Brackets are the components that attach one object to other object. It provides structural support for the component. Depending on the type, a bracket can be welded or fastened using fasteners. Proper design and positioning of brackets ensure better performance of the component. Brackets are small in size, but they play a very crucial role in the overall functioning of the components. The presented work deals with the finite element simulation of a bracket that needs to support the load of the diffuser. The simulation is done for the structural analysis. The bracket is made up of structural steel. The work is done to optimize the geometry of the bracket by using topology optimization and design of experiment techniques. Also, the vibration characteristics of bracket design in genset have great effects on the final quality of the product. To determine the vibration characteristics of the bracket, a modal analysis is performed. After performing the optimization, the weight of the bracket is reduced, and the natural frequency of the bracket is increased, which is the main objective of the work.