Free vibration of statically thermal postbuckled functionally graded material （FGM） beams with surface-bonded piezoelectric layers subject to both temperature rise and voltage is studied. By accurately considering t...Free vibration of statically thermal postbuckled functionally graded material （FGM） beams with surface-bonded piezoelectric layers subject to both temperature rise and voltage is studied. By accurately considering the axial extension and based on the Euler-Bernoulli beam theory, geometrically nonlinear dynamic governing equations for FGM beams with surface-bonded piezoelectric layers subject to thermo-electro- mechanical loadings are formulated. It is assumed that the material properties of the middle FGM layer vary continuously as a power law function of the thickness coordinate, and the piezoelectric layers are isotropic and homogenous. By assuming that the amplitude of the beam vibration is small and its response is harmonic, the above mentioned non-linear partial differential equations are reduced to two sets of coupled ordinary differential equations. One is for the postbuckling, and the other is for the linear vibration of the beam superimposed upon the postbuckled configuration. Using a shooting method to solve the two sets of ordinary differential equations with fixed-fixed boundary conditions numerically, the response of postbuckling and free vibration in the vicinity of the postbuckled configuration of the beam with fixed-fixed ends and subject to transversely nonuniform heating and uniform electric field is obtained. Thermo-electric postbuckling equilibrium paths and characteristic curves of the first three natural frequencies versus the temperature, the electricity, and the material gradient parameters are plotted. It is found that the three lowest frequencies of the prebuckled beam decrease with the increase of the temperature, but those of a buckled beam increase monotonically with the temperature rise. The results also show that the tensional force produced in the piezoelectric layers by the voltage can efficiently increase the critical buckling temperature and the natural frequency.展开更多
Hetero-structured thermally conductive spherical boron nitride and boron nitride nanosheets(BNN-30@BNNS)fillers were prepared via electro static self-assembly method.And the corresponding thermally conductive&elec...Hetero-structured thermally conductive spherical boron nitride and boron nitride nanosheets(BNN-30@BNNS)fillers were prepared via electro static self-assembly method.And the corresponding thermally conductive&electrically insulating BNN-30@BNNS/Si-GFs/E-44 laminated composites were then fabricated via hot compression.BNN-30@BNNS-Ⅲ(fBNN-30/fBNNS,1/2,wt/wt)fillers presented the optimal synergistic improvement effects on the thermal conductivities of epoxy composites.When the mass fraction of BNN-30@BNNS-Ⅲwas 15 wt%,λvalue of the BNN-30@BNNS-Ⅲ/E-44 composites was up to0.61 W m^(-1)K^(-1),increased by 2.8 times compared with pure E-44(λ=0.22 W m^(-1)K^(-1)),also higher than that of the 15 wt%BNN-30/E-44(0.56 W m^(-1)K^(-1)),15 wt%BNNS/E-44(0.42 W m^(-1)K^(-1)),and 15 wt%(BNN-30/BNNS)/E-44(direct blending BNN-30/BNNS hybrid fillers,1/2,wt/wt,0.49 W m^(-1)K^(-1))composites.Theλin-plane(λ//)andλcross-plane(λ_(⊥))of 15 wt%BNN-30@BNNS-Ⅲ/Si-GFs/E-44 laminated composites significantly reached 2.75 W m^(-1)K^(-1)and 1.32 W m^(-1)K^(-1),186.5%and 187.0%higher than those of Si-GFs/E-44 laminated composites(λ//=0.96 W m^(-1)K^(-1)andλ_(⊥)=0.46 W m^(-1)K^(-1)).Established models can well simulate heat transfer efficiency in the BNN-30@BNNS-Ⅲ/Si-GFs/E-44 laminated composites.Under the condition of point heat source,the introduction of BNN-30@BNNS-Ⅲfillers were conducive to accelerating heat flow trans fe r.BNN-30@BNNS-Ⅲ/Si-GFs/E-44 laminated composites also demonstrated outstanding electrical insulating properties(cross-plane withstanding voltage,breakdown strength,surface&volume resistivity of 51.3 kV,23.8 kV mm^(-1),3.7×10^(14)Ω&3.4×10^(14)Ω·cm,favorable mechanical properties(flexural strength of 401.0 MPa and ILSS of 22.3 MPa),excellent dielectric properties(εof 4.92 and tanδof 0.008)and terrific thermal properties(T_(g )of 167.3℃and T_(HRI) of 199.2℃).展开更多
基金supported by the National Natural Science Foundation of China (Nos. 10872083 and10602021)the Doctoral Foundation of Ministry of Education of China (No. 200807310002)
文摘Free vibration of statically thermal postbuckled functionally graded material （FGM） beams with surface-bonded piezoelectric layers subject to both temperature rise and voltage is studied. By accurately considering the axial extension and based on the Euler-Bernoulli beam theory, geometrically nonlinear dynamic governing equations for FGM beams with surface-bonded piezoelectric layers subject to thermo-electro- mechanical loadings are formulated. It is assumed that the material properties of the middle FGM layer vary continuously as a power law function of the thickness coordinate, and the piezoelectric layers are isotropic and homogenous. By assuming that the amplitude of the beam vibration is small and its response is harmonic, the above mentioned non-linear partial differential equations are reduced to two sets of coupled ordinary differential equations. One is for the postbuckling, and the other is for the linear vibration of the beam superimposed upon the postbuckled configuration. Using a shooting method to solve the two sets of ordinary differential equations with fixed-fixed boundary conditions numerically, the response of postbuckling and free vibration in the vicinity of the postbuckled configuration of the beam with fixed-fixed ends and subject to transversely nonuniform heating and uniform electric field is obtained. Thermo-electric postbuckling equilibrium paths and characteristic curves of the first three natural frequencies versus the temperature, the electricity, and the material gradient parameters are plotted. It is found that the three lowest frequencies of the prebuckled beam decrease with the increase of the temperature, but those of a buckled beam increase monotonically with the temperature rise. The results also show that the tensional force produced in the piezoelectric layers by the voltage can efficiently increase the critical buckling temperature and the natural frequency.
基金support and funding from Guangdong Basic and Applied Basic Research Foundation(2019B1515120093)National Natural Science Foundation of China(51773169 and 51973173)+3 种基金Natural Science Basic Research Plan for Distinguished Young Scholars in Shaanxi Province(2019JC11)Open Fund from Henan University of Science and Technology(2020-RSC02)Foundation for Doctor Dissertation of Northwestern Polytechnical University(CX202055)financially supported by Polymer Electromagnetic Functional Materials Innovation Team of Shaanxi Sanqin Scholars。
文摘Hetero-structured thermally conductive spherical boron nitride and boron nitride nanosheets(BNN-30@BNNS)fillers were prepared via electro static self-assembly method.And the corresponding thermally conductive&electrically insulating BNN-30@BNNS/Si-GFs/E-44 laminated composites were then fabricated via hot compression.BNN-30@BNNS-Ⅲ(fBNN-30/fBNNS,1/2,wt/wt)fillers presented the optimal synergistic improvement effects on the thermal conductivities of epoxy composites.When the mass fraction of BNN-30@BNNS-Ⅲwas 15 wt%,λvalue of the BNN-30@BNNS-Ⅲ/E-44 composites was up to0.61 W m^(-1)K^(-1),increased by 2.8 times compared with pure E-44(λ=0.22 W m^(-1)K^(-1)),also higher than that of the 15 wt%BNN-30/E-44(0.56 W m^(-1)K^(-1)),15 wt%BNNS/E-44(0.42 W m^(-1)K^(-1)),and 15 wt%(BNN-30/BNNS)/E-44(direct blending BNN-30/BNNS hybrid fillers,1/2,wt/wt,0.49 W m^(-1)K^(-1))composites.Theλin-plane(λ//)andλcross-plane(λ_(⊥))of 15 wt%BNN-30@BNNS-Ⅲ/Si-GFs/E-44 laminated composites significantly reached 2.75 W m^(-1)K^(-1)and 1.32 W m^(-1)K^(-1),186.5%and 187.0%higher than those of Si-GFs/E-44 laminated composites(λ//=0.96 W m^(-1)K^(-1)andλ_(⊥)=0.46 W m^(-1)K^(-1)).Established models can well simulate heat transfer efficiency in the BNN-30@BNNS-Ⅲ/Si-GFs/E-44 laminated composites.Under the condition of point heat source,the introduction of BNN-30@BNNS-Ⅲfillers were conducive to accelerating heat flow trans fe r.BNN-30@BNNS-Ⅲ/Si-GFs/E-44 laminated composites also demonstrated outstanding electrical insulating properties(cross-plane withstanding voltage,breakdown strength,surface&volume resistivity of 51.3 kV,23.8 kV mm^(-1),3.7×10^(14)Ω&3.4×10^(14)Ω·cm,favorable mechanical properties(flexural strength of 401.0 MPa and ILSS of 22.3 MPa),excellent dielectric properties(εof 4.92 and tanδof 0.008)and terrific thermal properties(T_(g )of 167.3℃and T_(HRI) of 199.2℃).
