• Steel and Composite Structures
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• v.42 no.6
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• pp.805-826
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• 2022

The free and live load-forced vibration behaviour of porous functionally graded (PFG) higher order nanobeams in the thermal and magnetic fields is investigated comprehensively through this work in the framework of nonlocal strain gradient theory (NLSGT). The porosity effects on the dynamic behaviour of FG nanobeams is investigated using four different porosity distribution models. These models are exploited; uniform, symmetrical, condensed upward, and condensed downward distributions. The material characteristics gradation in the thickness direction is estimated using the power-law. The magnetic field effect is incorporated using Maxwell's equations. The third order shear deformation beam theory is adopted to incorporate the shear deformation effect. The Hamilton principle is adopted to derive the coupled thermomagnetic dynamic equations of motion of the whole system and the associated boundary conditions. Navier method is used to derive the analytical solution of the governing equations. The developed methodology is verified and compared with the available results in the literature and good agreement is observed. Parametric studies are conducted to show effects of porosity parameter; porosity distribution, temperature rise, magnetic field intensity, material gradation index, non-classical parameters, and the applied moving load velocity on the vibration behavior of nanobeams. It has been showed that all the analyzed conditions have significant effects on the dynamic behavior of the nanobeams. Additionally, it has been observed that the negative effects of moving load, porosity and thermal load on the nanobeam dynamics can be reduced by the effect of the force induced from the directed magnetic field or can be kept within certain desired design limits by controlling the intensity of the magnetic field.

• Geomechanics and Engineering
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• v.32 no.2
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• pp.159-177
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• 2023

In the present work, a simple and refined shear deformation theory is used to analyze the effect of visco-elastic foundation on the buckling response of exponentially-gradient sandwich plates under various boundary conditions. The proposed theory includes indeterminate integral variables kinematic with only four generalized parameters, in which no shear correction factor is used. The visco-Pasternak's foundation is taken into account by adding the influence of damping to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's foundation modulus. The four governing equations for FGM sandwich plates are derived by employing principle of virtual work. To solve the buckling problem, Galerkin's approach is utilized for FGM sandwich plates for various boundary conditions. The analytical solutions for critical buckling loads of several types of powerly graded sandwich plates resting on visco-Pasternak foundations under various boundary conditions are presented. Some numerical results are presented to indicate the effects of inhomogeneity parameter, elastic foundation type, and damping coefficient of the foundation, on the critical buckling loads.

• Steel and Composite Structures
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• v.49 no.5
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• pp.487-502
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• 2023

In the realm of nanotechnology, the nonlocal strain gradient theory takes center stage as it scrutinizes the behavior of spinning cantilever nanobeams and nanotubes, pivotal components supporting various mechanical movements in sport structures. The dynamics of these structures have sparked debates within the scientific community, with some contending that nonlocal cantilever models fail to predict dynamic softening, while others propose that they can indeed exhibit stiffness softening characteristics. To address these disparities, this paper investigates the dynamic response of a nonlocal cantilever cylindrical beam under the influence of external discontinuous dynamic loads. The study employs four distinct models: the Euler-Bernoulli beam model, Timoshenko beam model, higher-order beam model, and a novel higher-order tube model. These models account for the effects of functionally graded materials (FGMs) in the radial tube direction, giving rise to nanotubes with varying properties. The Hamilton principle is employed to formulate the governing differential equations and precise boundary conditions. These equations are subsequently solved using the generalized differential quadrature element technique (GDQEM). This research not only advances our understanding of the dynamic behavior of nanotubes but also reveals the intriguing phenomena of both hardening and softening in the nonlocal parameter within cantilever nanostructures. Moreover, the findings hold promise for practical applications, including drug delivery, where the controlled vibrations of nanotubes can enhance the precision and efficiency of medication transport within the human body. By exploring the multifaceted characteristics of nanotubes, this study not only contributes to the design and manufacturing of rotating nanostructures but also offers insights into their potential role in revolutionizing drug delivery systems.