Frequency Finder branch are as follows: August 26, 2005 Inventory #002275 A 5 -4

Modal Analysis … Solution Options Training Manual – “Large Deflection” and “Weak Springs” are meant for static analysis cases and should not be changed. – “Solver Type” can be set to “Direct” or “Iterative” • “Program Controlled” or “Direct” result in the Block Lanczos eigenvalue extraction method with the sparse direct equation solver (MODOPT, LANB and EQSLV, SPARSE). This is the most robust eigensolver, as it handles small & large models and beam, shell, or solid meshes, so it is the default option. • “Iterative” results in the Power. Dynamics solution method, which is a combination of the subspace eigenvalue extraction method with the PCG equation solver (MODOPT, SUBSP and EQSLV, PCG). The Power. Dynamics eigensolver can be efficient for large models of solid elements, when requesting only a few modes. ANSYS Workbench – Simulation • For a regular modal analysis, none of the solution options except for “Solver Type” have much effect August 26, 2005 Inventory #002275 A 5 -5

Modal Analysis … Prestressed Modal Analysis Training Manual – A linear static analysis with PSTRES, ON is run – A modal analysis is then run right afterwards with PSTRES, ON to consider prestress effects ANSYS Workbench – Simulation • For prestressed modal analysis, Simulation performs the two necessary iterations internally: August 26, 2005 Inventory #002275 A 5 -6

Modal Analysis … Prestressed Modal Analysis Training Manual – No large-deflection prestress effects are currently supported in Simulation, so enabling the “Large Deflection: On” in the Solution branch is not permitted. – The equation solver for the static analysis and the eigensolver for the modal analysis currently cannot be independently set. Both will be affected by the “Solver Type” setting in the Solution branch. – If a Point Mass is present, rigid-body modes may be introduced in a prestressed modal analysis. This is due to the fact that the RBE 3 -type of surface constraint defined with CONTA 174 and TARGE 170 introduce 6 DOF but the MASS 21 element has no rotary inertial terms (3 DOF). • The user can usually ignore these rigid-body modes, as they are associated with the MASS 21 elements (verify by checking displacement scale of these mode shapes). • No such problems exist for a regular modal with Point Masses. ANSYS Workbench – Simulation • Other items useful for ANSYS users to keep in mind: August 26, 2005 Inventory #002275 A 5 -7

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