摘要:

The stability of the nonlinear periodic oscillations is discussed by solving a variational equation which characterizes small variations from the periodic states of equilibrium. This variational equation leads to a linear equation in which the coefficient is periodic in the time. If all solutions of this equation are bounded, then the oscillation is said to be stable, otherwise it is unstable. In order to establish the stability criterion, the characteristic exponents for the unbounded solutions are calculated by Whittaker's method. Then, the generalized stability condition is derived by comparing the said characteristic exponents with the damping of the system considered. Since the solutions of the variational equation have the form:e&mgr;&tgr;[sin (n&tgr;−&sgr;)+…], our stability condition is secured not only for the unbounded solutions having the fundamental frequency (n=1), but also for the unbounded solutions with higher harmonic frequencies (n=2, 3, 4, …). Hence the generalized stability condition obtained in this way is particularly effective in studying the oscillations in which the higher harmonics are excited. Finally our investigation is compared with one of the stability conditions derived by Mandelstam and Papalexi for the subharmonic oscillations.In the Appendix, the characteristic exponents are calculated at some length for the unbounded solutions of a variational equation in which the periodic coefficient involves sine series as well as cosine series.

ISSN:0021-8979    

DOI:10.1063/1.1721277

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

The high velocity collision of two solids is discussed as a problem in compressible fluid hydrodynamics. Such collisions may conveniently be divided into jetless and jet‐forming categories. A theory is presented which describes flow in the collision region for the jetless case and determines a critical collision angle (as a function of material velocities and equation‐of‐state properties of the materials) above which a jet must arise from the collision.The experimental study of solid collisions utilizes metal plates driven by high explosives, the impact of the plates being recorded with a high speed smear camera. Two experimental arrangements are used, and data for collisions employing Dural, mild steel, brass and lead are presented. Jetless and jet‐forming collisions are observed, and critical angles separating the two types are compared with theoretical predictions. Agreement seems sufficiently good to indicate that the theory is valid.

ISSN:0021-8979    

DOI:10.1063/1.1721278

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

By timing the successive arrivals of a shock at stations placed along the channel of a shock tube, measurements have been made of the decrease in shock velocity with travel. These measurements were carried out for shocks moving into air at atmospheric pressure.The attenuation per unit length of travel is greater for stronger shocks and in smaller tubes. Representing distance along the tube byxand using fractional increase in pressure across the shock, (P−P0)/P0=z, as a measure of shock strength, the dimensionless quantityR(dz/dx)/zis found to lie in the interval (3.5±2) ×10−4for shocks ranging in strength 0.1<z<1.0 and in tubes of hydraulic radius 0.30<R<3.80 cm. It is believed that this attenuation is due to wall interaction rather than to nonideal rupture of the diaphragm. However, the exact physical nature of this interaction has not as yet been determined.

ISSN:0021-8979    

DOI:10.1063/1.1721279

出版商:AIP    

年代:1953

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1721281

出版商:AIP    

年代:1953

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1721283

出版商:AIP    

年代:1953

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1721284

出版商:AIP    

年代:1953

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1721286

出版商:AIP    

年代:1953

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1721287

出版商:AIP    

年代:1953

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1721289

出版商:AIP    

年代:1953

数据来源: AIP