International Journal of Applied Mechanics

Static deformation for thermo-magneto-electro-elastic (TMEE) micro-/nano-beams subjected to applied load is investigated in this paper based on Timoshenko beam model incorporating the extended modified couple stress theory (MCST). Conventional material coefficients are converted into alternative ones, electric potential, magnetic potential, and thermal entropies are solved analytically based on Maxwell equations and heat equation. Governing equations for the TMEE Timoshenko micro-/nano-beams are derived for the first time by using the principle of minimum total potential energy, a 50% BaTiO₃–CoFe₂O₄ bilaminate is demonstrated as an example, validity and efficiency are examined. It is found that microstructure effect (MCST) causes the deflections to decrease, and extra equivalent rigidity due to the existence of thermal/pyroelectric/pyromagnetic terms tends to weaken the beam structure. Meanwhile, the magnitude for electric/magnetic potential is bigger than that based on pure MEE modeling, in addition, deflections with couple stress are found to be smaller than those without couple stress especially for very thin structures.

This research presents a novel design method for mechanical metamaterials with programmable Poisson’s ratio. Poisson’s ratio of metamaterials can be quantitatively controlled by geometric parameters such as the side length of the rhombus, rhombus angle, and reentrant angle. The parametric study was conducted through finite element method (FEM) analysis, revealing the influence of geometric parameters on Poisson’s ratio and nominal modulus. The FEM results have a good agreement with the experiments. Additionally, based on the design concept of nonuniform stiffness, we have designed different structural parameters for different areas to achieve multiple Poisson’s ratio effects within the same structure. Ultimately, two types of nonuniform stiffness metamaterials, featuring distinct three Poisson’s ratios and asymmetrical Poisson’s ratios were obtained, respectively. This work expands the design methods in the research of programmable Poisson’s ratio metamaterials and provides guidance for the design of nonuniform stiffness lattice structures with tunable Poisson’s ratio.

In this paper, a cross-hole fractal phononic crystal (CHF-PnC) structure is proposed, which consists of vertical cross-holes repeating their original shapes in a certain ratio. Using the finite element method, the complex energy band curves and frequency responses of the CHF-PnC are calculated, and three complete bandgaps with strong attenuation characteristics are obtained, with bandwidths of 193.4, 55.7 and 216.8 MHz, respectively. The mechanism of the generation of the bandgap of the CHF-PnC structure is analyzed, and the sensitivities of the geometrical parameters W and $𝜃$ to the band gap are investigated. Subsequently, applying this structure to piezoelectric microelectromechanical systems (MEMS) resonators, it is found that the anchor point loss quality factor ($Q_{\mathrm{\text{anc}}}$) of the CHF-PnC resonator is 116,951.5% higher than the conventional resonator when a 6-row × 5-column combination is used. In addition, compared to the conventional resonator, the CHF-PnC resonator has a 69.7% reduction in insertion loss and a 3.6-fold improvement in unloaded quality factor, while maintaining the same electromechanical coupling coefficient.

The problem of the propagation of Love waves in multilayers of generalized magneto-thermoelastic materials has been investigated using Haskell matrix method. The dispersion relations for the Love waves are derived for the topmost layer with the help of appropriate conditions. We have observed that there are two wavefronts of Love-type surface waves: the first wavefront is due to the electro-magnetic parameters and the second wavefront appears due to the thermal parameters. The dispersion curves of both these fronts are computed for two and three layers and results are represented graphically. The phase velocity corresponding to first wavefront is non-attenuating, while that of second wavefront is attenuating. The 3D pictures of displacement, conductive temperature and heat flux have shown that transverse displacement, conductive temperature and heat flux are sinusoidal natures.

Designing structures that can isolate specified frequency ranges of vibration or noise while maintaining sufficient stiffness presents a significant challenge. Since locally resonant acoustic metamaterials (LRAMs) can create subwavelength bandgaps, this work proposes a multiscale topology optimization method for such structural designs utilizing multiple types of LRAM cells. To achieve the objectives, the methodology aims to minimize the dynamic responses at a specified point and the structural compliance at the macroscale. At the microscale, it aims to design microstructures with specified bandgaps and minimize macrostructural compliance. Compared to most existing methods, the LRAM design incorporated at the microscale in this approach can create specified bandgaps, enhancing the ability to control vibration isolation. The use of multiple types of LRAMs with bandgaps across different frequency ranges can extend the vibration isolation to a wider frequency range. Since the macrostructures consist of multiple microstructures and the microstructures are composed of various materials, a parameterized level-set-based multi-material approach is employed to optimize the topologies at both scales. The bandgap analysis during optimization is conducted using a homogenization framework. The efficacy of the method is demonstrated through numerical examples, which successfully generate structures capable of isolating vibrations within specified frequency ranges while maintaining minimal compliance. The method shows significant potential to design structures that are capable of effectively attenuating vibrations within a specified frequency range while maintaining load-bearing capacity.

The distinguishing response ratio between the impulsive loadings and macroscale materials is one of the main challenges to develop efficient energy-dissipative materials. A multiscale cellular solid–fluid composite (SFC) consisting of open-cell metallic foam and nanofluidic composite (NLC) is developed and analyzed in this work. The effects of strain rate, pore size, and skeletal materials are performed experimentally to determine the mechanical response and energy absorption of SFCs under quasi-static and dynamic compressions. The results demonstrate that the intrinsic property of skeletal foams determines the quasi-static responses of SFCs. The mechanical response and macroscale failure modes are insensitive to the strain rate, while the yield stress of SFCs experiences a noteworthy increase of more than 1000% at elevated strain rates, indicating the excellent potential for various dynamic scenarios. The enhancement effect is significantly determined by the nanofluidic behavior, which is confirmed to have a considerable influence on the energy absorption capacity. Across a wide range of strain rates, the energy absorption of SFCs is categorized into three phases based on the distinct solid–fluid interactions, where the plastic domain, along with weak and strong multiscale solid–fluid synergistic interactions, are identified as the key mechanisms of response and energy absorption. This study deepens the understanding of multiscale SFCs and offers significant strategic insights and inspiration for developing efficient and hierarchical energy-absorbing materials.

Elastic metamaterials, renowned for their ability to control elastic waves, have garnered widespread scholarly attention in recent years. In the field of bandgap engineering, designing the unit cell structure of an elastic metamaterial focuses on achieving a lower opening frequency and a higher relative bandwidth for the first local resonance bandgap (LRBG), while maintaining practical structural considerations. This study explores the effect of the spiral rod on the relative bandwidth of the first LRBG and proposes a spiral rod–mass 3D unit cell structure (SMS). Numerical band structure calculations reveal that the corresponding metamaterial possesses an LRBG with an exceptionally low frequency and a relative bandwidth of 150%. Furthermore, the analysis demonstrates that the opening and closing frequencies of the first LRBG in the proposed SMS can be adjusted independently, enriching the bandgap characteristics of the structure. To achieve this, we develop a scheme to independently adjust the opening and closing frequencies of the first LRBG by modifying the two parameters individually without affecting the static effective stiffness of the structure. The SMS unit cell and corresponding meta-structure are fabricated using 3D printing. The transmission spectrum is analyzed through numerical calculations and vibration experiments. These results confirm the isolation of elastic waves within the bandgap. Finally, quasi-static compression tests are performed on the 3D-printed samples. The results demonstrate that the SMS has an acceptable static effective stiffness, further validating its practical potential.

Non-uniform beam structures are widely applied in various engineering fields, and the accurate estimation of modal parameters is significant to the design and optimization of non-uniform beams. This work aims to investigate the transverse free vibration of non-uniform beams with exponentially varying rectangular and circular cross-sections. When solving the governing equations for non-uniform beams in transverse free vibration, utilizing the Adomian Decomposition Method (ADM) can achieve semi-analytical expressions for natural frequencies and modal shape functions. To verify the efficiency of ADM, comparisons are made among the results obtained by the present proposed method, previous studies, the Finite-Element-Method (FEM) model and the experimental modal testing. Variations of natural frequencies and modal shapes under representative constraint boundary conditions are illustrated considering the effects of exponential factors. The results indicate that the modal parameters of non-uniform beams depend on the exponential factors significantly. Especially, for non-uniform beams with varying rectangular cross-sections, the exponential factor of the thickness direction has a greater impact on the modal parameters compared to the width direction. In addition, the positions of modal nodes and antinodes in non-uniform beams will shift compared to uniform beams due to the exponential non-uniformity.