An approach for maximizing the smallest eigenfrequency of structure vibration based on piecewise constant level set method

Maximization of the smallest eigenfrequency of the linearized elasticity system with area constraint is investigated. The elasticity system is extended into a large background domain, but the void is vacuum and not filled with ersatz material. The piecewise constant level set (PCLS) method is applied to present two regions, the original material region and the void region. A quadratic PCLS function is proposed to represent the characteristic function. Consequently, the functional derivative of the smallest eigenfrequency with respect to PCLS function takes nonzero value in the original material region and zero in the void region. A penalty gradient algorithm is proposed, which initializes the whole background domain with the original material and decreases the area of original material region till the area constraint is satisfied. 2D and 3D numerical examples are presented, illustrating the validity of the proposed algorithm. •Propose a method to extend the linearized elasticity system, using a characteristic function.•Use a piecewise constant level set method to fulfil the shape optimization of the original material region.•The localized modes are eliminated by using the total variation regularization and no-filling ersatz material method.