Shape Optimization for Brake Squeal

1. Abstract The present paper describes a solution to a non-parametric shape optimization problem of a brake model suppressing squeal noise. The brake model consists of a rotor and a pad between which the Coulomb friction occurs. A main problem is defined as a complex eigenvalue problem of the brake model obtained from the equation of motion. As an objective cost function, we use the positive real part of the complex eigenvalue causing the brake squeal. The volume of the pad is used as a constraint cost function. The Fréchet derivative of the objective cost function with respect to the domain variation, which we call the shape derivative of the objective cost function, is evaluated using the solution of the main problem and the adjoint problem. A scheme to solve the shape optimization problem is presented using an iterative algorithm based on the H gradient method (the traction method) for reshaping. A numerical result of a simple rotor-pad model illustrates that the real part of the target complex eigenvalue monotonously decreases satisfying the volume constraint. 2.