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This article investigates topology optimization for piezoelectric thin-shell structures under the linear quadratic regulator optimal control. In the optimization model, the structural dynamic compliance is taken as the measure of control performance, and the relative densities describing the distribution of the piezoelectric material are considered as design variables. An artificial material model with penalization on both mechanical and piezoelectric properties is employed. For the purpose of improving computational efficiency of the sensitivity and response analysis, modal superposition method is adopted. The derivative of the Riccati equation governing the linear quadratic regulator control with respect to the design variables is shown to be a Lyapunov equation. In conjunction with the adjoint variable method, the design sensitivities of the dynamic compliance are obtained using the solution of the Lyapunov equation. Numerical examples demonstrate the validity of the proposed method and show the significance of layout design of piezoelectric sensors/actuators. The influences of some key factors on the optimization solutions are discussed. It is shown that the optimized layout of the piezoelectric patches may be significantly influenced by the excitation frequency, but only slightly affected by the choice of the weighting matrix in the linear quadratic regulator control. This work aims to provide an efficient gradient-based mathematical programming method for guiding the layout design of actuators and sensors in smart structures under optimal vibration control. However, the considered model is a purely mathematical one without consideration of engineering realization, thus the optimization result may only serve as an upper bound for practically realizable control performance. [ABSTRACT FROM AUTHOR]

It is often desirable to simultaneously optimize the damping and stiffness distribution in the design of shell structures incorporating damping material layers for achieving the best vibration mitigation performance. This paper investigates the integrated topology optimization of host structures and damping layers for reducing the vibration level in the presence of harmonic excitations. Therein, the global damping matrix is a nonproportional one due to distributed damping effects. For an efficient frequency response analysis of the system with nonproportional damping, reduced-order equations are obtained by using lower-order eigenvectors of the undamped system, and then the method of complex mode superposition is employed for solving the dynamic equations in the state space. In the optimization model, the vibration amplitudes at specified positions are taken as the objective function. The relative densities of the elements are considered as design variables, and an artificial damping material model relating the local damping properties to the elemental density variables is employed. The Rational Approximation of Material Properties model is adopted to avoid localized modes in low-density areas during the optimization process. Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed framework. [ABSTRACT FROM AUTHOR]

This article 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 relative densities of the elements in the actuator layer and the sensor layer are considered as topological design variables. The optimization problem is then formulated by using an artificial material model with penalization for both mechanical and piezoelectric properties. It is pointed out that the global-level damping property, consisting of the structural damping and the active damping effects, is a nonproportional one. 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 sensitivity analysis scheme is also derived. The effectiveness and efficiency of the proposed method are demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]

The mechanism and the characteristics of the cable-deck coupled nonlinear vibration in a cable-stayed bridge are studied using numerical methods. A simple three-degrees-of-freedom (d.f.) model, with one independent d.f. for modeling the bridge deck movement, is proposed for describing the nonlinear interactions between the in-plane/out-of-plane vibration of the cable and the oscillation of the bridge deck. The governing equations are discretized with the Galerkin method and then solved with a numerical time integration algorithm. It is pointed out that the periodic variation of cable tension caused by vibration of a bridge deck will lead to the parametric resonance of the stay cable under certain tuning conditions. Numerical results also confirm that energy transfer between different vibration modes and beating phenomenon of the cable-deck vibration may be exhibited in the case of parametric resonance. [ABSTRACT FROM PUBLISHER]

This article presents a study on topology optimization of planar piezoelectric actuators assembled with repetitive component patterns. Repetitive configuration has the advantage of ease of engineering implementation, especially for relatively slender structures. For realizing this concept in the design of piezoelectric actuators, topology optimization techniques are employed for seeking the optimal layout within the design domain of the structural components. The design objective is to maximize the work delivered by the displacement output port, while constraints are imposed on the actuation energy consumption and the material volume. Both the distributions of the actuation voltage and the topologies of the host layer and the piezoelectric layers are optimized. Power-law penalization functions are used to suppress intermediate values of material densities and actuation voltage. Numerical techniques for a sensitivity analysis of structural response are presented, and the proposed optimization problem is solved with a gradient-based mathematical programming approach. Two numerical examples are given to demonstrate the applicability of the proposed approach. Compared with the method directly treating the whole design domain, this approach is shown to have a better convergence behavior and is able to provide final topologies that are better acceptable from engineering point of view. [ABSTRACT FROM PUBLISHER]