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Flexural and longitudinal wave behaviors of nanobeams made of nanoporous-graded materials while surrounded by Winkler-Pasternak foundation, subjected to the longitudinal magnetic field and exposed to the hygrothermal environment are studied analytically. To this end, the governing equation derived by Euler–Bernoulli beam theory in conjunction with the nonlocal strain gradient theory is defined by employing Hamilton's principle. By adopting an analytic model, the flexural and longitudinal dispersion relations between phase velocity and wave number are derived. The reliability of the present method is confirmed by comparing the obtained results with those stored in the literature. Finally, the effects of the power-law index, porosity volume fraction, nonlocal and material characteristic parameters, uniform temperature and moisture rise, elastic foundation parameters, magnetic field intensity, and wave number are also investigated in detail. It is found that the small-scale parameters are more influential in higher wave numbers where the wavelength is close to the length scale of nanostructures. However, foundation parameters, porosity volume fraction, and longitudinal magnetic field are more influential in lower wave numbers. [ABSTRACT FROM AUTHOR]

In this work, analytical solutions are presented for the wave propagation in functionally graded (FG) nanoplates using a nonlocal strain gradient theory and four-variable refined plate theory considering the magnetic field. The size effects are included using nonlocal strain gradient theory that has two length scale parameters, and the nanoplate is modeled as a plate using four-variable refined plate theory. From the knowledge of authors, it is the first time that the influences of magnetic field on the wave propagation in FG nanoplates are investigated based on present methodology. [ABSTRACT FROM AUTHOR]

This study is focused on the wave propagation analysis of nanoplate made of temperature-dependent porous functionally graded (FG) materials rested on Winkler-Pasternak foundation under in-plane magnetic field. The material properties of FG nanoplate are supposed to vary through the thickness direction and described by power-law rule, in which the porosity distribution is considered as an even pattern. Hamilton's principle is utilized to derive the governing equations on basis of second-order shear deformation theory in conjunction with nonlocal strain gradient theory. The influence of smalllength parameters, thermal distribution, magnetic field, material composition, porosity, and Winkler-Pasternak foundation on wave dispersion is explored. [ABSTRACT FROM AUTHOR]

A size-dependent model is developed for the hygrothermal wave propagation analysis of an embedded viscoelastic single layer graphene sheet (SLGS) under the influence of in-plane magnetic field. The bi-Helmholtz nonlocal strain gradient theory involving three small scale parameters is introduced to account for the size-dependent effects. The size-dependent model is deduced based on Hamilton's principle. The closed-form solution of eigenfrequency relation between wave number and phase velocity is achieved. By studying the size-dependent effects on the flexural wave of SLGS, the dispersion relation predicted by the developed size-dependent model can show a good match with experimental data. The influence of in-plane magnetic field, temperature and moisture of environs, structural damping, damped substrate, lower and higher order nonlocal parameters and the material characteristic parameter on the phase velocity of SLGS is explored. [ABSTRACT FROM AUTHOR]

This paper is focused on the initial stress affected wave dispersion in mounted graphene. To capture the size-dependent and shear deformation effects, the second-order shear deformation theory (SSDT) and nonlocal strain gradient elasticity theory are used to model the graphene. A size-dependent shear deformation plate model is established on the basis of the orthotropic constitutive equations, the nonlocal strain gradient theory as well as the SSDT. Analytical solutions are developed for the wave frequency and phase velocity. The influences of small-scale parameters, initial stress and elastic medium on wave propagation behaviors of the graphene sheets are explored. It is found that the developed model reasonably interprets the softening effects of flexural frequencies and phase velocities. Unlike the classical (scaling-free) model, the developed size-dependent model shows a reasonably good agreement with the experimental frequencies and phase velocities. The wave frequencies and phase velocities of single layer graphene sheets (SLGS) will decrease with increasing compression load, and can increase by increasing tension load. The developed size-dependent 2D continuum model is hopeful to provide a possible theoretical approach to explore the wave behaviors of Graphene-like 2D materials. [ABSTRACT FROM AUTHOR]

This article deals with the static bending response of a functionally graded polymer composite (FG-PC) curved beam reinforced with carbon nanotubes (CNTs) subjected to sinusoidal and uniform loads. The effective material properties of beam are approximated according to modified rule of mixture. Four types of CNT distribution are also considered. Assuming Timoshenko beam theory and a higher-order strain gradient theory, size-dependent equilibrium equations are extracted. Using Navier solution procedure, nonlocal strain gradient governing equations are solved for simply-supported edges. Ultimately, numerical results are expanded to show the influence of weight fraction and distribution patterns of CNTs, small scale parameters, and opening angle on the static bending response of CNTs reinforced nanocomposite curved beam. • Size-dependent static bending of FG-PC curved beam reinforced with CNTs is studied. • Transverse displacement plus axial and shear-transverse stresses are illustrated. • Both softening and hardening machinimas of nanostructures are captured. • Variations in weight fraction, and arrangements of CNTs, and curved nanobeam geometry are examined. [ABSTRACT FROM AUTHOR]