Magnetic and vibrational amplitude dependences of MRE grid composite sandwich plates
Graphical abstract
Fig. 8. A theoretical model of an MREGCSP structure.
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).
References (74)
- et al.
Free vibration analysis of a rotating graphene nanoplatelet reinforced pre-twist blade-disk assembly with a setting angle
Appl Math Model
(2021) - et al.
Design and dynamic characteristics of a double-layer permanent-magnet buffer under intensive impact load
J Sound Vib
(2021) - et al.
Thermal vibration analysis of functionally graded conical-cylindrical coupled shell based on spectro-geometric method
Thin Wall Struct
(2022) - et al.
A novel diagnosis indicator for rub-impact of rotor system via energy method
Mech Syst Signal Pr
(2023) - et al.
Vibration and damping study of multifunctional grille composite sandwich plates with an IMAS design approach
Compos Part B
(2021) - et al.
Magnetorheological elastomer composites: modeling and dynamic finite element analysis
Compo Struct
(2020) - et al.
A new type of nonlinear hysteretic model for magnetorheological elastomer and its application
Mater Lett
(2021) - et al.
Stability analysis of multifunctional smart sandwich plates with graphene nanocomposite and porous layers
Int J Mech Sci
(2020) - et al.
Cell-size graded sandwich enhances additive manufacturing fidelity and energy absorption
Int J Mech Sci
(2021) - et al.
A multifunctional honeycomb metastructure for vibration suppression
Int J Mech Sci
(2020)
Wave propagation analysis of a ceramic-metal functionally graded sandwich plate with different porosity distributions in a hygro-thermal environment
Compos Struct
The plastic behavior of sandwich beams with core gradation
Int J Mech Sci
Bending of symmetrically sandwich beams and I-beams – analytical study
Int J Mech Sci
Influence of the visco-Pasternak foundation parameters on the buckling behavior of a sandwich functional graded ceramic–metal plate in a hygrothermal environment
Thin Wall Struct
Free vibration of composite sandwich plates and cylindrical shells
Compos Struct
A semi-analytical method for vibration analysis of functionally graded (FG) sandwich doubly-curved panels and shells of revolution
Int J Mech Sci
A review on magneto-mechanical characterizations of magnetorheological elastomers
Compos Part B Eng
Use of magnetorheological elastomer in an adaptive sandwich beam with conductive skins, Part I: magnetoelastic loads in conductive skins
Int J Solids Struct
Dynamic behavior analysis of a magnetorheological elastomer sandwich plate
Int J Mech Sci
Semi-active control of a sandwich beam partially filled with magnetorheological elastomer
Mech Syst Signal Proc
Dynamic analysis of MRE embedded sandwich plate using FEM
Proc Eng
Modeling and simulation of the static and vibratory behavior of hybrid composite plate off-axis anisotropic
Compos Struct
Nonlinear vibration of symmetrically laminated composite skew plates by finite element method
Int J Non-L Mech
Dynamic analysis of magnetorheological elastomer-based sandwich beam with conductive skins under various boundary conditions
J Sound Vib
Multi-frequency excitation of magnetorheological elastomer-based sandwich beam with conductive skins
Int J Non-Linear Mech
Stochastic micro-vibration response analysis of a magnetorheological viscoelastomer based sandwich beam under localized magnetic fields
Appl Math Model
Dynamic analysis of the non-linear behavior of a composite sandwich beam with a magnetorheological elastomer core
Acta Mech Solida Sin
A nonlinear analytical model of composite plate structure with an MRE function layer considering internal magnetic and temperature fields
Comp Sci Tech
Modeling of amplitude dependent damping characteristics of fiber reinforced composite thin plate
Appl Math Model
A nonlinear vibration model of fiber metal laminated thin plate with amplitude dependent property
Appl Acous
On the vibrations of the electrorheological sandwich disk with composite face sheets considering pre and post-yield regions
Thin Wall Struct
Detection of blade substrate crack parameters of hard-coated blisk based on mistuning identification technology
Mech Syst Signal Pr
An iterative method for identification of temperature and amplitude dependent material parameters of fiber-reinforced polymer composites
Int J Mech Sci
A nonlinear dynamic model of fiber-reinforced composite thin plate with temperature dependence in thermal environment
Compos Part B
Nonlinear vibration characteristics of fibre reinforced composite cylindrical shells in thermal environment
Mech Syst Signal Pr
Nonlinear vibration analysis of fiber metal laminated plates with multiple viscoelastic layers
Thin-Walled Struct
Microplasticity behavior of multiphase high-strength nanobainitic steel based on a modified law of mixtures
Mater Sci Eng A
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