The hyperbolic Lindstedt-Poincaré method is applied to determine the homoclinic and heteroclinic solutions of cubic strongly nonlinear oscillators of the form x + c1 x + c3 x 3= ε f (μ,x,x).In the method,the hyperbolic functions are employed instead of the periodic functions in the Lindstedt-Poincaré procedure.Critical value of parameter μ under which there exists homoclinic or heteroclinic orbit can be determined by the perturbation procedure.Typical applications are studied in detail.To illustrate the acc... 相似文献
With the help of double hydrogen bonds between urea groups, a self-healing anti-icing coating was prepared from polydimethylsiloxane (PDMS)-based polyurea (PDMSPU) that was synthesized from bis(3-aminopropyl)-terminated PDMS and 2,4-toluene diisocyanate. Furthermore, by incorporating a lubricant of inert silicone oil and the cross-linking agent of 1,3,5-tris-(4-aminophenoxy)benzene (TAPOB), the anti-icing coatings exhibited elastic, slippery and durable properties. The wettability, ice shear strength, abrasion-resistance, mechanical and self-healing properties of the prepared anti-icing coatings were systematically investigated. Results showed that the ice shear strength of the PDMSPU anti-icing coating with 150 wt% silicone oil was 7.9±2.9 kPa, significantly lower than that of pristine PDMSPU (74.7±7.2 kPa). The additional introduction of 2 wt% TAPOB could effectively counteract the adverse effect of the lubricant so that the tensile strength (∼1 MPa) of the coating could be comparable to pristine PDMSPU (855±96 kPa). The PDMSPU coating containing 150 wt% silicone oil and 2 wt% TAPOB could maintain the ice shear strength below 50 kPa against 10 icing/deicing cycles and at 12.0±3.3 kPa after 5000 abrasion cycles, and exhibit self-healing properties after treating at 60°C for 10 or 15 h. The slippery self-healing PDMSPU anti-icing coatings could be suitable for anti-icing surfaces in low temperature environments.