Eigenvalue topology optimization of structures using a parameterized level set method

Preventing a structure from resonance is important in many real-world applications. Because an external excitation frequency can be lower than the fundamental eigenfrequency or between the eigenfrequencies of a structure, there is a strong need for eigenfrequency optimization technology to optimize the fundamental eigenfrequency and, in addition, the k-th eigenfrequency and to maximize the gap between eigenfrequencies. However, previous optimization studies on vibrating elastic structures that used the level set method have been devoted to the optimization of the fundamental eigenfrequency, whereas the higher-order eigenfrequencies optimization problem has seldom been considered. This paper presents an eigenfrequency optimization technology that is based on the compactly supported radial basis functions (CS-RBFs) parameterized level-set method, using the fundamental eigenfrequency, the eigenfrequency of a given higher-order, and the gap between two consecutive eigenfrequencies as the optimization objectives. Furthermore, to address the oscillation problem of the objective function, we adopt an exponential weighted optimization model of a number of the lower eigenfrequencies for multiple eigenvalue optimizations, and we utilize mode-tracking technology for the single eigenvalue optimization.In addition, we further extend the CS-RBFs parameterized level-set method to an optimization that is performed with geometric constraints, which means that the size and position of the regular holes in the structure can be optimized with the shape and topology. This approach is useful in real-world applications. The effectiveness of this method is demonstrated by several widely investigated examples that have various objectives.