S7-1 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation SECTION 7 NORMAL MODES ANALYSIS FOR PRE-STIFFENED STRUCTURES

S7-2 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation

S7-3 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation n Section 2 was for normal modes analysis of unloaded structures. In this section normal modes analysis of structures which have a static pre-load applied to them will be considered. n Typical real-world examples are u Thin walled pressure vessels where the pressurization dominates stiffness, hence the natural frequencies, such as rocket fuel tanks and satellite oxygen tanks. u Structures subject to significant dead weight loading, such as suspension cable bridges and oil tankers. u Tensioning of strings in musical instruments to achieve required frequencies. u Structures subject to centrifugal loading such as jet engine turbine and fan blades. NORMAL MODES ANALYSIS FOR PRE-STIFFENED STRUCTURES

S7-4 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation n The objective of applying a static load to a structure during to a normal modes analysis is to use the loaded structure in obtaining the stiffness matrix for the modal analysis. n There are three terms/effects that can influence the stiffness matrix. u Material nonlinearity, e.g. elastic-plastic behavior u Geometric stiffness, due to changes in the structural shape l These can be due to small or large displacement behavior u Follower-force stiffness, arising as the loading changes its line of action relative to the displacements l These can be due to small or large displacement behavior NORMAL MODES ANALYSIS FOR PRE-STIFFENED STRUCTURES (Cont.)

S7-5 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation n The standard eigenvalue problem has two requirements u The stiffness matrix must be constant. This means deflections are small and the structures strains and stresses are due to elastic material behavior. u Applied loading does not affect stiffness. n This standard approach requires the following u Small deformations u Linear material n For pressure vessels and other structures that are under large tensile or constant loads, the stiffness and natural frequencies of the structure are affected by this load. NORMAL MODES ANALYSIS FOR PRE-STIFFENED STRUCTURES (Cont.)

S7-6 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation NORMAL MODES ANALYSIS FOR PRE-STIFFENED STRUCTURES (Cont.) n The eigenvalue problem equation corresponding to pre- stiffened structures is u where [K] D is the differential stiffness matrix. n MSC.Nastran can analyze this phenomena. n There are two approaches to solving this problem. They involve using u SOL 103 l linear static loading, then eigenvalue extraction u SOL 106 l nonlinear static loading, then eigenvalue extraction

S7-7 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation n Three basic approaches are taken in Nastran. u Run SOL 103 as a cold start run with two subcases, the first subcase being used to obtain the differential stiffness matrix from a linear static analysis, and the second subcase being used to solve the eigenvalue problem using the differential stiffness from the prior subcase. This approach permits only geometric stiffness and follower forces stiffness small displacement theory updates. u Run SOL 106 as a cold start run and use the stiffness matrix created at the completion of the final load step for a nonlinear analysis, for the normal modes analysis. This approach permits all nonlinear material and large displacement geometric and follower force terms to be included. u Run SOL 106 as a cold start, then restart using SOL 103. This method was used prior to MSC.Nastran V2001. This is not recommended for inexperienced users as many parameters need to be controlled. All nonlinear effects can be used. NORMAL MODES ANALYSIS FOR PRE-STIFFENED STRUCTURES (Cont.)

S7-8 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation n Recommendations u If the displacements are small and no significant nonlinearity is present, use the SOL103 method. u If nonlinear or large displacements are important, use the SOL106 method. n MSC.Patran supports the SOL106 method directly including multiple subcases. n The SOL103 method is supported directly in MSC.Patran by selecting a previously created static subcase with the prefix of (Preload). n A case study of each method is now shown. NORMAL MODES ANALYSIS FOR PRE-STIFFENED STRUCTURES (Cont.)

S7-9 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY: NORMAL MODES FOR PRE-STIFF. STR. USING SOL 106 n The normal modes analysis of a simple thin walled cylinder with closed ends is considered under two conditions a) No pre-load. b) Internal pressurization with 100 psi. t l d Geometry of the Cylinder:

S7-10 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation n The detail of the setup of condition (a) is not shown. n For Case (b), define a static loading in the normal way, and then set up SOL 106. Cylinder Wall Thickness inches Cap Thickness0.25 inches Length (l)10 inches Diameter (d)2 inches Elastic Modulus1.0E7 psi Material Density0.101 lbm/in 3 Poisson Ratio0.33 CASE STUDY: NORMAL MODES FOR PRE-STIFF. STR. USING SOL 106 (Cont.)

S7-11 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation The pressure loading is set up as a load case called pre-stiffened. 100 psi internal pressure is applied to all elements. CASE STUDY: NORMAL MODES FOR PRE-STIFF. STR. USING SOL 106 (Cont.)

S7-12 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation Request a SOL 106 nonlinear solution type. The solution parameters permit us to include large displacement and follower force stiffness terms if so desired. Nonlinear material effects can be included if present. CASE STUDY: NORMAL MODES FOR PRE-STIFF. STR. USING SOL 106 (Cont.)

S7-13 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation Pick the subcase which includes the pressure loading. Then select subcase parameters and check the normal modes box to allow the normal modes analysis to be defined. Notice that the submenu is identical to the standard normal modes form. CASE STUDY: NORMAL MODES FOR PRE-STIFF. STR. USING SOL 106 (Cont.)

S7-14 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation Looking at the MSC.Nastran.bdf file output this is seen: NLPARM and METHOD are called out in Case Control. Static preload is called out via LOAD = 2 and points to the pressure loading. LGDISP invokes the large displacement if selected. PARAM NMLOOP 1 forces the calculation of the normal modes using the updated stiffness matrix. NLPARM reflects the settings of the nonlinear solution strategy menu chosen in the subcase parameter form. EIGRL reflects the normal modes analysis parameters requested. CASE STUDY: NORMAL MODES FOR PRE-STIFF. STR. USING SOL 106 (Cont.)

S7-15 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation n Eigenvalue table from the normal modes analysis n Eigenvalue table from the pre-stiffened normal modes analysis CASE STUDY: NORMAL MODES FOR PRE-STIFF. STR. USING SOL 106 (Cont.) The results of pre-stiffened analysis are compared with a previous normal modes analysis.

S7-16 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation n First mode for normal modes analysis n First mode for normal modes analysis for pre-stiffened structure Investigation of the first mode for the two analysis shows that the presence of the pressurization has also changed the mode shape from 3 lobes to 2 lobes. CASE STUDY: NORMAL MODES FOR PRE-STIFF. STR. USING SOL 106 (Cont.)

S7-17 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation Modify the previous SOL106. bdf file to perform a SOL103 pre-stiffened normal modes analysis Change the Solution Type to SOL 103, Normal Modes analysis Create a second subcase for normal modes analysis. Use STATSUB to refer to the static analysis case. CASE STUDY: NORMAL MODES FOR PRE-STIFF. STR. USING SOL 103 Delete NLPARM reference

S7-18 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation The modified bdf file that will be submited to Nastran for pre-stiffened normal modes analysis. CASE STUDY: NORMAL MODES FOR PRE-STIFF. STR. USING SOL 103 (Cont.)

S7-19 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation n The Normal Modes using the 2 methods are shown u Pre-stiffened normal modes analysis using the SOL 103 method. u Pre-stiffened normal modes analysis using the SOL 106 method CASE STUDY: NORMAL MODES FOR PRE-STIFF. STR. USING SOL 103 (Cont.)

S7-20 NAS122, Section 7, August 2005 Copyright 2005 MSC.Software Corporation WORKSHOP 12a and 12b n Carry out Workshop 12a described in the workshop manual. This consists of using SOL 103, w/o and w/ preload, and SOL 106 w/ preload. n Then, carry out Workshop 12b, for which multiple load cases are to be created, using both SOL 103 and SOL 106. n The workshops will take you through step by step if you are unfamiliar with MSC.Nastran and MSC.Patran. n If you have some experience, then try to set up the analysis without referring to the step by step guide. n Please feel free to ask your tutor for help. Flat Plate y x z 5,000 rpm Fixed edge displacements Rotating Fan Blade