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The vibration and stability of spinning viscoelastic Y-shaped bifurcated nanotubes conveying fluid in complex environments by considering additional concentrated masses and springs are studied based on the nonlocal strain gradient theory (NSGT). A detailed investigation is also performed to clarify the effect of influential parameters such as Knudsen number, magnetic nanoflow, scale parameter ratio, spin speed, fluid velocity, downstream bifurcation angle, viscoelastic coefficient, attached springs, localized masses, boundary conditions, and magneto-hygro-thermal environments on the system dynamics. The size-dependent dynamical equations of the system are derived utilizing Hamilton’s principle. The Galerkin discretization scheme is adopted, and the eigenvalue problem is numerically solved. Campbell diagrams, forward and backward frequencies, divergence and flutter instability maps are acquired. Besides, the static instability threshold of the system is determined analytically. Results revealed that although the magnetic nanoflow has a decreasing effect on system vibrational frequencies, it delays the occurrence of the dynamical instability and prevents the buckling phenomenon. It is demonstrated that by considering simultaneous stiffness-softening effects induced by nonlocality and hygro-thermal environments, the flutter instability could occur instead of divergence condition in the system stability evolution. The present modeling and results could be applied as a benchmark for the performance improvement of innovative bi-gyroscopic nanofluidic devices.

This paper examines the deflection and vibration of the circular nanoplates made of functionally graded (FG) materials. The material properties of the system vary across the thickness based on the power-law distribution. The system is assumed to be subjected to hygro-thermo-electrical loadings based on nonlinear relations. The first-order shear deformation theory (FSDT) is applied to model the circular plate as a continuous system. The nonlocal strain gradient theory is employed to consider the small-scale impacts. The dynamic equations of the motion of the FG circular nanoplate for diverse boundary conditions are derived using Hamilton’s principle, and the differential quadrature (DQ) procedure is used to obtain the deflection and frequency of the system in a discrete state. The effects of various parameters, such as small-scale factors, FG material characteristics, external voltage, and hygro-thermal loadings, on the vibration of FG circular nanoplates are explored.

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Forced and free dynamic responses of nanobeams resting on a three-parameter foundation subjected to a moving force in magneto-hygro-thermal conditions are investigated based on the nonlocal strain gradient theory. Also, a detailed parametric study is conducted to identify the impact of slender ratio, axial and distributed tangential loads on the vibration characteristics and dynamic phenomena of the small-scale system. Comparative studies with existing results in the literature are performed to ensure the accuracy of the presented model and solution approach. Analytical and numerical methods are implemented to detect the effects of foundation coefficients, environmental conditions, geometrical and scale parameters on the dynamic amplification factor, critical moving force velocity, cancellation, and maximum free response mechanisms of the system. The outcomes revealed that the critical moving force velocity is enhanced by ascending the slender ratio, elastic, and shear moduli of the foundation. It is found that when the damping factor is considered for the foundation, it is feasible to prevent the occurrence of the cancellation phenomenon. Also, it is concluded that by fine-tuning scale parameters and environmental conditions, unwanted vibration of the system can be suppressed. The attained results of this study can be helpful in the vibration control of nanoscale actuators, switches, and resonators.