Magnetic and vibrational amplitude dependences of MRE grid composite sandwich plates

https://doi.org/10.1016/j.ijmecsci.2022.107978Get rights and content

Highlights

  • Both magnetic and vibration amplitude dependent properties are studied.

  • Experimental tests are performed to identify the nonlinear vibration phenomenon.

  • A theoretical model is developed to reveal the nonlinear vibration mechanism.

  • Suggestions are provided to improve vibration control capability of the structure.

Abstract

In this work, both magnetic and vibration amplitude dependent properties of magnetorheological elastomer (MRE) grid composite sandwich plates (MREGCSPs) are investigated. Initially, to prove such a nonlinearly dependent phenomenon, a series of characterization tests are performed on the MREGCSP specimens with different magnetic field intensities and base vibrational amplitudes. Then, using the Jones-Nelson nonlinear material theory, the strain energy density function method, the complex modulus approach, and the Biot-Savart law, the nonlinear material assumption of MRE is defined. A theoretical model consisting of an MRE grid core and two fiber-reinforced polymer (FRP) skins is also proposed to obtain the solutions for the nonlinear frequency, damping, and vibration response parameters, which is based on the modified first-order shear deformation theory, the energy principle, the eigenvalue increment method, the Newmark- beta approach, etc. Finally, a detailed comparison of magnetic and vibrational amplitude dependent natural frequencies, loss factors, and vibration responses is performed to confirm the effectiveness and superiority of the current model over a linear model. This provides a solid basis to reveal the nonlinear dynamic mechanism of the studied smart structure subjected to complex excitation loads. Also, some practical suggestions are summarized for improving its active vibration control capability.

Graphical abstract

Fig. 8. A theoretical model of an MREGCSP structure.

Image, graphical abstract
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Introduction

Due to the diversity and complexity of loading conditions [1], [2], [3], [4], [5], [6], the limitations of composite sandwich structures become increasingly apparent in the aerospace section. As one of the novel integrated multifunctional structures, a magnetorheological elastomer (MRE) grid composite sandwich plate (MREGCSP) has been proven to be helpful in improving the active and passive vibration performances and maintaining relatively good strength and stiffness [7, 8], which plays a vital role in the field of smart vibration control [9], [10], [11], [12]. However, the related research is still in its infancy, especially on the nonlinear dynamic modeling, analysis, control, and experiment of MRE grid composite sandwich structures, since the nonlinear mechanical behavior of MRE without magnetic field effect has been found to be somewhat similar to the one of viscoelastic material [13,14].

During the past years, composite sandwich structures have attracted much attention since their extensive features possess the advantages of better mechanical properties [15,16], multifunctionality [17], and designability [18]. In different studies, these sandwich structures are utilized in such shapes as beams [19], plates [20], and shells [21]. The rapid rise in the application of them has led to the necessity of understanding their static and dynamic mechanical behaviors. As a result, the studies of bending deformation [22], stress and strain [23], buckling [24], and vibration [25] of composite sandwich structures have already been presented by many scholars. In general, the theoretical framework of these studies in the current literature is based on different shear deformation theories, including the classical laminated theory [26], the improved or traditional first-order shear deformation theory [27], the refined higher-order shear deformation theory [28,29], etc.

MRE has gained considerable research interest over the other smart materials in the past two decades due to the high yield strength, low manufacturing cost, active controllability of stiffness and damping, and insensitivity to temperature variation [30,31]. Initially, extensive research has been centered on evaluating the material properties and applications of MRE. After that, theoretical and experimental investigations on the vibration behaviours of MRE-based sandwich structures have been gradually conducted to examine the damping properties and attenuate the vibration efficiently. For instance, based on an experimental method, Demchuk and Kusmin [32] measured the vibration response of an MRE sandwich beam to determine the relationship between the magnetic field and shear modulus of MRE. Zhou and Wang [33] studied the vibration suppression performance of a sandwich beam composed of conductive outer skins and an MRE core under a uniform external magnetic field. Yeh [34] built an analytical model of a plate covered with MRE and constrained layer damping materials. They also estimated the damping performance with various external magnetic fields. By utilizing the finite element method (FEM) and the Ritz approach, Aguib et al. [35] predicted the fundamental frequencies and loss factors of sandwich plates consisting of two aluminum skins and an MRE core at different external magnetic fields. They also validated the calculated results via detailed experimental tests. By employing the FEM, Ramesh et al. [36] performed the free vibration analysis of composite MRE sandwich beams under various boundary conditions. Based on a mathematical model of three-layer sandwich elastomer beams with an MRE core, Dyniewicz et al. [37] suppressed a particular structural vibration mode with a semi-active damping element whose elastic modulus was affected by an external magnetic field. With help of the Lagrange principle and FEM, Kumar and Dwivedy [38] investigated the natural frequencies and modal loss factors of an MRE sandwich plate under different external magnetic fields. To evaluate the vibration suppression properties of composite sandwich beams with magnetorheological honeycomb core, Eloy et al. [39,40] conducted both experimental and numerical investigations on natural frequencies and vibration amplitudes under various external magnetic field energies. Based on the Rayleigh-Ritz approach and FEM, Kobzili et al. [41] compared the natural frequencies and damping parameters of off-axis anisotropic MRE sandwich plates when different magnetic field intensities were considered.

With the deepening of research, many researchers have recently investigated the nonlinear vibrations of composite structures with and without MRE. However, the magnetic and vibrational amplitude dependent behaviors of such structures have been examined separately, with the damping performance being ignored by most of them. For example, based on the FEM, Galerkin's approach, and Von Kármán's assumption, the large amplitude free vibration properties of laminated composite skew plates were analyzed by Singha and Daripa [42]. By considering magnetic field dependence, the frequency response characteristics of an MRE sandwich beam with different steel skin thicknesses were studied by Choi et al. [43]. To analyze the forced vibrations in both time and frequency domains with magnetic field dependence, a mathematical model of MRE sandwich beams with conductive skins was proposed by Nayak et al. [44]. Moreover, the nonlinear parametric resonance phenomenon of such structures with multi-frequency excitation loads was discovered by his team [45]. The stochastic micro-vibration analysis of an MRE sandwich beam was conducted by Ying et al. [46] when it was assumed that the complex shear modulus of MRE could vary with a localized magnetic region. The nonlinear loss factors of an MRE sandwich beam under different magnetic field amplitudes were measured by Chikh et al. [47], in which the nonlinear damping phenomenon was found to be caused by the effect of the loading rate of microscopic ferromagnetic particles in MRE. By considering internal magnetic and temperature dependence, the nonlinear natural frequencies and resonant displacements of composite plates with MRE functional layer were predicted by Li et al. [48]. His-team also developed a nonlinear dynamic model of fiber-reinforced polymer plates, where the amplitude and temperature dependent natural frequencies and damping parameters were successfully solved [49,50]. By using the Jones-Nelson nonlinear theory and the Newton-Raphson iteration method, the nonlinear natural frequencies and vibration responses of fiber metal hybrid plates with amplitude dependence were investigated by Xu et al. [51]. On the basis of first and third order shear deformation theories and von Kármán geometrical nonlinear relations, the nonlinear dynamic responses of electrorheological sandwich circular plates with composite face sheets were predicted by Kong et al. [52] when the pre and post-yield regions are considered.

To date, it is quite clear that there is no study reporting on the nonlinear modeling and analysis of MRE grid composite sandwich plates, especially when both magnetic and vibrational amplitude dependent behaviors are taken into account. This research attempts to fill this knowledge gap. First, to prove the nonlinearly dependent phenomenon associated with magnetic and vibrational amplitude, a series of characterization tests are performed on such plates with different magnetic field intensities and vibration amplitudes. Then, a theoretical model is established based on experimental data and the solution process of nonlinear vibration parameters is clarified. Finally, detailed comparison studies of magnetic and vibrational amplitude dependent natural frequencies, loss factors, and vibration responses are conducted to validate the model developed. This paper can provide a useful model for evaluating the nonlinear natural frequencies, damping ratios, and vibration displacements with consideration of magnetic and vibrational amplitude dependences. Also, some practical suggestions are summarized for improving the active vibration control capability of such structures.

Section snippets

Characterization test

In this section, a series of characterization tests are first conducted on the studied structure with different magnetic field intensities and base vibrational amplitudes, which can demonstrate the existence of such a nonlinearly dependent phenomenon associated with magnetic and vibrational amplitude. Also, the measured data can be employed to validate the proposed model and the related calculation results in Sections 3 and 4.

Theoretical work

Based on the measured data in Section 2, a theoretical model of the MREGCSP structures is established in this section, and the key equations are derived to solve the nonlinear natural frequencies, damping ratios, and resonant displacements, with the magnetic and vibrational amplitude dependences being considered.

Comparison and discussion of calculated and experimental results

In this section, the calculated and measured results of the MREGCSP structures are compared to verify the proposed model in Section 3. Meanwhile, discussions are performed to summarize some useful suggestions for future design, which also helps enhance the active vibration control capability of such structures.

Conclusions

In this paper, a series of characterization tests are performed on the MREGCSP structures, in which the magnetic and vibrational amplitude dependent phenomenon is discovered. Furthermore, a theoretical model is developed to reveal the nonlinear vibration mechanism, with its superiority relative to a linear model being compared and verified. Compared to the measured results of such a smart structure when different S&C regions are controlled, the analysis errors of natural frequencies, damping

CRediT authorship contribution statement

Hui Li: Conceptualization, Methodology, Writing – original draft. Xintong Wang: Formal analysis, Software, Visualization. Zhihan Dai: Formal analysis, Software, Visualization. Yuen Xia: Investigation, Visualization. Sung Kyu Ha: Conceptualization, Supervision. Xiangping Wang: Methodology, Supervision. Yunpeng Ren: Methodology, Formal analysis. Qingkai Han: Conceptualization, Writing – review & editing. Haihong Wu: Writing – review & editing, Supervision.

Declaration of Competing Interest

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Acknowledgments

The authors are grateful for the financial support of the National Natural Science Foundation of China (Grant Nos. 52175079, 12272087), the Key Laboratory of Vibration and Control of Aero-Propulsion System, Ministry of Education, Northeastern University (VCAME202102), the Brain Korea 21 FOUR program at Dept of Mechanical Eng, Hanyang University, the Fundamental Research Funds for the Central Universities of China (Grant No. N2103026), and the China Postdoctoral Science Foundation (2020M680990).

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