Wave propagation in Rayleigh nanobeams resting on nonlocal media is investigated in this paper. Small-scale structure-foundation problems are formulated according to a novel consistent nonlocal approach extending the special elastostatic analysis in Barretta et al. (2022). Nonlocal effects of the nanostructure are modelled according to a stress-driven integral law. External elasticity of the nano-foundation is instead described by a displacement-driven spatial convolution. The developed methodology leads to well-posed continuum problems, thus circumventing issues and applicative difficulties of the Eringen–Wieghardt nonlocal approach. Wave propagation in Rayleigh nanobeams interacting with nano-foundations is then analysed and dispersive features are analytically detected exploiting the novel consistent strategy. Closed form expressions of size-dependent dispersion relations are established and connection with outcomes available in literature is contributed. A general and well-posed methodology is thus provided to address wave propagation nanomechanical problems. Parametric studies are finally accomplished and discussed to show effects of length scale parameters on wave dispersion characteristics of small-scale systems of current interest in Nano-Engineering.

本文研究了非局域介质上的瑞利纳米束中的波传播。小规模结构基础问题是根据 Barretta 等人的一种新颖的一致非局部方法来制定的，该方法扩展了特殊的弹性静力分析。（2022）。纳米结构的非局部效应根据应力驱动积分定律进行建模。纳米基础的外部弹性由位移驱动的空间卷积来描述。所开发的方法导致了适定的连续体问题，从而规避了 Eringen-Wieghardt 非局部方法的问题和应用困难。然后分析与纳米基础相互作用的瑞利纳米束中的波传播，并利用新颖的一致策略分析检测色散特征。建立了尺寸相关色散关系的闭合形式表达式，并贡献了与文献中可用结果的联系。因此提供了一种通用且适当的方法来解决波传播纳米力学问题。最后完成并讨论了参数研究，以显示长度尺度参数对当前纳米工程感兴趣的小尺度系统的波色散特性的影响。