$ $ THIS ALTER IS CONFIDENTIAL AND A TRADE SECRET OF THE $ MSC.SOFTWARE CORP. THE RECEIPT OR POSSESSION OF $ THIS ALTER DOES NOT CONVEY ANY RIGHTS TO REPRODUCE OR $ DISCLOSE ITS CONTENTS, OR TO MANUFACTURE, USE, OR SELL $ ANYTHING HEREIN, IN WHOLE OR IN PART, WITHOUT THE $ SPECIFIC WRITTEN CONSENT OF THE MSC.SOFTWARE CORPORATION. $ Alter to Add Rigid Rotor Gyroscopic Terms in Dynamic Analyses Alter Name ridgyroa.v2001 Purpose This alter adds gyroscopic terms to dynamic analysis using the structured solution sequences. These solution sequences include direct and modal frequency response, direct and modal transient response, and direct and modal complex eigenvalue analyses. The alter does not support real eigenvalue analysis. Solution Sequences SOL 107-112 Input Executive Control Include 'ridgyroa.v2001'. Bulk Data The alter supports either nonsynchronous or synchronous addition of the gyroscopic terms. The nonsynchronous option adds the gyroscopic terms such that they are proportional to a user-supplied rotation speed. The nonsynchronous option is available in direct and modal frequency response, direct and modal transient response, and direct and modal complex eigenvalue analyses. The synchronous option adds the gyroscopic terms such that they are proportional to the excitation frequency (for frequency response analysis) or natural frequency (complex eigenvalue) of the structure. The synchronous option is available only in direct and modal frequency response and direct and modal complex eigenvalue analyses. The synchronous option is not supported in transient analysis and a DMAP error will occur if this combination is attempted. PARAM,SYNC,yy where yy=no is the default value. The value of yy causes the following actions in the DMAP alter: NO = Nonsynchronous option. YES = Synchronous option. PARAM,RPM,xx where xx is the base rotation speed in revolutions/minute. Gyroscopic terms are scaled in relation to this entry for the nonsynchronous option. This parameter is not used for the synchronous option. The above parameters may appear in either the Case Control or Bulk Data Section. In addition to the above parameters, the following information must also be supplied on DTI bulk data entries. DTI RGYRO 0 DTI RGRYO i GRIDIDi IPOLARi RAXISi SCALEi where, i the record number (integer). GRIDIDi grid location which will have the added gyroscopic terms (integer). IPOLARi Polar moment of inertia of the mass about the rotation axis (real). The unit must be mass units. RAXISi rotation axis in global coordinates (integer): 1 for x-axis, 2 for y-axis, 3 for z-axis. SCALEi scale factor for rotation speed relative to base rotation speed (real); for the nonsynchronous option the PARAM, RPM entry defines the base rotation speed, for the synchronous option the base rotation speed is the excitation frequency (frequency analysis) or the natural frequency (complex eigenvalue analysis). One DTI record must be entered for each grid point location which will have the added gyroscopic terms. All fields on the DTI record must be provided. All grid points specified on the DTI entry must be part of the residual structure. If there is a format error on a DTI entry or a specified grid point is not part of the residual structure, then an error message will be issue and the solution will be terminated. Output Standard dynamic analysis output including the effects of the gyroscopic terms. Limitations The gyroscopic terms added to the analysis are based on the assumption that the rotating component is rigid. The added terms do not take into account any flexibility of the rotating part. Sample Files ridgyro2a.dat (SOL 103) Eigenvalue analysis without the gyroscopic effects. ridgyro2b.dat (SOL 107) Direct complex eigenvalue analysis including the gyroscopic effects. ridgyro2b.xls Microsoft Excel file comparing analytical and MSC/NASTRAN results. Additional Documentation: Below is some additional documentation of ridgyro2b.dat (Jeffcott Rotor). Structure: The model consists of a shaft of length 1m which is rigidly supported at both ends. In the middle of the shaft there is a rigid rotor. z ^ | III Rotor III/ | III | |-------------------------| --> x |1 2 I3I 4 5| III III Problem Data: Shaft: Circular Cross Section with a radius of 0.01m Material is steel with a Young's modulus of 2.E11N/m and a mass density of 7850kg/m^3. Rotor: Mass: m =10kg Polar Moment of Inertia: Ixx=200kgm^2 Diametral Moments of Inertia: Iyy=Izz=100kgm^2 Units: N, kg, m Analytical Solution: The rotor has rotational vibrations around the y- and z-axis. The frequencies of these vibrations depend on the rotational speed. They are given by Omega*Ixx 4*k*Iyy omega_1/2 = --------- | 1 +/- sqrt ( 1 + ------------- ) | 2*Iyy Omega^2*Ixx^2 where k = Stiffness of the shaft Ixx = Polar Moment of Inertia Iyy = Diametral Moment of Inertia Omega = Speed of Rotation (rad/s): Omega = 2*pi*U/60