Considering the geometric nonlinearity due to the large elastic deformations of flexible links, the superharmonic resonances of elastic linkages in the forms of ω1/3 and ω1/2 are studied by the method of multiple sc...Considering the geometric nonlinearity due to the large elastic deformations of flexible links, the superharmonic resonances of elastic linkages in the forms of ω1/3 and ω1/2 are studied by the method of multiple scales. The research shows that the analytical results are coincident with the experimental results.展开更多
The superharmonic resonances of elastic linkages are studied by using the method of multiple scales under the excitation of its inertial foree。 The analyses demonstrate that the superharmonic resonances cau...The superharmonic resonances of elastic linkages are studied by using the method of multiple scales under the excitation of its inertial foree。 The analyses demonstrate that the superharmonic resonances caused by the quadratic and cubic nonlinearities due to large elastic deformations of the flexible links and multi-frequencies of the inertial force of linkages are the reason to produce the critical speeds. The results of explaining of the lower order harmonic reso- nances by“1/n' method are verified theoretically。展开更多
In this paper,for the solution of the torsion problem about the equation Δu=-2 with homogeneous Dirichlet boundary conditions in a bounded convex domain in Rn,we find a superharmonic function which implies the strict...In this paper,for the solution of the torsion problem about the equation Δu=-2 with homogeneous Dirichlet boundary conditions in a bounded convex domain in Rn,we find a superharmonic function which implies the strict concavity of u ^(1/2) and give some convexity estimates.It is a generalization of Makar-Limanov’s result(Makar-Limanov(1971))and Ma-Shi-Ye’s result(Ma et al.(2012)).展开更多
As two crucial indicators of bistable energy harvesting performance,band width and power amplitude are simultaneously investigated for obtaining the synergy effect.Toward this goal,a nonlinear electromechanical-couple...As two crucial indicators of bistable energy harvesting performance,band width and power amplitude are simultaneously investigated for obtaining the synergy effect.Toward this goal,a nonlinear electromechanical-coupled distributed-parameter model of the bistable piezoelectric energy harvester is established.Based on the electromechanical decoupled method,approximate higher-order analytical solutions of the beam displacement,harvested power and effective bandwidth are derived.The cubic-function discriminant of the analytical solution is introduced to determine the nonlinear excitation-frequency boundaries of multiple solutions and power peak.The stability of the multiple solutions is analyzed through Jacobi matrix of the modulation equation.Superharmonic resonance is notified.Upward and downward sweep experiments and numerical solutions of time history curves,phase portraits and power spectra confirm the analytical findings.To realize optimized broadband energy harvesting,the parametric study on the coefficients of the linear and cubic elastic external forces with the corresponding optimal load resistance is performed.For the nonlinear hardening case,more positive linear coefficient is preferred.For the nonlinear softening case,the cubic coefficient slightly larger than its optimal value is recommended at each given linear coefficient.By tuning the load resistance and linear and cubic coefficients of the external force,broadband bistable energy harvesting with optimized power is realized.展开更多
Ultrasound imaging is the most widely used noninvasive medical imaging modality. Its latest elite concept is Superharmonic Imaging which is the most talked-about future of medical diagnostic ultrasound. In this paper,...Ultrasound imaging is the most widely used noninvasive medical imaging modality. Its latest elite concept is Superharmonic Imaging which is the most talked-about future of medical diagnostic ultrasound. In this paper, the computational and analytical study for superharmonic field generation from phased array transducer of 16 × 16 elements is presented. For this, the model preferred, includes the calculation for diffraction effect in frequency domain and nonlinear effect in time domain. The attenuation is included along with the diffraction in frequency domain as well. The comparative analysis of superharmonic field is also carried out with simulated fundamental and second harmonic fields by the same model. Similarly, the comparison with the results from the literature is also reported.展开更多
In this paper, we study some geometrical and analytic properties of manifolds with non- negative sectional curvature at, infinity. Then, we apply these results to the study of harmonic maps.
We find and prove 3G inequalities for the Laplacian Green function with the Dirichlet boundary condition, which are applied to show the existence of positive continuous solutions of the nonlinear equation Δu-Vu=g（&#...We find and prove 3G inequalities for the Laplacian Green function with the Dirichlet boundary condition, which are applied to show the existence of positive continuous solutions of the nonlinear equation Δu-Vu=g（·,u）, where V and g are Borel measurable functions, required to satisfy suitable assumptions related to a new functional class J. Our approach uses the Schauder fixed point theorem.展开更多
文摘Considering the geometric nonlinearity due to the large elastic deformations of flexible links, the superharmonic resonances of elastic linkages in the forms of ω1/3 and ω1/2 are studied by the method of multiple scales. The research shows that the analytical results are coincident with the experimental results.
文摘The superharmonic resonances of elastic linkages are studied by using the method of multiple scales under the excitation of its inertial foree。 The analyses demonstrate that the superharmonic resonances caused by the quadratic and cubic nonlinearities due to large elastic deformations of the flexible links and multi-frequencies of the inertial force of linkages are the reason to produce the critical speeds. The results of explaining of the lower order harmonic reso- nances by“1/n' method are verified theoretically。
基金supported by National Key Research and Development Project (Grant No. SQ2020YFA070080)National Natural Science Foundation of China (Grant Nos. 11871255 and 11721101)supported by National Natural Science Foundation of China (Grant Nos. 11971137 and 11771396)
文摘In this paper,for the solution of the torsion problem about the equation Δu=-2 with homogeneous Dirichlet boundary conditions in a bounded convex domain in Rn,we find a superharmonic function which implies the strict concavity of u ^(1/2) and give some convexity estimates.It is a generalization of Makar-Limanov’s result(Makar-Limanov(1971))and Ma-Shi-Ye’s result(Ma et al.(2012)).
基金supported by National Natural Science Foundation of China(Grants 11802071,11902193,and 11625208)Natural Science Foundation of Shanghai(Grant 19ZR1424300).
文摘As two crucial indicators of bistable energy harvesting performance,band width and power amplitude are simultaneously investigated for obtaining the synergy effect.Toward this goal,a nonlinear electromechanical-coupled distributed-parameter model of the bistable piezoelectric energy harvester is established.Based on the electromechanical decoupled method,approximate higher-order analytical solutions of the beam displacement,harvested power and effective bandwidth are derived.The cubic-function discriminant of the analytical solution is introduced to determine the nonlinear excitation-frequency boundaries of multiple solutions and power peak.The stability of the multiple solutions is analyzed through Jacobi matrix of the modulation equation.Superharmonic resonance is notified.Upward and downward sweep experiments and numerical solutions of time history curves,phase portraits and power spectra confirm the analytical findings.To realize optimized broadband energy harvesting,the parametric study on the coefficients of the linear and cubic elastic external forces with the corresponding optimal load resistance is performed.For the nonlinear hardening case,more positive linear coefficient is preferred.For the nonlinear softening case,the cubic coefficient slightly larger than its optimal value is recommended at each given linear coefficient.By tuning the load resistance and linear and cubic coefficients of the external force,broadband bistable energy harvesting with optimized power is realized.
文摘Ultrasound imaging is the most widely used noninvasive medical imaging modality. Its latest elite concept is Superharmonic Imaging which is the most talked-about future of medical diagnostic ultrasound. In this paper, the computational and analytical study for superharmonic field generation from phased array transducer of 16 × 16 elements is presented. For this, the model preferred, includes the calculation for diffraction effect in frequency domain and nonlinear effect in time domain. The attenuation is included along with the diffraction in frequency domain as well. The comparative analysis of superharmonic field is also carried out with simulated fundamental and second harmonic fields by the same model. Similarly, the comparison with the results from the literature is also reported.
文摘In this paper, we study some geometrical and analytic properties of manifolds with non- negative sectional curvature at, infinity. Then, we apply these results to the study of harmonic maps.
文摘We find and prove 3G inequalities for the Laplacian Green function with the Dirichlet boundary condition, which are applied to show the existence of positive continuous solutions of the nonlinear equation Δu-Vu=g（·,u）, where V and g are Borel measurable functions, required to satisfy suitable assumptions related to a new functional class J. Our approach uses the Schauder fixed point theorem.
