Instability of functionally graded micro-beams via micro-structure-dependent beam theory

This paper focuses on the buckling behaviors of a micro-scaled bi-directional functionally graded （FG） beam with a rectangular cross-section, which is now widely used in fabricating components of micro-nano-electro-mechanical systems （MEMS/NEMS） with a wide range of aspect ratios. Based on the modified couple stress theory and the principle of minimum potential energy, the governing equations and boundary conditions for a micro-structure-dependent beam theory are derived. The present beam theory incorporates different kinds of higher-order shear assumptions as well as the two familiar beam theories, namely, the Euler-Bernoulli and Timoshenko beam theories. A numerical solu- tion procedure, based on a generalized differential quadrature method （GDQM）, is used to calculate the results of the bi-directional FG beams. The effects of the two exponential FG indexes, the higher-order shear deformations, the length scale parameter, the geomet- ric dimensions, and the different boundary conditions on the critical buckling loads are studied in detail, by assuming that Young＇s modulus obeys an exponential distribution function in both length and thickness directions. To reach the desired critical buckling load, the appropriate exponential FG indexes and geometric shape of micro-beams can be designed according to the proposed theory.

Rational design of thermoelastic damping in microresonators with phase-lagging heat conduction law

The design of thermoelastic damping(TED)affected by the phase-lagging non-Fourier heat conduction effects becomes significant but challenging for enlarging the quality factor of widely-used microresonators operating in extreme situations,including ultra-high excitation frequency and ultra-low working temperature.However,there does not exist a rational method for designing the TED in the framework of non-Fourier heat conduction law.This work,therefore,proposes a design framework to achieve low thermoelastic dissipation of microresonators governed by the phase-lagging heat conduction law.The equation of motion and the heat conduction equation for phase-lagging TED microresonators are derived first,and then the non-Fourier TED design problem is proposed.A topology optimization-based rational design method is used to resolve the design problem.What is more,a two-dimensional(2D)plain-strain-based finite element method(FEM)is developed as a solver for the topology optimization process.Based on the suggested rational design technique,numerical instances with various phase lags are investigated.The results show that the proposed design method can remarkably reduce the dissipation of microresonators by tailoring their substructures.

Abnormal enhancement to the quality factors of carbon nanotube via defects engineering

Low quality(Q) factor is often the limiting factor for high performance carbon nanotube(CNT) resonators. The most commonly used approach to enhance the Q factor of CNTs is to reduce/eliminate the intrinsic defects.Herein, we show surprisingly that hole defects of suitable size and position are able to enhance the Q factor of CNT, which strongly contradicts to the common notion that the presence of defects promote intrinsic dissipation via defects dissipation. By analyzing the strain distribution, we find that such abnormal enhancement in Q factor of defected CNT originates from a coupling competition mechanism between the atomic mismatch around defected atoms and the thermoelastic damping. Although the presence of holes will introduce an additional defect dissipation source, suitable holes are capable of reducing the energy dissipation arisen from the thermoelastic damping, through changing the spatial strain field of defected CNT. This coupling competition mechanism provides a new route for designing high performance CNT resonators via defects engineering.

A spatiotemporally-nonlocal continuum field theory of polymer networks

A physically-based continuum theory that captures the microstructure-dependent and temporal effects of both permanent and transient polymer networks is still lacking,despite the fact that it is greatly needed for the analysis of polymeric microstructures.To fill in this gap,this work proposes a physically-based spatiotemporally nonlocal continuum field theory.A general frame-work is established that quantitatively connects microscopic descriptions of polymer networks(chain energetics,chain-length distribution,assembly structure of the interpenetrating network,and rate of bond exchange reactions)to key components in the spatiotemporally nonlocal constitutive relations(explicit form of the nonlocal kernel function,magnitude of nonlocal characteris-tic length,two-phase weighting factors,and explicit form of the relaxation function),based on three hypotheses on the continuum viewpoint of the underlying discrete network structure:the existence of a finite bottom bound of volume to define intensive quan-tities,uniformity of energy density field inside the representative volume of a polymer network,and the condition for initiation of chain stretch.Applying the general framework to a permanent 8-chain concentric network yields a concrete two-phase nonlocal elasticity constitutive relation,where the explicit form of the kernel function can be derived by simply assuming an implicit form.Application to a transient network with bond exchange reactions yields a spatiotemporally nonlocal constitutive relation.The spatiotemporally nonlocal continuum theory can be helpful for exploring transformative and subversive high-performance materials involving the specific spatial stacking and arrangement of functional units through artificial design.