An investigation is made of the aeroeiastic stability of thin, orthotropic wings and panels of low aspect ratio. The configurations analyzed here are simply supported along two spanwise edges but have free leading and trailing edges. The mathematical model is obtained using classical plate theory and a two term binomial expansion of piston theory. The application of the boundary conditions gives rise to a complex eigenvalue problem which is thoroughly analyzed. An exact solution for the critical speeds is derived. I t is shown that the flutter speed can be closely approximated by a simple expression which also permits the evaluation of the effects of the pertinent design parameters. I t is also shown that the flutter speed of an orthotropic wing may be closely approximated by that of an isotropic wing with a different aspect ratio. The present investigation also extends the existing work of flutter of panels tha t are simply supported along all four edges to the orthotropic case.
{"title":"On the Aeroelastic Stability of Orthotropic Panels in Supersonic Flow","authors":"A. Perlmutter","doi":"10.2514/8.9807","DOIUrl":"https://doi.org/10.2514/8.9807","url":null,"abstract":"An investigation is made of the aeroeiastic stability of thin, orthotropic wings and panels of low aspect ratio. The configurations analyzed here are simply supported along two spanwise edges but have free leading and trailing edges. The mathematical model is obtained using classical plate theory and a two term binomial expansion of piston theory. The application of the boundary conditions gives rise to a complex eigenvalue problem which is thoroughly analyzed. An exact solution for the critical speeds is derived. I t is shown that the flutter speed can be closely approximated by a simple expression which also permits the evaluation of the effects of the pertinent design parameters. I t is also shown that the flutter speed of an orthotropic wing may be closely approximated by that of an isotropic wing with a different aspect ratio. The present investigation also extends the existing work of flutter of panels tha t are simply supported along all four edges to the orthotropic case.","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123029496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Transition from laminar to turbulent flow in the hypersonic wakes of spheres was detected in laboratory measurements of the radiation from the flow field. A hypervelocity gun facility was used to fire models, 0.22-in. in diameter, into a range at velocities from 10,000 to 17,000 ft/sec. Experiments were performed by changing: (a) the material of the projectile; (b) the ambient gas in the range; and (c) the pressure in the range. Three optical techniques were used to observe the wake radiation: (1) Direct photographs of the projectile and flow field in air, which show a turbulent viscous wake as the pressure in the range is decreased from one atmosphere to about 20 cm Hg. (2) Drum-camera photographs of the wake in air and argon, which show the luminous flow field a t pressures between 30 and 0.5 cm Hg. At 30 cm Hg the trail is characterized by the presence of short luminous streaks, which disappear suddenly as the pressure is decreased below 3 cm Hg for air, and below 0.8 cm Hg for argon. (3) Photomultiplier records taken through a thin slit with both air and argon, which show the main features of the flow field. Above the transition pressure, the intensity of radiation from the wake is always associated with fluctuations that appear to be the same phenomenon as the drum-camera streaks. The appearance of the streaks in the drum camera and photomultiplier data is interpreted as transition from laminar to turbulent flow in the viscous wake, because experimental evidence shows tha t their appearance is not controlled by chemical, radiative, or ablative processes, but depends on aerodynamic effects. This conclusion is supported by other experiments based on optical and schlieren techniques. The transition in the wake a t positions very close to the body is given by a local Reynolds number of 10 for air, and 3 X 10 for argon. The results indicate a possible local-Mach-number effect. D = diameter of sphere I = relative radiation intensity k = thermal conductivity, Btu/ft-sec-°R (3.9 X 10~ for nylon; 3.1 X 10 _ 1 for lexan) L = distance downstream from shoulder of sphere M — Mach number P — pressure, cm Hg Rn = radius of sphere, ft Re = Reynolds number based on local, inviscid-flow properties and dimension L or 1 S = space coordinate, unsteady frame of reference / = time, jusec T = temperature, °R unless otherwise specified Vm = flight velocity, ft/sec Vg — particle velocity in steady-state frame of reference Vp = particle velocity in unsteady-state frame of reference, Vp = Vm Vs X = space coordinate, steady-state frame of reference Z — distance from gun barrel to test window, ft a = thermal diffusivity, ft/sec (a = k/pc) p = density, lb/ft (70 for nylon and lexan) 0 = angle generated by rotation of nose radius away from stagnation point; also, laminar-boundary-layer momentum thickness M = viscosity, lb/ft-sec
通过室内流场辐射测量，检测了高超声速球尾迹中由层流向湍流的过渡。超高速炮设施用于射击模型，0.22英寸。在直径上，进入速度范围从10000到17000英尺/秒。实验通过改变:(a)弹丸材料进行;(b)工作范围内的环境气体;(c)范围内的压强。采用三种光学技术观测尾迹辐射:(1)直接的照片弹和流场在空气中,显示一个湍流粘性后,从一个大气压力范围减少到大约20厘米Hg。(2)Drum-camera照片后的空气和氩气,这显示了光流场30 t之间的压力,在30厘米0.5厘米Hg。Hg的特点是短明亮的条纹,这突然消失的压力减少3厘米以下Hg空气,氩气低于0.8 cm Hg。(3)空气和氩气通过细缝拍摄的光电倍增管记录，显示了流场的主要特征。在过渡压力以上，尾迹的辐射强度总是与波动有关，这种波动似乎与鼓式相机的条纹现象相同。鼓式相机和光电倍增管数据中的条纹的出现被解释为粘性尾流从层流到湍流的转变，因为实验证据表明，它们的出现不受化学、辐射或烧蚀过程的控制，而是取决于气动效应。这一结论得到了其他基于光学和纹影技术的实验的支持。在非常靠近物体的位置上，尾迹中的过渡由空气的局部雷诺数为10，氩气的局部雷诺数为3 × 10给出。结果表明可能存在局域马赫数效应。D =球体直径I =相对辐射强度k =导热系数，Btu/ft-sec-°R (3.9 X 10~尼龙);L =从球肩向下的距离M -马赫数P -压力，cm Hg Rn =球半径，ft Re =基于局部非粘性流动性质和尺寸L或1的雷诺数S =空间坐标，非定常参照系/ =时间，jusec T =温度，°R，除非另有说明Vm =飞行速度，ft/sec Vg -稳态参照系中的粒子速度Vp =非稳态参照系中的粒子速度，Vp = Vm Vs X =空间坐标，稳态参照系Z -炮管到测试窗口的距离，ft a =热扩散系数，ft/sec (a = k/pc) p =密度，lb/ft(尼龙和lexan为70)0 =机头半径从停滞点旋转产生的角度;层边界层动量厚度M =粘度，lb/ft-sec
{"title":"Transition in the Viscous Wakes of Blunt Bodies at Hypersonic Speeds","authors":"H. Hidalgo, R. Taylor, J. Keck","doi":"10.2514/8.9802","DOIUrl":"https://doi.org/10.2514/8.9802","url":null,"abstract":"Transition from laminar to turbulent flow in the hypersonic wakes of spheres was detected in laboratory measurements of the radiation from the flow field. A hypervelocity gun facility was used to fire models, 0.22-in. in diameter, into a range at velocities from 10,000 to 17,000 ft/sec. Experiments were performed by changing: (a) the material of the projectile; (b) the ambient gas in the range; and (c) the pressure in the range. Three optical techniques were used to observe the wake radiation: (1) Direct photographs of the projectile and flow field in air, which show a turbulent viscous wake as the pressure in the range is decreased from one atmosphere to about 20 cm Hg. (2) Drum-camera photographs of the wake in air and argon, which show the luminous flow field a t pressures between 30 and 0.5 cm Hg. At 30 cm Hg the trail is characterized by the presence of short luminous streaks, which disappear suddenly as the pressure is decreased below 3 cm Hg for air, and below 0.8 cm Hg for argon. (3) Photomultiplier records taken through a thin slit with both air and argon, which show the main features of the flow field. Above the transition pressure, the intensity of radiation from the wake is always associated with fluctuations that appear to be the same phenomenon as the drum-camera streaks. The appearance of the streaks in the drum camera and photomultiplier data is interpreted as transition from laminar to turbulent flow in the viscous wake, because experimental evidence shows tha t their appearance is not controlled by chemical, radiative, or ablative processes, but depends on aerodynamic effects. This conclusion is supported by other experiments based on optical and schlieren techniques. The transition in the wake a t positions very close to the body is given by a local Reynolds number of 10 for air, and 3 X 10 for argon. The results indicate a possible local-Mach-number effect. D = diameter of sphere I = relative radiation intensity k = thermal conductivity, Btu/ft-sec-°R (3.9 X 10~ for nylon; 3.1 X 10 _ 1 for lexan) L = distance downstream from shoulder of sphere M — Mach number P — pressure, cm Hg Rn = radius of sphere, ft Re = Reynolds number based on local, inviscid-flow properties and dimension L or 1 S = space coordinate, unsteady frame of reference / = time, jusec T = temperature, °R unless otherwise specified Vm = flight velocity, ft/sec Vg — particle velocity in steady-state frame of reference Vp = particle velocity in unsteady-state frame of reference, Vp = Vm Vs X = space coordinate, steady-state frame of reference Z — distance from gun barrel to test window, ft a = thermal diffusivity, ft/sec (a = k/pc) p = density, lb/ft (70 for nylon and lexan) 0 = angle generated by rotation of nose radius away from stagnation point; also, laminar-boundary-layer momentum thickness M = viscosity, lb/ft-sec","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123036301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
1 Schapker, R. L., Comment on the Temperature Distribution in a Spinning Sphere During Atmospheric Entry, Journal of the Aerospace Sciences, Vol. 29, No. 8, Aug. 1962. 2 Reismann, H., Temperature Distribution in a Spinning Sphere During Atmospheric Entry, Journal of the Aerospace Sciences, Vol. 29, No. 2, Feb. 1962. 3 Morgenthaler, G. W., and Reismann, H., Temperature in a Rotating Cylinder in a High-Speed Gas Flow, Martin Co. Research Rep. No. R-61-44, May 1962 (to be published). 4 Reismann, H., Two-Dimensional Periodic Flow of Heat in Polar Coordinates, J. Franklin Inst., Vol. 266, No. 4, Oct. 1958.
{"title":"Improvement on Gauss-Seidel Iteration of Simultaneous Equations","authors":"F. L. Ryder","doi":"10.2514/8.9824","DOIUrl":"https://doi.org/10.2514/8.9824","url":null,"abstract":"1 Schapker, R. L., Comment on the Temperature Distribution in a Spinning Sphere During Atmospheric Entry, Journal of the Aerospace Sciences, Vol. 29, No. 8, Aug. 1962. 2 Reismann, H., Temperature Distribution in a Spinning Sphere During Atmospheric Entry, Journal of the Aerospace Sciences, Vol. 29, No. 2, Feb. 1962. 3 Morgenthaler, G. W., and Reismann, H., Temperature in a Rotating Cylinder in a High-Speed Gas Flow, Martin Co. Research Rep. No. R-61-44, May 1962 (to be published). 4 Reismann, H., Two-Dimensional Periodic Flow of Heat in Polar Coordinates, J. Franklin Inst., Vol. 266, No. 4, Oct. 1958.","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123487133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Vibration Modes of a Two-Beam System by the Holzer Method","authors":"H. E. Fettis","doi":"10.2514/8.9838","DOIUrl":"https://doi.org/10.2514/8.9838","url":null,"abstract":"","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127066545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reply to Notes on Matrix Methods of Structural Analysis and Further Comments on the Inversion of Large Structural Matrices","authors":"B. Klein","doi":"10.2514/8.9835","DOIUrl":"https://doi.org/10.2514/8.9835","url":null,"abstract":"","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125615991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Corrections and Comments on The Effect of Slip, Particularly for Highly Cooled Walls","authors":"N. Rott","doi":"10.2514/8.9829","DOIUrl":"https://doi.org/10.2514/8.9829","url":null,"abstract":"","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120946289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary Asymptotic solutions of Novozhilov's equations are derived for a constant-thick ness,, nonshailow shell of revolution. Two cases of loading are considered: (1) Sinusoidal loading. Two-term asymptotic solutions of Novozhilov's uncoupled second-order equations are obtained in terms of the equation of the generating curve. (2) Higher harmonic load distribution. The asymptotic solu tions for this case are shown to depend on a single second order differential equation. This equation may be solved exactly for three types of shells. For shells of slowly varying contour, an iterative method of solution is indicated. The asymptotic solutions are obtained by the use of smallparameter expansions and by the use of a standard method3 for the singular perturbation problem and are valid for nonshailow shells free of singularities . The series are truncated to two terms for all cases of loading. It is recommended that the second term be retained in the edge-effect solutions.
{"title":"Asymptotic Solution of Nonshallow Shells of Revolution Subjected to Nonsymmetric Loads","authors":"R. Schile","doi":"10.2514/8.9817","DOIUrl":"https://doi.org/10.2514/8.9817","url":null,"abstract":"Summary Asymptotic solutions of Novozhilov's equations are derived for a constant-thick ness,, nonshailow shell of revolution. Two cases of loading are considered: (1) Sinusoidal loading. Two-term asymptotic solutions of Novozhilov's uncoupled second-order equations are obtained in terms of the equation of the generating curve. (2) Higher harmonic load distribution. The asymptotic solu tions for this case are shown to depend on a single second order differential equation. This equation may be solved exactly for three types of shells. For shells of slowly varying contour, an iterative method of solution is indicated. The asymptotic solutions are obtained by the use of smallparameter expansions and by the use of a standard method3 for the singular perturbation problem and are valid for nonshailow shells free of singularities . The series are truncated to two terms for all cases of loading. It is recommended that the second term be retained in the edge-effect solutions.","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"57 21","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114006262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimizing the Aft Configuration of a Passive-Entry Capsule","authors":"P. Jaffe","doi":"10.2514/8.9826","DOIUrl":"https://doi.org/10.2514/8.9826","url":null,"abstract":"","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"343 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122848088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
T N RECENT YEARS a large number of investigations have been made in problem areas involving the nonlinear, large-deflection theory for the static deflection, vibration, and buckling of shells. These investigations require the use of the nonlinear relationships between the strains and curvatures and the displacements. For example, a very good approach to these problems is by means of the Rayleigh-Ritz technique. Using this technique one can readily avoid the solution of the difficult nonlinear differential equations by choosing combinations of deflection functions with undetermined coefficients which satisfy the boundary conditions exactly. The coefficients are then determined so as to make the total energy of the elastic system a minimum, thereby giving the best approximation—e.g., deflection, vibration frequency, buckling load—to the exact solution as is obtainable with the functions chosen. The strain energy stored in a shell is given by. 2
{"title":"On the Nonlinear Strain-Curvature-Displacement Relationships for Thin Elastic Shells","authors":"A. Leissa","doi":"10.2514/8.9818","DOIUrl":"https://doi.org/10.2514/8.9818","url":null,"abstract":"T N RECENT YEARS a large number of investigations have been made in problem areas involving the nonlinear, large-deflection theory for the static deflection, vibration, and buckling of shells. These investigations require the use of the nonlinear relationships between the strains and curvatures and the displacements. For example, a very good approach to these problems is by means of the Rayleigh-Ritz technique. Using this technique one can readily avoid the solution of the difficult nonlinear differential equations by choosing combinations of deflection functions with undetermined coefficients which satisfy the boundary conditions exactly. The coefficients are then determined so as to make the total energy of the elastic system a minimum, thereby giving the best approximation—e.g., deflection, vibration frequency, buckling load—to the exact solution as is obtainable with the functions chosen. The strain energy stored in a shell is given by. 2","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126347657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The principle of the minimum of the total potential is employed to obtain stresses and displacements for clamped, short, •oval cylindrical shells under hydrostatic pressure. Classical •shell theory, in which buckling effects are not considered, was used. A Fourier series is assumed for the deflections in the closed circumferential direction so tha t the partial differential equations of equilibrium are replaced by a set of ordinary differential equations. The energy solution is compared with a simplified approximation which can be considered an equivalent circular cylinder solution. Graphs of the significant stresses and displacements are presented for oval cylinders having major to minor axis ratios of 1.10, 1.30, and 1.50. It is shown tha t the maximum stresses and displacements increase significantly as the major to minor axis ratio is increased.
{"title":"Clamped Short Oval Cylindrical Shells Under Hydrostatic Pressure","authors":"W. P. Vafakos, F. Romano, J. Kempner","doi":"10.2514/8.9810","DOIUrl":"https://doi.org/10.2514/8.9810","url":null,"abstract":"The principle of the minimum of the total potential is employed to obtain stresses and displacements for clamped, short, •oval cylindrical shells under hydrostatic pressure. Classical •shell theory, in which buckling effects are not considered, was used. A Fourier series is assumed for the deflections in the closed circumferential direction so tha t the partial differential equations of equilibrium are replaced by a set of ordinary differential equations. The energy solution is compared with a simplified approximation which can be considered an equivalent circular cylinder solution. Graphs of the significant stresses and displacements are presented for oval cylinders having major to minor axis ratios of 1.10, 1.30, and 1.50. It is shown tha t the maximum stresses and displacements increase significantly as the major to minor axis ratio is increased.","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1962-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114457700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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