A semi-analytical multi-harmonic balance method on full-3D contact model for dynamic analysis of dry friction systems

Dry friction damping structures are widely-used in aero-engines to mitigate vibration.The nonlinear nature of friction and the two-dimensional in-plane motion on the contact interface bring challenges to accurately and efficiently predict the forced response of frictionally damped structures.The state-of-the-art Multi-Harmonic Balance Method(MHBM)on quasi-3D contact model in engineering cannot precisely capture the kinematics on the friction interface although the efficiency is high.The full-3D contact model can describe the constitutive relationship of the interface in a more accurate manner;however,the efficiency and convergence are not guaranteed for large-scale models.In this paper,a semi-analytical MHBM on full-3D contact model is proposed.The original Trajectory Tracking Method(TTM)for evaluating the contact force is reformulated to make the calculation more concise and the derivation of the Analytical Jacobian Matrix(AJM)feasible.Based on the chain rule of derivation,the AJM which is the core to upgrade the performance is deduced.Through a shrouded blade finite element model,the accuracy and efficiency of the proposed method are compared with both the MHBM on full-3D contact model with numerical Jacobian matrix and the MHBM on quasi-3D contact model with AJM.The results show that the AJM improves significantly the efficiency of the MHBM on full-3D contact model.The time cost of the proposed method is in the same order of magnitude as that of the MHBM on quasi-3D contact model.We also confirm that the full-3D contact model is necessary for the dynamic analyses of shrouded blades.If one uses the quasi-3D model,the estimation relative error of damping can even reach 31.8%in some cases.In addition,the AJM also brings benefits for stability analysis.It is highly recommended that engineers use the MHBM on full-3D contact model for the dynamic analysis and design of shrouded blades.

Nonlinear modal electromechanical coupling factor for piezoelectric structures containing nonlinearities

Within the linear framework,the Modal Electromechanical Coupling Factor(MEMCF)is an important indicator to quantify the dynamic conversion of mechanical energy and electrical energy of piezoelectric structures.It is also an important tool to guide the piezoelectric damping design of linear structures.Advanced aircraft often fly in maneuvers,and the variable working conditions induce drastic changes in the load level on structures.Geometric and contact nonlinearities of thin-walled structures and joint structures are often activated.To achieve a good vibration reduction effect covering all working conditions,one cannot directly use linear electromechanical coupling theory to instruct the piezoelectric damping design for nonlinear structures.Therefore,this paper defines the Nonlinear Modal Electromechanical Coupling Factor(NMEMCF)and proposes the corresponding numerical method for the first time to quantitatively evaluate the electromechanical coupling capability of nonlinear piezoelectric structures.Three candidate definitions of the NMEMCF are given,including two frequency definitions and one energy definition.The energy definition is the most promising one.It is not only applicable to both conservative and dissipative nonlinear structures but also compatible with the linear MEMCF.In addition,based on the energy formula,the NMEMCF can be obtained by only performing one nonlinear modal analysis in the open-circuit state.The analytical findings and the numerical tool are validated against two piezoelectric structures with different types of nonlinearities.A strong correlation among the NMEMCF,geometric parameters,and energy dissipation is observed.The results confirm that the proposed NMEMCF captures the physics of the electromechanical coupling phenomenon associated with nonlinear piezoelectric structures and can be used as an essential design indicator of piezoelectric damping,especially for variable working conditions.

Mechanism of interconnected synchronized switch damping for vibration control of blades

The Synchronized Switch Damping(SSD)is regarded as a promising alternative to mitigate the vibration of thin-walled structures in aero-engines,especially for blades or bladed disks.The common manner is to shunt the switch circuit independently to a single piezoelectric structure.This paper is aimed at exploring a novel way of using the SSD,i.e.,the SSD is interconnected between two piezoelectric structures or substructures.The damping mechanism,performance,and effective range of the interconnected SSD are studied numerically and experimentally.First,based on a dual cantilever beam finite element model,the time domain and frequency domain modeling and solving methods of the interconnected SSD are deduced and validated.Then,the influence of the amplitude and phase relationship on the damping effect of the interconnected SSD is numerically studied and compared with the shunted SSD.A self-sensing SSD control board is developed,and experimental studies are carried out.The results show that the interconnected SSD establishes an additional energy channel between the corresponding piezoelectric structures.When the amplitudes of the two cantilever beams are different,the interconnected SSD balances the vibration level of each beam.When the amplitudes of the two cantilever beams are the same,if the appropriate interconnection manner is selected according to the phase,the resonance peak can be reduced by more than 30%.When the vibration is in-phase/out-of-phase,the damping generated by the interconnected SSD in a cross/parallel manner is even more significant than the shunted SSD.Furthermore,this novel connection scheme reduces the number of SSD circuits in half.Finally,for engineering applications,we implement the proposed damping technology to the finite element model of a typical dummy bladed disk.A piezoelectric damping ratio of 13.7%is achieved when the amount of piezo material is only 10%of blade mass.Compared with traditional friction dampers,the major advancements of the interconnected SSD are:(A)it can reduce the vibration level of blades without friction interface;(B)the space constraint is overcome,i.e.,the vibration energy is not necessarily dissipated independently in one sector or through physically adjacent blades,and instead,the dissipation and transfer of vibrational energy can be realized between any blade pair.If a specific gating circuit is adopted to adjust the interconnection manner of the SSD,vibration mitigation under variable working conditions with different engine orders will be expected;(C)designers do not need to worry about the annoying nonlinearities related to working conditions anymore.

Platelet-rich plasma accelerates skin wound healing by promoting re-epithelialization

Background:Autologous platelet-rich plasma(PRP)has been suggested to be effective for wound healing.However,evidence for its use in patients with acute and chronic wounds remains insufficient.The aims of this study were to comprehensively examine the effectiveness,synergy and possible mechanism of PRP-mediated improvement of acute skin wound repair.Methods:Full-thickness wounds were made on the back of C57/BL6 mice.PRP or saline solution as a control was administered to the wound area.Wound healing rate,local inflammation,angiogenesis,re-epithelialization and collagen deposition were measured at days 3,5,7 and 14 after skin injury.The biological character of epidermal stem cells(ESCs),which reflect the potential for re-epithelialization,was further evaluated in vitro and in vivo.Results:PRP strongly improved skin wound healing,which was associated with regulation of local inflammation,enhancement of angiogenesis and re-epithelialization.PRP treatment significantly reduced the production of inflammatory cytokines interleukin-17A and interleukin-1β.An increase in the local vessel intensity and enhancement of re-epithelialization were also observed in animals with PRP administration and were associated with enhanced secretion of growth factors such as vascular endothelial growth factor and insulin-like growth factor-1.Moreover,PRP treatment ameliorated the survival and activated the migration and proliferation of primary cultured ESCs,and these effects were accompanied by the differentiation of ESCs into adult cells following the changes of CD49f and keratin 10 and keratin 14.Conclusion:PRP improved skin wound healing by modulating inflammation and increasing angiogenesis and re-epithelialization.However,the underlying regulatory mechanism needs to be investigated in the future.Our data provide a preliminary theoretical foundation for the clinical administration of PRP in wound healing and skin regeneration.