A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation

Effect of Sinusoidal Corrugated Geometries on the Vibrational Response of Viscoelastic Nanoplates

“…In this framework, herein, we apply a non-local strain gradient model to investigate the nanoscale effects. A similar elasticity model includes both non-local and strain gradient impressive effects for nanoplates [10,31,32], as follows…”

Yerel Olmayan Şekil Değiştirme Gradyanı Teorisi Kullanılarak Elastik Zemine Gömülü Nano Çubuğun Eksenel Titreşim Analizi

“…Based on the nonlocal strain gradient theory proposed by Lim et al [32], the generalized nonlocal strain gradient constitutive relation for a one-dimensional structure can be given as; …”

“…By connecting the nonlocal elasticity and the strain gradient theory, Challamel [31] proposed a generalized hybrid nonlocal law to investigate static bending, buckling, and free vibration of beams using different beam theories. Recently, Lim et al [32] have presented nonlocal strain gradient theory that combine the nonlocal elasticity and the strain gradient theory for the wave propagation in EulerBernoulli and Timoshenko beams. Li and Hu [33] have investigated the post-buckling behavior of Euler-Bernoulli beam based on the nonlocal strain gradient theory.…”

Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory

“…Although there exist numerous applications on the wave propagation analysis of smallscaled systems via nonlocal continuum theory (see, e.g., [14,15,49,50]). However, the capability of the nonlocal continuum theory for predicting the size-dependent stiffness may exist some limited problems [51,52]. For example, the stiffness enhancement phenomenon noticed from experimental observation and as well as the modified couple stress theories [53] can not be predicted well by considering the nonlocal elastic model [54][55][56][57][58].…”

“…As can be seen, it the nonlocal continuum theory and the strain gradient theory describe two entirely different physical characteristics of small-scaled structures. To assess the true effects of the two size-dependent problems on the structural responses, more recently, Lim et al [52] presented a high-order nonlocal strain gradient theory (called the nonlocal strain gradient theory) to bring both of the sizedependent scales into a single theory. The stress of the nonlocal strain gradient theory accounts for not only the non-gradient nonlocal elastic stress field [62], but also the nonlocality of higher-order strain gradients stress field.…”