Optimal design of metallic corrugated sandwich panels with polyurea-metal laminate face sheets for simultaneous vibration attenuation and structural stiffness
Introduction
Ultralight all-metallic sandwich constructions with periodic lattice cores possess versatile features that are technically important for innovating engineering structures [1]. They not only outperform monolithic/stiffened structures of the same mass in stiffness and strength, but also provide additional attributes, such as thermal transport [2], sound insulation/absorption [3], blast/impact resistance [4], anti-penetration [5]. With ever-rising need for passive vibration attenuation, structural damping has drawn burgeoning attention. For example, engineering structures (e.g., ship hulls, automotive bodies, pulse detonation engines, and the like) often serve in a vibration-rich environment, which may lead to severe structural damage (induced by resonant vibration or high cycle fatigue) and even passenger discomfort. However, due to intrinsically low loss factor of most metal materials [6], [7], all-metallic sandwich constructions do not work well in passively controlling undesirable external vibration. Thus, how to enhance the vibration and damping properties of all-metallic sandwich structures by modifying their face sheets and cores becomes a necessity.
Of particular relevance to the current study is the method of viscoelastic layer treatment [8], [9], which has been envisioned as an effective approach to achieve higher structural damping. To date, the two most widely-used configurations are the base/viscoelastic/base laminate with constrained layer damping (CLD) [8] and the viscoelastic/base laminate with free layer damping (FLD) [9]. The former exhibits a greater capacity for vibration attenuation due to transverse shear deformation of the viscoelastic layer, while the latter almost relies on both in-plane extension and compression deformation to dissipate vibration energy [10]. Theoretically, existing modelling efforts [11], e.g., the Guyader model [12], [13], the RKU model [14] and the Lamb wave model [15], have broadened insights into physical mechanisms underlying the CLD treatment. Besides, the vibration and instability phenomena associated with layered structures could be accurately investigated via numerical tools [16], [17], [18], [19], [20]. More recently, the CLD treatment was introduced to construct a hybrid face sheet for all-composite lattice-core sandwich structures [21], [22], [23]: upon sandwiching the fiber-reinforced composite face sheet with thin viscoelastic layers, the damping and stiffness efficiency of the sandwich structure was dramatically improved. However, thus far, few studies concerned the vibration/damping characteristics of all-metallic sandwich panels with 2D/3D lattice truss cores. This deficiency was squarely addressed in our prior study by replacing the monolithic metallic face sheets with polyurea-metal laminate (PML) ones [24].
Upon our recent work [24], novel laser-welded corrugate-core (LASCOR) sandwich panels with polyurea-metal laminate (PML) face sheets were fabricated, tested and numerically simulated using the method of finite element - modal strain energy (FE-MSE). Results demonstrated remarkable improvement of damping loss factors, quantitatively by as large as 10 times. However, a decline in natural frequencies was also observed, implying undesirable variation of structural stiffness and weight. In recent years, multifunctional sandwich constructions with high stiffness, lightweight and other functionalities (e.g., vibration damping, heat dissipation, energy absorption) have become increasingly attractive. To date, previous literatures as well as our own work have mainly focused on exploring the structural novelty and damping mechanisms of lattice-cored sandwich structures, with little attention devoted to setting up an optimization framework for simultaneous vibration attenuation and structural stiffness. For example, while both damping and stiffness efficiency of all-composite lattice-core sandwich structures were accounted for by Yang et al. [25], they did not carry out the corresponding multi-objective optimization; the optimization of Aumjaud et al. [26], [27] focused on vibration damping and added mass of novel DSLJ-inserted honeycomb-core sandwiches, but not structural stiffness. Therefore, multi-objective optimization combining stiffness, damping, and weight of all-metallic lattice-core sandwich panels remains elusive.
Recently, incorporating the technique of surrogate modeling with optimization algorithms has advanced the applications of multi-objective optimal designs [28], [29]. On one hand, coupling optimization algorithm with full numerical simulation usually requires a large amount of computational effort, burdens a high risk of premature simulation crash, and thus may be inefficient. On the other hand, deriving an exact equation to express the highly nonlinear relationship between a specific design objective and design variables is often difficult. Based on the principle of sampling estimation, the surrogate modeling technique is expected to overcome the above two barriers of optimal designs by bridging design objectives and variables. Nowadays, the commonly used surrogate models (sometimes also called machine learning models) include response surface (RS), radial basis function (RBF), kriging (KRG), orthogonal polynomial (OP), artificial neural network (ANN), support vector regression (SVR), and so on. For instance, concerning the optimization of sandwich structures, the RS model was implemented into the multi-objective optimal design of peak force and specific energy absorption for all-metallic truncated conical sandwich shells with corrugated cores [30], while the KRG model was adopted to develop a optimization scheme of blast resistance and structural weight for foam-core sandwich panels [31].
In this work, surrogate modeling was also selected to perform the multi-objective, multi-variable optimization task. The scope was to provide a comprehensive understanding of novel LASCOR sandwich panels with PML face sheets: (i) sensitivity of natural frequencies and damping loss factors to key geometric parameters, (ii) accuracy of surrogate model for the first damping loss factor, and (iii) multi-objective optimization framework of simultaneous vibration attenuation and structural stiffness with key geometric parameters as design variables. The paper was organized as follows. Section 2 reviewed briefly experiments carried out in our previous work [24]. Section 3 introduced the numerical simulation principle of FE-MSE method, with frequency-dependent mechanical behaviors of viscoelastic polyurea considered. How key geometric parameters affected natural frequencies and damping loss factors of LASCOR sandwich panels with PML face sheets were systematically investigated in Section 4. The superiority of such novel panels over monolithic panels having equal mass was also highlighted. Section 5 analyzed the fidelity of surrogate model on damping loss factor, and proposed a series of optimization problems to explore superior performance of structural stiffness and vibration attenuation.
Section snippets
Review of experiments
In a previous study [24], LASCOR sandwich panels with PML face sheets were proposed and fabricated, and their effectiveness for passive vibration suppression was systematically estimated. For completeness of the current study, relevant fabrication process and experimental results were briefly reviewed below.
FE-MSE method
In order to predict the vibration damping features of LASCOR sandwich panels with PML face sheets, a combined finite element-modal strain energy (FE-MSE) method was employed based on the commercial FE code ABAQUS/CAE 2016.
Firstly, we construct the FE models of LASCOR sandwich panels with PML face sheets with their detailed geometric parameters illustrated in Fig. 2. Both the face sheets and the corrugated core were modeled using the linear 4-node shell element S4R, while the polyurea layers
Parametric study
In this section, a comprehensive parametric investigation on the vibration damping characteristics of LASCOR sandwich panels with PML face sheets was carried out to determine the optimization variables. From the experimental results (Fig. 4), specimen S-6 with two symmetric PML-A face sheets exhibited the best performance in passive vibration suppression. As the corresponding damping enhancement mechanisms had already been explored [24], the present parametric study and further multi-objective
Optimal design
An optimum structure is expected to combine high structural stiffness, high capacity of passive vibration and lightweight. To this end, the optimal design of LASCOR sandwich panels with two symmetric PML-A skins (Fig. 8) for combined vibration damping and structural stiffness were carried out in this section. Based on the commercially available mathematics software MATLAB R2019b, the flow chart of the current optimization was presented in Fig. 13.
Concluding remarks
With focus placed upon laser-welded corrugated-core (LASCOR) sandwich panels with polyurea-metal laminate face sheets (PML) face sheets, this study aimed to reveal the sensitivity of the vibration damping characteristics and propose a multi-objective optimization framework factoring vibration attenuation, structural stiffness and total weight of these novel multifunctional sandwich constructions. For enhanced calculation efficiency, surrogate modeling was validated and implemented into the
CRediT authorship contribution statement
Xin Wang: Conceptualization, Methodology, Writing - original draft, Writing - review & editing. Xue Li: Investigation, Data curation. Zeng-Shen Yue: Investigation, Software. Run-Pei Yu: Methodology. Qian-Cheng Zhang: Formal analysis, Writing - review & editing. Shao-Feng Du: Validation. Zhi-Kun Yang: Resources. Bin Han: Investigation. Tian Jian Lu: Supervision, Conceptualization, Funding acquisition, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by National Key Research and Development Program of China (2017YFB1102801), National Natural Science Foundation of China (12072250, 11972185, 12002156 and 11902148), China Postdoctoral Science Foundation (2020M671473), Open Project for Key Laboratory of Intense Dynamic Loading and Effect (KLIDLE1801), Aviation Science Foundation Project (20170970002), Natural Science Fund Project in Jiangsu Province (BK20190392), and Open Fund of State Key Laboratory of Mechanics and
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