Translated Abstract
As micro-nano manufacturing technology develops, the devices are increasingly tend to be miniaturization and lightweight. If device’s external characteristic length is comparable to its material’s internal characteristic one, size effect will be remarkable, and not be neglected. In such case, macroscopic theory will not be applicable to mechanical, thermal, and thermoelastic analysis of micro/nano structures. In other words, the conditions that classical elastic, heat conductive and thermoelastic theory satisfy are no longer met. While, it is important for micro/nano strucutres in MEMS/NEMS to perform heat transfer analysis, thermoelastic analysis, trength and stiffness analysis. To this end, theoretical formulation and applications of heat conduction, elasticity and their coupling at the micro/nano scale will be conducted.
The classical thermodynamics, i.e. the conservation of energy and the entropy increase principle, is extended, and nonlocal thermoelasticity is established by introducing three order stress-like tensor and its conjugate tensor into the strain energy and the flux of heat flux into the entropy flux. The classical thermodymanics is generalized into nanoscale. The theory of thermoelastic coupling for metals at the micro/nano scale is established with the aids of nonlocal two-temperature heat conductive model and nonlocal elasticity. It may be regarded as a microscopic explanation of nonlocal thermoelasticity established from extended thermodynamics.
Based upon the nonlocal thermoelasticity, the transient thermoelastic responses of a bi-layered structure with imperfect interface, buckling of nanobeam under non-uniform temperature distribution and thermoelastic damping of the micro/nano scale Euler beam are analyzed. The responses, i.e. displacemet, stress and tempearature are obtained. It is observed that: the nonlocal effect of heat transfer strengthens heat transfer process, as a result, the structure’s temperature and compressive stress increase; The predicatiuon from the classicical theory will be dangerous; While the deformation and compressive stress are reduced once the nonlocal effect of elasticity is incorporated. Analytical solution to critical load is obtained for nonlocal Euler beam, and the effect of temperature and its nonlcoal parameter on the critical load is systematically discussed. It is gotten that: The critical load is decreased by elastic nonlocal parameter, and the effect is stronger if the restraint at the end is more powerful; When thermal effect is taken into account, the critical load may be further decreased; Thermal nonlocal parameter has great effect on the critical load. Thermoelastic damping of the micro/nano scale Euler beam is investigated using the complex-frequency approach, and the effects of the nonlocal parameters, structure size and material constants are discussed. it is obtaiend that: Nonlocal parameter of elasticity makes the inverse Q-factor increase (decrease) at higher (lower) frequency; Considering size effect of heat conduction, the inverse Q-factor may be larger than that from classical thermoelasticity; and the effect of nonlocal parameter of both heat conduction and elasticity will be more significant for higher order mode. In a word, if the nonlocal effects are not considered, the results should be dangerous, indicating the significant improtance of nonlcoal effect in thermoelastic analysis of micro/nano strucutures.
By introducing the concepts of Caputo fractional order derivative and memory dependent derivative (MDD), the theories of fractional order GL thermoelasticity and generalized LS thermoelasticity are established. To aviod the discontinity at the wave front of GL model, GL thermoelasticity is extended by further introducing the strain change rate. Based upon these models, transient thermoelastic responses are studied. The results show that: Once Caputo fractional order derivative is considered, the propagation velocity of heat becomes larger, and the temperature is higher. The deformation around the wave front of temperature is larger. If the kernel function of MDD is fixed, the memory dependnet parameter becomes larger for larger time delay. And in such case, the medium temperature and the compressive stress may be higher; If memory dependent parameter keeps constant, it is observed that the flatter the kernel function, the larger thermal transient responses. The introduction of strain rate will eliminate the displacement discontinuity predicted by GL model at the elastic and thermal wave front, and the presented model predicts smaller displacement and lower stress than that from the GL thermoelastic model.
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