K.B. Mustapha

Eigenanalyses of Functionally Graded Micro-Scale Beams Entrapped in an Axially-Directed Magnetic Field with Elastic Restraints

Approximate numerical solutions are obtained for the vibration response of a functionally graded (FG) micro-scale beam entrapped within an axially-directed magnetic field using the differential transformation method (DTM). Idealized as a one-dimensional (1D) continuum with a noticeable microstructural effect and a thickness-directed material gradient, the microbeam’s behavior is studied under a range of nonclassical boundary conditions. The immanent microstructural effect of the micro-scale beam is accounted for through the modified couple stress theory (MCST), while the microscopic inhomogeneity is smoothened with the classical rule of mixture. The study demonstrates the robustness and flexibility of the DTM in providing benchmark results pertaining to the free vibration behavior of the FG microbeams under the following boundary conditions: (a) Clamped-tip mass; (b) clamped-elastic support (transverse spring); (c) pinned-elastic support (transverse spring); (d) clamped-tip mass-elastic support (transverse spring); (e) clamped-elastically supported (rotational and transverse springs); and (f) fully elastically restrained (transverse and rotational springs on both boundaries). The analyses revealed the possibility of using functional gradation to adjust the shrinking of the resonant frequency to zero (rigid-body motion) as the mass ratio tends to infinity. The magnetic field is noted to have a negligibly minimal influence when the gradient index is lower, but a notably dominant effect when it is higher.

A new modeling approach for the dynamics of a micro end mill in high-speed micro-cutting

This study presents a distributed parameter model for the transverse vibration analysis of a micro end mill. Owing to its geometrical nonuniformity, the micro end mill is spatially sub-structured into three distinct spinning elastic systems. With the application of the extended Hamilton’s principle to the energy expressions of the spinning elastic systems, the governing equations of each sub-structured system are obtained. The overall analytical model incorporates a number of nonclassical structural effects that range from rotary inertia, shear deformation, taper ratio, to the rate of twist. For detailed frequency analyses, systematic solution of the elastodynamics governing equations is provided with the spectral finite element method. To assess the accuracy of the presented method, the frequency values of each of the spatial sub-structure are validated through available results in the literature. In the same vein, the solution of the entire ensemble of the distributed parameter system compares well with ANSYS® simulation. The investigation reveals the spinning rate to have the most significant effect on the frequency value of the micro tool followed by the taper ratio and the complex geometry of the micro flute.

Vibration Behavior of Gravity-Loaded Whirling Micro-Scale Shafts Influenced by an Axial Magnetic Field

Some high-speed rotating micro-machines and micro-vibration devices rely on the use of whirling micro-shafts subject to the effect of gravity and magnetic fields. At present, the consequences of the interaction between the elastic deformation of such shafts and the magnetic/gravitational field effects remain unresolved. Focusing on micro-scale whirling shafts with very high torsional rigidity, this study presents a theoretical treatment grounded in the theory of micro-continuum elasticity to examine the ramification of this interaction. The differential transformation method (DTM) is used to obtain extensive numerical results for qualitative assessments of the magnetic-gravitational effects interaction on standing, hanging and horizontally positioned spinning micro-scale shafts. The influence of bearing-support flexibility on the response of the whirling micro-shaft is also considered with rotational and translational springs. The gravitational sag reduces the stability of whirling standing micro-shafts and increases that of the hanging micro-shafts. Further, for all the micro-shafts configurations investigated, the magnetic field is observed to stiffen the response of the shaft and favorably shifts the critical points of vibration of the whirling shafts forward.

Dynamic behaviours of spinning pre-twisted Rayleigh micro-beams

Abstract Developments in micro-systems’ operations rely on identifying and controlling the dynamic responses of micrometre-scale elements. Pre-twisted micro-elements feature prominently in these systems, yet very little is known about the interacting effect of motley factors on their behaviours. Presented here is a model of pre-twisted micro-beams that accounts for the coupling of scale-dependent, rotary inertia and spinning effects in vibratory and wave propagation analyses. In tackling the problem, the system’s physical domain is transformed into the mathematical realm via a scale-dependent micro-continuum theory, while its time evolution is captured by Hamiltonian mechanics. Analytic expressions are obtained for the long-wavelength limit and dispersion relations. The spectrum relations of the waves are established from an octic characteristics equation (which, being in violation of the Abel–Ruffini theorem is treated numerically). Splitting of the waves within the system is observed, and the frequencies of the split shift for altered values of the pre-twist angle and rotary inertia effect. Thinner, highly pre-twisted micro-scale beams experience a widening (narrowing) of the difference between the two phase speeds (group velocities) of the waves. Further, pre-twisting lowers the natural frequencies associated with odd-numbered modes of vibration of the element, while the small-scale effect strongly affects the higher vibration modes.

Modeling of Light Propagation and Phonon Conduction inside Metallic Nanoparticles Enhanced Thin-Film Solar Cells

The main aim of this work is to analyze the various heat transport mechanisms and their roles in efficiency enhancement of a thin-film solar cell due to embedded metallic nanoparticles at the rear of the cell, from both electrical and thermal aspects. The nanoparticles present deep inside the cell reflect incident radiation which then increases the optical path length for enhanced electricity generation. The increase in the optical path length also tends to induce additional but undesirable thermal heating which reduces the performance of the cells. The relationship between the improved conversion efficiency and the thermal effect is the crucial factor of maximizing the performance of thin-film solar cells and has yet to be explored. An accurate theoretical/numerical modeling is warranted in this case. Here, we present an analysis of combined light propagation and preliminary phonon transport in the cell to study solar-energy deposition and the associated thermal gradient.

Coupled extensional-flexural vibration behaviour of a system of elastically connected functionally graded micro-scale panels

This study is concerned with the free vibration behaviour of a system of elastically connected functionally graded micro-scale panels. The mechanical properties of the micro-panel are assumed to have a through-thickness variation and governed by a power-law relation in terms of the constituents’ volume fractions. The biharmonic equations governing the motion of each micro-panel are formulated through the adoption of the energy method along with the postulates of the Kirchhoff–Love plate theory. Concentrating on the asynchronous motion of the connected micro-panels, the study investigates the shift of the natural frequencies of the system as a result of variation in the: aspect ratio of the micro-panel, span-to-thickness ratio of the micro-panel; gradient index; small-scale effect; and the ratio of the Young’s modulus. Estimates of the natural frequencies, under the assumption of simply-supported edges of the micro-panels, are provided by the Navier’s solution method. The qualitative assessment of the model’s parameters indicates that the effect of the gradient index is stifled by the presence of the size effect. Moreover, it is observed that higher values of the ratio of the constituents’ Young’s modulus generate a stiffer response of the micro-panel than higher values of the connectors’ stiffness and the constituents’ density ratio.

On the Dynamic Model of a Functionally Graded Spinning Structural Element of an Aircraft Appendage

The use of advanced materials in automotive, aerospace and communication technologies has called for re-assessment of classical models of many structural elements. The primary objective of this study relates to the use of a higher-order continuum model for discerning the contribution of certain geometric and material properties on wave propagation behavior of a spinning appendage of an aircraft appendage. The spinning appendage is characterized by a through-thickness functional material gradation and subjected to an axial dead load. The foundation of the present model rests on the trio of the mechanics of functionally graded solid structures, the extended Hamilton’s principle and the thin beam theory. Numerical results from the wave mechanics analyses reveal the noticeable influence of axial dead load and attendant wave splitting effect caused by the gyroscopic moment of the system. The wave mechanics result paves the way for the non-destructive damage testing of the element.