Yuji Aoyama

Component mode synthesis for large-scale structural eigenanalysis

Abstract This paper proposes new combination of the mode to be used in the component mode synthesis (CMS). Although the CMS is a method adequate enough to make a large-scale eigenanalysis of structures, it is to be shown in this paper that the improved CMS will become a method more adequate for extremely large-scale eigenanalysis than the conventional one. The method is also demonstrated on a parallel system. We present the analysis of a scale of ten million degrees of freedom can be made by the proposed method and the accuracy of the eigenfrequency to be obtained is satisfactory.

Solution Algorithm of Large Scale Eigenvalue Analysis with Damping.

This paper presents a solution algorithm of nonlinear eigenvalue problem which occurs in an eigenvalue analysis of a structure with damping. The solution of nonlinear eigenvalue problems usually require operations of a complex matrix and complex vectors to generate Krylov subspace. The proposed algorithm is especially effective in terms of large scale analysis, because it does not use complex matrix nor complex vectors. Therefore, the number of operations and the size of memory used in the analysis is reduced. Furthermore, the accuracy of the solutions is confirmed to be satisfactory.

High Accuracy Eigenvalue-Analysis Using Non-Positive Definite Mass Matrix.

This paper presents a solution algorithm of generalized eigenvalue problem with non-positive definete mass matrix. The accuracy of the natural frequency is much higher using 20-node hexahedral elements than using 8-node elements. However, lumped mass matrix which reduces the computation cost could not be used combined with the 20-node elements, because the mass matrix would be non-positive definite in the case. Applying the proposed algorithm, the generalized eigenvalue problem with non-positive definite mass matrix can be solved with the same computation cost as for the solution of eigenvalue problem with positive difinite mass matrix.

Energy trapping behavior of AT‐cut quartz crystal resonators with a groove ring on main electrodes

This paper considers an energy trapping AT-cut quartz crystal resonator, and proposes a quartz crystal resonator with a groove ring having a cutoff frequency higher than that of the periphery, located near the outer periphery of the electrode. A numerical analysis is performed from the viewpoint of the purely elastic and isotropic cases. The results are verified by numerical calculation by the three-dimensional finite-element method. It is shown that the following properties are realized for any geometrical parameters of the main electrodes by providing the groove ring structure. (1) The frequency difference between the main resonant frequency and the anharmonic spurious component can be increased on the order of 10%. (2) If the frequency difference between the anharmonic spurious components is kept the same, the displacement of the quartz crystal substrate edge can be reduced by several tens of percent. These properties help to reduce vibration energy leakage from the edge support, and to reduce the size of the quartz crystal resonator.