Nonlocal Free Vibration of Embedded Short-Fiber-Reinforced Nano-/Micro-Rods with Deformable Boundary Conditions

Abstract

An efficient eigenvalue algorithm is developed for the axial vibration analysis of embedded short-fiber-reinforced micro-/nano-composite rods under arbitrary boundary conditions. In the formulation, nonlocal elasticity theory is used to capture the size effect, and the deformable boundary conditions at the ends are simulated using two elastic springs in the axial direction. In addition, to determine the reinforcing effect of restrained nano-/micro-rods, a new system of linear equations with the concept of the infinite power series is presented. After performing the mathematical processes known as Fourier sine series, Stokes’ transformation and successive integration, we finally obtain a coefficient matrix in terms of infinite series for various rigid or deformable boundary conditions. Some accurate eigenvalue solutions of the free axial vibration frequencies of the short-fiber-reinforced micro-/nano-composite rods with and without being restrained by the means of elastic springs are given to show the performance of the present method. The presence of the elastic spring boundary conditions changes the axial vibration frequencies and corresponding mode shapes.

A Review on Nonlocal Theories in Fatigue Assessment of Solids

“…Hence, in microscopic analyses of field quantities, numerous size-dependent theories have been developed in the literature. These theories have been facilitated with appropriate intrinsic length scales, so they are capable of capturing size effect phenomena [ 8 , 9 , 10 , 11 ].…”

Stability analysis of arbitrary restrained nanobeam embedded in an elastic medium via nonlocal strain gradient theory

“…Ebrahimi and Barati 10 have presented the hygrothermal and NSG impacts on the buckling of graphene. In addition to the articles summarized briefly above and dealing with NSG theory, there are various studies based on the other higher-order theories like nonlocal elasticity, [11][12][13][14][15][16][17][18][19][20][21][22][23] nonlocal couple stress theory, [24][25][26] modified couple stress theory, [27][28][29][30][31][32][33][34][35][36][37][38] SG theory, 39,40 doublet mechanics theory [41][42][43][44][45] in the literature.…”

Nonlocal strain gradient‐based nonlinear dynamics of sinusoidal impulsive actuated porous/piezoelectric multilayer energy nanoharvesters

“…[1][2][3][4] Nanoelectromechanical systems (NEMS) use small-scale mechanical vibrations or motions to enable computation, actuation, and sensing in a wide variety of applications. 5,6 This popularity has induced the development of cutting-edge nanostructured composites with the combination of functionally graded (FG) nano-materials and piezoelectric electromechanical smart materials. 7 These integrated systems contain actuators, sensors, and energy harvesters, to feed different applications within minuscule systems and capture specific electrical signals through the conversion of mechanical energy into electrical power.…”

“…At nano scale, ultra‐compact intelligent devices are becoming increasingly popular in spanning electronics, aerospace, and biotechnology 1–4 . Nanoelectromechanical systems (NEMS) use small‐scale mechanical vibrations or motions to enable computation, actuation, and sensing in a wide variety of applications 5,6 . This popularity has induced the development of cutting‐edge nanostructured composites with the combination of functionally graded (FG) nano‐materials and piezoelectric electromechanical smart materials 7 .…”