Analysis of Nonlinear Vibration of Functionally Graded Simply Supported Fluid-Conveying Microtubes Subjected to Transverse Excitation Loads

Abstract

This paper presents a nonlinear vibration analysis of functionally graded simply supported fluid-conveying microtubes subjected to transverse excitation loads. The development of the nonlinear equation of motion is based on the Euler–Bernoulli theory, Hamilton principle and Strain gradient theory. The nonlinear equation of motion is reduced to a second-order nonlinear ordinary differential equation by the Galerkin method. The Runge–Kutta method is adapted to solve the equation, and the effects of the dimensionless microscale parameters, the amplitude and frequency of excitation loads on the stability of the microtubes system are analyzed. It is found that when the microtube diameter is equal to the material length scale parameter, the microtube movement pattern is quasi-periodic. With the increase of the dimensionless microscale parameter, the microtube movement changes from quasi-periodic to chaos. The smaller the power-law index of volume fraction, the smaller the vibration displacement of microtubes and the better the stability. The larger the amplitude of excitation loads is, the larger the vibration displacement of the microtubes will be. When the frequency of excitation loads is equal to the natural frequency of the microtubes, it will have resonance and the vibration displacement will increase significantly.

Mechanics of Small-Scale Spherical Inclusions Using Nonlocal Poroelasticity Integrated with Light Gradient Boosting Machine

“…The number of base functions for the inclusion displacement and pressure are denoted by M and N, respectively. The proposed solution for the displacement and fluid pressure are not uniform, as can be seen from Equations ( 27) and (28). The second part of the solution on the right-hand side of these equations describes how radial displacement and fluid pressure change by the radial coordinate r. However, it is assumed that the loading condition on the surface of the inclusion is uniform.…”

“…In this analysis, the ultrasound elastography mode is of a quasi-static form, resulting in a static uniform load on the inclusion surface. Substituting Equations ( 27) and (28) into Equations ( 20) and ( 21), multiplying both sides of each governing equation by its appropriate base function, and integrating over the whole volume of the spherical inclusion, the following discretised equations are obtained…”

“…Peddieson et al [20] applied a version of nonlocal elasticity, which was first introduced by Eringen [21], to develop scale-dependent beam models suitable for describing the mechanics of nanoscale devices such as smallscale actuators with nanocantilevers as building blocks. Following this pioneering work, several researchers across the world have extended the application of nonlocal theories to other small-scale structures and devices such as nanobeams [22], nanoscale sensors [23], nanoplates [24][25][26] and fluid-conveying microtubes [27,28].…”