Dynamic Topology Optimization Of Damping And Active Controlled Structures

Control of structural vibration and noise has gained extensive attention by scientists and engineers. In particular, passive vibration control of shell structures by incorporating damping layers into the host structure and active vibration control of thin-shell structures by arranging the spatial distribution of piezoelectric actuator/sensor patches have received ever-increasing attention. It is obviously that applying a full-coverage damping layer or piezoelectric material layer treatment into a structure will add excessive mass and affect control performance. To achieve the best control performance, finding the optimal layouts of the damping layers or the piezoelectric actuators/sensors patches in the vibrating structures becomes highly important.For structures partially covered with damping material or piezoelectric material, the whole structure presents non-proportional damping properties, that will bring great difficulties in structural vibration analysis and sensitivity analysis, and this dissertation just efforts to resolve this problem. Base on the idea of topology optimization design, the topology optimization of damping layer in vibrating structures for minimizing structural vibration and sound radiation, integrated topology optimization of host structures and damping layers, topology optimization of piezoelectric layers or their electrode coverage with active vibration control for reducing the frequency response and transient response are investigated in this dissertation. The main content and results are obtained as follows:1. The topology optimization of damping layer and host structures for reducing the structural vibration, we consider the topology optimization problem for layout design of the damping material surface layer and simultaneously optimize the damping and stiffness distribution with the aim to reduce the vibration amplitude under harmonic excitations. An artificial damping model with penalization on intermediate density values is proposed for acquiring a clear black-and-white damping material distribution. The structural system with a partially-covered damping layer has a non-proportional global damping matrix. For alleviating the computational burden involved in the frequency response analysis, the dynamic equations are solved with the complex mode superposition in the state space after a model reduction transformation. In this context, the adjoint-variable scheme for the design sensitivity analysis is derived.2. Topology optimization of damping layers for minimizing sound radiation of shell structures. This dissertation investigates acoustic sensitivity analysis and topology optimization of attached damping layers for minimizing sound radiation of a vibrating structure under harmonic excitations. The vibrating structure is discretized with the finite element method, while the exterior acoustic analysis is implemented by using the boundary element method. In this context, an adjoint variable scheme for the design sensitivity analysis of sound pressure is developed. In the optimal design problem, the design objective is to minimize the structural vibration-induced sound pressure at a specified point in the acoustic medium by distributing a given amount of damping material. The optimal structural topologies obtained under different damping coefficients, excitation frequencies and reference point positions are also compared.3. Topology optimization of piezoelectric layers in plates with active vibration control. This dissertation investigates topology optimization of the piezoelectric actuator and sensor layers in a plate for achieving the best vibration control performance. Therein, the actuator patches and sensor patches are symmetrically attached to the host layer, and the classical negative velocity feedback control strategy is adopted for reducing the vibration level of the structure. In the optimization model, the dynamic compliance under a specific excitation frequency or the aggregated dynamic compliance in a given frequency range is taken as the objective function. The optimization problem is then formulated by using an artificial material model with penalization for both mechanical and piezoelectric properties. In this context, the sensitivity analysis scheme is also derived.4. Topology optimization of electrode coverage of piezoelectric thin-walled structures with active control for minimizing sound radiation. This dissertation develops a topological design method of surface electrode distribution over piezoelectric sensors/actuators attached to a thin-walled shell structure for reducing the sound radiation in an unbounded acoustic domain. In the optimization model, the sound pressure norm at specific reference points under excitations at a certain excitation frequency or in a given frequency range is taken as the objective function. The pseudo densities for indicating absence and presence of surface electrodes at each element are taken as the design variables, and a penalized relationship between the densities and the active damping effect is employed. The applied voltage on each actuator is determined by the constant gain velocity feedback (CGVF) control law.5. Dynamic topology optimization of piezoelectric structures with active control for reducing transient response. This dissertation investigates topology optimization of the piezoelectric actuator/sensor coverage attached to a thin-shell structure to improve the active control performance for reducing the dynamic response under transient excitations. The structural dynamic response under the corresponding active damping effect is evaluated with a direct time integration method. In the mathematical formulation of the considered topology optimization model, the time integral of the displacement response over a specified time interval of interest is taken as the objective function. The adjoint-variable sensitivity analysis scheme for a general integral function within a given time interval is derived, which facilitates a gradient-based mathematical programming solution of the optimization problem. Numerical examples demonstrate that the proposed method can generate meaningful optimal topologies of piezoelectric layers. The proposed method can be used for providing useful guidance to the layout design of the actuator/sensor layers attached to a thin-shell structure subject to dynamic excitations, in particular impact forces.