In this article, size-dependent vibrations and the stability of moving viscoelastic axially functionally graded (AFG) nanobeams were investigated numerically and analytically, aiming at the stability enhancement of translating nanosystems. Additionally, a parametric investigation is presented to elucidate the influence of various key factors such as axial gradation of the material, viscosity coefficient, and nonlocal parameter on the stability boundaries of the system. Material characteristics of the system vary smoothly along the axial direction based on a power-law distribution function. Laplace transformation in conjunction with the Galerkin discretization scheme was implemented to obtain the natural frequencies, dynamical configuration, divergence, and flutter instability thresholds of the system. Furthermore, the critical velocity of the system was evaluated analytically. Stability maps of the system were examined, and it can be concluded that the nonlocal effect in the system can be significantly dampened by fine-tuning of axial material distribution. It was demonstrated that AFG materials can profoundly enhance the stability and dynamical response of axially moving nanosystems in comparison to homogeneous materials. The results indicate that for low and high values of the nonlocal parameter, the power index plays an opposite role in the dynamical behavior of the system. Meanwhile, it was shown that the qualitative stability of axially moving nanobeams depends on the effect of viscoelastic properties in the system, while axial grading of material has a significant role in determining the critical velocity and natural frequencies of the system.

Metamaterials are man-made substances with unique spatial alternations in their constituent components. They are widely used in modifying elastic, acoustic, or electromagnetic properties of materials. Metamaterials induce low/high-frequency band gaps to control wave propagations with different wavelengths and are also frequently applied in microwave engineering, waveguides, dispersion compensation, smart antennas, and lenses. For instance, permittivity and permeability of the metamaterials can take positive or negative values. Due to smaller single-cell dimensions than their wavelength, the selective frequency of surface-based metamaterials is used for waveguiding. The need for adjustable bandgaps can also lead to a plethora of research into metamaterials’ tunability for structures that operate at different speeds. In this article, recent studies in the field of metamaterials and their applications are reviewed. The piezoelectric metamaterials and the electromagnetic metamaterials are introduced that is followed by a review of new types of chiral metamaterials. Additionally, absorber, nonlinear, terahertz, tunable, photonic, selective surface-based frequency in acoustic metamaterials are comparedand some remarks on tuning bandgaps methods in locally resonant metamaterials are provided.

Complex mechanical systems usually include nonlinear interactions between their components which can be modeled by nonlinear equations describing the sophisticated motion of the system. In order to interpret the nonlinear dynamics of these systems, it is necessary to compute more precisely their nonlinear frequencies. The nonlinear vibration process of a conservative oscillator always follows the law of energy conservation. A variational formulation is constructed and its Hamiltonian invariant is obtained. This paper suggests a Hamiltonian-based formulation to quickly determine the frequency property of the nonlinear oscillator. An example is given to explicate the solution process.