Dynamics of Stress-Driven Two-Phase Elastic Beams

Abstract

The dynamic behaviour of micro- and nano-beams is investigated by the nonlocal continuum mechanics, a computationally convenient approach with respect to atomistic strategies. Specifically, size effects are modelled by expressing elastic curvatures in terms of the integral mixture of stress-driven local and nonlocal phases, which leads to well-posed structural problems. Relevant nonlocal equations of the motion of slender beams are formulated and integrated by an analytical approach. The presented strategy is applied to simple case-problems of nanotechnological interest. Validation of the proposed nonlocal methodology is provided by comparing natural frequencies with the ones obtained by the classical strain gradient model of elasticity. The obtained outcomes can be useful for the design and optimisation of micro- and nano-electro-mechanical systems (M/NEMS).

Well-posed two-phase nonlocal integral models for free vibration of nanobeams in context with higher-order refined shear deformation theory

“…It can be observed from Table 1 that for different length-height ratio L/h = 5, 20, the first three dimensionless frequencies of the simply supported beam predicted by both the StrainDTPN and StressDTPN models agree well with the results of the local elasticity theory (Thai and Vo, 2012). Besides, in Table 2, the first dimensional frequency of cantilever beams evaluated by the case of f ðzÞ ¼ z, gðzÞ ¼ 0 is compared with the existing results for two-phase nonlocal Euler-Bernoulli beams (Fakher et al, 2020;Vaccaro et al, 2021). Also, a good agreement is obtained.…”

“…Besides, in Table 2, the first dimensional frequency of cantilever beams evaluated by the case of f(z)=z, g(z)=0 is compared with the existing results for two-phase nonlocal Euler–Bernoulli beams (Fakher et al, 2020; Vaccaro et al, 2021). Also, a good agreement is obtained.…”

Nonlocal analysis of edge‐cracked nanobeams under Mode I and Mixed‐Mode (I + II) static loading

“…Lattice-based nonlocal models, Eringen's nonlocal models, gradient theory of elasticity, strain-and stress-driven nonlocal models, and peridynamic theory are some of the most widely known and accepted GCTs. 4,5 In the context of the stress-driven nonlocal model (SDM), that is the GCT employed in the present research work, it has been successfully applied to solve numerous engineering problems, such as static bending behavior, [6][7][8][9][10][11] buckling, 12,13 and free transverse vibrations [14][15][16][17][18] of nanobeams. It is important to highlight that the above cited papers refer to intact nanobeams.…”

“…In the context of the stress‐driven nonlocal model (SDM), that is the GCT employed in the present research work, it has been successfully applied to solve numerous engineering problems, such as static bending behavior, 6–11 buckling, 12,13 and free transverse vibrations 14–18 of nanobeams. It is important to highlight that the above cited papers refer to intact nanobeams.…”

Special Issue of Nanomaterials: Mechanics of Nanostructures and Nanomaterials

“…In the presented Special Issue, six research papers [ 1 , 2 , 3 , 4 , 5 , 6 ] are published. Topics of published papers cover analyses of different engineering problems of nanostructures.…”