shape optimization, vibration modes, frequency band gaps
In typical household refrigeration systems, the compressor is structurally connected to the cabinet through an assembly composed of rubber mounts and a steel support plate, usually called base-plate. This plate works as a vibration energy path from the compressor to other refrigerator components, and its dynamic behavior must be known in order to avoid the coincidence of resonances and operational frequencies , a situation in which the energy flow is maximized. One way to design a support that satisfies this requirement is to optimize the shape of the plate, locating its structural modes as far as possible from the operational frequency and first harmonics. In this work, the Finite Element Method (FEM) is used to solve the eigenvalue problem and to parameterize the optimization procedure, which is based on positioning of the nodes of a design region (the plate) in a FEM simplified model. Due to the large number of variables, a gradient-based method is adopted. The objective of the methodology is to maximize the difference between two adjacent eigenvalues near the fundamental operation frequency of the compressor, in order to obtain a large and effective bandgap. A geometrical constraint is imposed to the problem and it is represented by a maximum allowed deformation of the plate. The gradients needed are obtained using elementary stiffness and mass matrices information. The obtained results show that the procedure leads to a new shape which ensures the desired dynamic characteristics for the support plate.