Topology Optimization of Constrained Layer Damping Processing Panel with Smooth Boundary Representation

Frequency- and temperature-dependent properties of viscoelastic materials have a significant effect on vibration characteristics of constrained layer damping (CLD) structures. In this article, parametrized level set method (PLSM) is extended to solve the topology optimization problem of CLD plates, in which the viscoelastic material with frequency- and temperature-dependent characteristics is employed as damping core. The single/weighted modal loss factors, which are solved by an iterative method, are defined as objective functions, and topology optimization problem is formulated based on the finite element model for CLD plates which are described by combining parametric level set (PLS) functions. The sensitivities of objective functions with respect to expansion coefficients in PLS are calculated by the use of adjoint vector method. As the optimized results with complex constant shear modulus for viscoelastic core indicates, the proposed method is effective for topology optimization of CLD structures and insensitive to initial design. Numerical examples with the consideration of frequency- and temperature-dependent characteristics for “soft” and “hard” viscoelastic core are implemented. Through comparing the optimal results with different models for viscoelastic core, the influences of frequency- and temperature-dependent characteristics for viscoelastic core on natural frequencies, modal loss factors and optimized layouts are analyzed. Similarity indices are defined for distinguishing the difference among optimized layouts and initial design induced by modal strain energy contour. The optimal design dependence on layer thicknesses is further discussed with additional mass of CLD materials unchanged.

An efficient coupling reduction model-based evolutionary topology optimization method

Structural topology optimization is a crucial approach for achieving lightweight design. An effective topology optimization algorithm must strike a balance between the objective functions, constraints, and design variables, which essentially reflects the symmetry and tradeoff between the objective and constraints. In this study, a topology optimization method grounded in load path theory is proposed. Element bearing capacity is quantified using the element birth and death method, with an explicit formulation derived via finite element theory. The effectiveness in evaluating structural performance is assessed through comparisons with stress distributions and topology optimization density maps. In addition, a novel evaluation index for element bearing capacity is proposed as the objective function in the topology optimization model, which is validated through thin plate optimization. Subsequently, sensitivity redistribution mitigates checkerboard patterns, while mesh filtering suppresses multi-branch structures and prevents local optima. The method is applied for the lightweight design of a triangular arm, with results benchmarked against the variable density method, demonstrating the feasibility and effectiveness of the proposed method. The element bearing capacity seeks to homogenize the load distribution of each element; the technique in this study can be extended to the optimization of symmetric structures.

A Fourier neural operator-based lightweight machine learning framework for topology optimization

Smoothing topology optimization results using pre-built lookup tables

This work presents a new analytical model for constrained layer damping (CLD). CLD is an effective vibration suppression approach. Unfortunately, most of the existing research involving analytical models for constrained layer damped structures considered the simple beam structure and are therefore not applicable for many real systems. As a result, it is important to be able to model the CLD of structures like plates and improve both the accuracy and versatility of the predictions. Most existing research assumes that shear deformation of the damping layer is the dominant source of damping, despite the fact that some research has noted that this assumption is often not valid. To address these needs, this work provides development of an analytical model for a three-layer CLD plate structure. Unlike previous models, this analytical model treats the three-layer plate as not only having shear deformation, but also as having longitudinal extension and transverse compression deformation in the damping layer. Because of these new considerations, all types of damping in the intermediate layer have been taken into account. This newly developed analytical mode is validated by comparing it with experimental data from published literature. Then, a parametric study between this newly developed compression plate analytical model and another newly developed plate analytical model that neglects compression damping is conducted in order to explore the impact of some design parameters on the structure's modal characteristics. For cases when the face layers have different thicknesses, it is shown that it may be necessary to include the transverse compressional damping component to provide an accurate prediction of the natural frequencies and loss factors.

This study proposes a new element-based method to solve structural topology optimization problems with non-uniform meshes. The objective function is to minimize the compliance of a structure, subject to a volume constraint. For a structure of a fixed volume, the method is intended to find a topology that could almost conform to the compliance minimum. The method is refined from the evolutionary switching method, whose policy of exchanging elements is improved by replacing some empirical decisions with ones according to optimization theories. The method has the evolutionary stage and the element exchange stage to conduct topology optimization. The evolutionary stage uses the evolutionary structural optimization method to remove inefficient elements until the volume constraint is satisfied. The element exchange stage performs a procedure refined from the element exchange method. Notably, the procedures of both stages are refined to conduct non-uniform finite element meshes. The proposed method was implemented to use the Abaqus Python scripting interface to call the services of Abaqus such as running analysis and retrieving the output database of an analysis. Numerical examples demonstrate that the proposed optimization method could determine the optimal topology of a structure that is subject to a volume constraint and whose mesh is non-uniform.

A hybrid passive/active noise control system utilizing constrained layer damping and model predictive feedback control is presented. This system is used to control the sound radiation of panels due to broadband disturbances. To facilitate the hybrid system design, a methodology for placement of constrained layer damping which targets selected modes based on their relative radiated sound power is developed. The placement methodology is utilized to determine two constrained layer damping configurations for experimental evaluation of a hybrid system. The first configuration targets the (4,1) panel mode which is not controllable by the piezoelectric control actuator, and the (2,3) and (5,2) panel modes. The second configuration targets the (1,1) and (3,1) modes. The experimental results demonstrate the improved reduction of radiated sound power using the hybrid passive/active control system as compared to the active control system alone.

The synthesis of structural health monitoring and vibration control is important in order to provide facilities for constructing smart structures. In recent years, some techniques have been developed to integrate structural identification and optimal vibration control. However, it is still challenging to integrate the identification and vibration control of time-varying structures subject to unknown earthquake excitation. The main difficulties are that structural dynamic responses collected by a simple harmonic motion system are absolute responses under unknown earthquake ground motion while previous identification approaches for unknown external excitation are not applicable for this situation and the need of an efficient algorithm to accurately track the various scenarios of time-varying structures with inexpensive computation to ensure the real-time performance requested by structural vibration control. In this paper, a novel algorithm is presented, in which structural time-varying parameters are treated as ‘virtual unknown inputs’ to the underlying time-invariant structure, a generalized Kalman filter with unknown inputs is proposed for joint identification of joint structural state, unknown earthquake excitation and ‘virtual unknown inputs’ with only partially measured structural absolute responses, and the identification results are integrated in real-time with the instantaneous optimal control scheme to reach the goal of optimal semi-active control provided by magneto-rheological dampers. Some numerical examples of integrated identification and vibration control of various time-varying structures subject to unknown earthquake excitation are used to demonstrate the performances of the proposed algorithm.

In this work, we present an adaptive feature-driven topology optimization method with the adaptability realized by using the well-known SIMP method. The proposed new method inherits the merits of both the feature-driven approach and SIMP method, and optimized results with clear and smooth boundaries can therefore be obtained without initial layout dependence. Specifically, in the early stage of optimization design, engineer features (i.e. design primitives) are systematically introduced into the design domain according to the sensitivity analysis result of the SIMP method, in view of its high numerical stability and strong versatility; and in the final stage, the topology optimization is implemented based solely on the feature-driven method, so that the high-quality design result can be achieved with very few variables. The transition between the two methods is carried out automatically by a novel volume restriction scheme, in which the structural volume obtained by the SIMP approach is limited to the difference between the prescribed maximum volume and the features’ total volume. It should be noted that the number and volume of engineer features are quite small at first several iterations, hence the effective force transferring path could not be formed just by using these features. But benefiting from the proposed volume restriction scheme, the connection between the load application and the displacement constraint positions can always be guaranteed because the optimization design is dominated by the SIMP method at initial iterations. The superiority and universality are demonstrated by typical numerical examples including the topology optimization design of the stiffest structure and compliant mechanism.KeywordsFeature drivenSIMPTopology optimizationAdaptabilityVolume restriction

ACTIVE VIBRATION CONTROL AND SUPPRESSION FOR INTELLIGENT STRUCTURES

Topology optimization has been considered as a promising tool for conceptual design due to its capability of generating innovative design candidates without depending on the designer's intuition and experience. Various optimization methods have been developed through the years, and one of the promising options is the level-set-based topology optimization method. The benefit of this alternative method is that the design is characterized by its clear boundaries. This advantage can avoid postprocessing work in conventional topology optimization process to a large extent and realize direct integration between topology optimization and additive manufacturing (AM). In this paper, practical algorithms and a matlab-based open source framework are developed to seamlessly integrate the level-set-based topology optimization procedure with AM process by converting the design to STereoLithography (STL) files, which is the de facto standard format for three-dimensional (3D) printing. The proposed algorithm and code are evaluated by a proof-of-concept demonstration with 3D printing of both single and multimaterial topology optimization results. The algorithm and the open source framework proposed in this paper will be beneficial to the areas of computational design and AM.

The topology optimization design for continuum structures based on the element free Galerkin method

The synthesis of structural identification with vibration control is cost-effective and beneficial for developing smart building structures. In the past several decades, techniques have been put forward for the combination of structural identification and vibration control. However, it is still a challenging task to synthesize identification and vibration control of time-varying structures under unknown earthquake excitation. First, structural dynamic responses collected by a structural health monitoring (SHM) system are absolute responses under unknown earthquake excitation, so existing identification approaches for unknown external excitations are not applicable for this situation. Moreover, it is essential to have an efficient algorithm for accurately tracking the various scenarios of time-varying structural physical parameters with inexpensive computation to ensure the real-time performance requested by structural vibration control. In this paper, an algorithm is put forward to tackle this challenging problem. It is proposed to treat structural time-varying effect as “virtual unknown inputs” to the corresponding time-invariant structure. A generalized extended Kalman filtering with unknown input (GEKF-UI) is proposed to circumvent the limitations of the existing EKF-UI approaches. The proposed GEKF-UI can simultaneously identify structural system, unknown earthquake excitation, and the “virtual unknown inputs” using only partially measured structural absolute responses. Then, the identified structural state is synthesized in real time with the instantaneous optimal control strategy for optimal semiactive control provided by magnetorheological dampers. Therefore, the proposed algorithm can track various structural time-varying with much less computation, which is more suitable for synthesis with structural control compared with other existing approaches. Some numerical cases of synthesizing identification and vibration control of various type time-varying structures under unknown earthquake motion are adopted to investigate the feasibilities of the proposed algorithm.

Active damping can be generated in a number of ways, the most obvious one being applying a force to the structure which is proportional to the velocity at a point on the structure. Another technique is to actively increase the damping of a structure by using a passive damping element i.e. dissipate the energy of vibration by increasing the relative motion of the structure with respect to the passive damping element. A practical way to achieve this is by using constrained layer damping (CLD). It is well known that CLD is effective because of the relative motion of the structure and the constraining layer which produces extra shear in a layer of viscoelastic material. The work described in this paper is concerned with controlling the strain of the constraining layer of a composite structure in such a way as to enhance the shear generated in the viscoelastic material and hence improve the overall damping of the composite structure. If the control law selected forces the constraining layer to move 180 degrees out of phase with the structure then the viscoelastic damping layer undergoes maximum shear and active damping is achieved. The results have indicated that this concept of active damping produces very effective levels of vibration suppression. In the case of cantilever beams the first two modes can be almost eliminated when velocity feedback of the beam tip is used. The results show that the addition of active control and passive damping in a single structure combines the advantages of passive damping in the higher modes and active control in the lower modes. In addition active damping as defined in this paper produces a fail safe mechanism in case of instability occurring in the feedback system since passive damping is always present.