This can lead to purely imaginary eigenfrequencies which physicallyĪ special kind of frequency calculations is a cyclic symmetry calculation for which the keyword cards *SURFACE, *TIE, *CYCLIC SYMMETRY MODEL and *SELECT CYCLIC SYMMETRY MODES are available. Due to preloading the stiffness matrix is not necessarily positiveĭefinite. Symmetric), but it is positive only for positive definite stiffness TheĮigenvalue is guaranteed to be real (the stiffness and mass matrices are The eigenvalue of the generalizedĮigenvalue problem is actually the square of the eigenfrequency. in a linear dynamic step).Īll output of the eigenmodes is normalized by means of the mass (STORAGE=YES) on the *FREQUENCY card the eigenfrequencies,Įigenmodes and mass matrix are stored in binary form in a "problem.eig" file for further use (e.g. Furthermore, if the parameter STORAGE is set to yes ``problem'' stands for any name, the eigenfrequencies are stored in If the input deck is stored in the file ``problem.inp'', where The loading at the end of a perturbation step is reset to zero. Thus, the effect of the centrifugal force on the frequencies in a turbine blade can be analyzed by first performing a static calculation with these loads, and selecting the perturbation parameter on the *STEP card in the subsequent frequency step. If the perturbation parameter is activated, the stiffness matrix is augmented by contributions resulting from the displacements and stresses at the end of the last non-perturbative static step, if any, and the material parameters are based on the temperature at the end of that step. Any steps preceding the frequency step do not have any influence on the results. If the perturbation parameter is not activated on the *STEP card, the frequency analysis is performed on the unloaded structure, constrained by the homogeneous SPC's and MPC's. A frequency step is triggered by the key word *FREQUENCY and can be perturbative or not. The inversion is performed by calling the linear equation solver SPOOLES. For large problems this results in execution times cut by about a factor of 100 (!). A crucial point in the present implementation is that, instead of looking for the smallest eigenfrequencies of the generalized eigenvalue problem, the largest eigenvalues of the inverse problem are determined. The theory can be found in any textbook on vibrations or on finite elements, e.g. In CalculiX, the mass matrix is not lumped, and thus a generalized eigenvalue problem has to be solved. In a frequency analysis the lowest eigenfrequencies and eigenmodes of the structure are calculated. Next: Complex frequency analysis Up: Types of analysis Previous: Static analysis Contents
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