Because most piezoelectric devices have interfaces with fluid in engineering, it is valuable to study the coupled field between fluid and piezoelectric media. As the fundamental problem, the 3D Green＇s functions for ...Because most piezoelectric devices have interfaces with fluid in engineering, it is valuable to study the coupled field between fluid and piezoelectric media. As the fundamental problem, the 3D Green＇s functions for point forces and point charge loaded in the fluid and piezoelectric bimaterials are studied in this paper. Based on the 3D general solutions expressed by harmonic functions, we constructed the suitable harmonic functions with undetermined constants at first. Then, the couple field in the fluid and piezoelectric bimaterials can be derived by substitution of harmonic functions into general solutions. These constants can be obtained by virtue of the compatibility, boundary, and equilibrium conditions. At last, the characteristics of the electromechanical coupled fields are shown by numerical results.展开更多
In this article, by using a fixed point theorem, we study following fourth-order three-point BVP:<br /> <img src="Edit_1ba3ab24-dbef-4a90-8fe1-dc466461e2e3.bmp" alt="" /> <span style...In this article, by using a fixed point theorem, we study following fourth-order three-point BVP:<br /> <img src="Edit_1ba3ab24-dbef-4a90-8fe1-dc466461e2e3.bmp" alt="" /> <span style="white-space:normal;">where </span><span style="white-space:nowrap;"><em>f</em> <span style="white-space:nowrap;"><span style="white-space:nowrap;">∈</span></span> <em>C</em>([0,1]×[0,+∞),[0,+∞)) <span style="white-space:nowrap;"><em>α</em></span> <span style="white-space:nowrap;"><span style="white-space:nowrap;">∈</span> </span>[0,6)</span> and <img src="Edit_35fdded4-50be-48af-b9e0-1e97c719aeba.bmp" alt="" /> . The main point to emphasize is that although the corresponding Green’s function is changing signs, by applying the fixed point theorem, we can still obtain at least two positive solutions and degreased solutions under certain suitable conditions.展开更多
基金financial support from the National Natural Science Foundation of China(11572119)
文摘Because most piezoelectric devices have interfaces with fluid in engineering, it is valuable to study the coupled field between fluid and piezoelectric media. As the fundamental problem, the 3D Green＇s functions for point forces and point charge loaded in the fluid and piezoelectric bimaterials are studied in this paper. Based on the 3D general solutions expressed by harmonic functions, we constructed the suitable harmonic functions with undetermined constants at first. Then, the couple field in the fluid and piezoelectric bimaterials can be derived by substitution of harmonic functions into general solutions. These constants can be obtained by virtue of the compatibility, boundary, and equilibrium conditions. At last, the characteristics of the electromechanical coupled fields are shown by numerical results.
文摘In this article, by using a fixed point theorem, we study following fourth-order three-point BVP:<br /> <img src="Edit_1ba3ab24-dbef-4a90-8fe1-dc466461e2e3.bmp" alt="" /> <span style="white-space:normal;">where </span><span style="white-space:nowrap;"><em>f</em> <span style="white-space:nowrap;"><span style="white-space:nowrap;">∈</span></span> <em>C</em>([0,1]×[0,+∞),[0,+∞)) <span style="white-space:nowrap;"><em>α</em></span> <span style="white-space:nowrap;"><span style="white-space:nowrap;">∈</span> </span>[0,6)</span> and <img src="Edit_35fdded4-50be-48af-b9e0-1e97c719aeba.bmp" alt="" /> . The main point to emphasize is that although the corresponding Green’s function is changing signs, by applying the fixed point theorem, we can still obtain at least two positive solutions and degreased solutions under certain suitable conditions.
