Technische Schwingungslehre

Klotter, Karl

doi:10.1007/978-3-642-67992-6

Cited by 69 publications

(17 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Since all the coefficients ai, i = o, 1, 2, 3, 4 are positive, the necessary condition for stability is fulfilled [4]. Moreover, it turns out that the Hurwitz determinants…”

Section: R(t) = R O + Or(t)mentioning

confidence: 97%

On bubble motion in a rotating liquid under simulated low and zero gravity

Siekmann

Johann

1976

Ing. arch

View full text Add to dashboard Cite

Summary : The motion of a gas bubble in a rotating liquid has been investigated theoretically and experimentally. The fluid system gas-liquid is placed into a zero-g-centrifuge. The test apparatus consists essentially of two parallel flat glass plates very close together. The space between the plates is filled with liquid. By means of a syringe bubbles are injected into the latter. In case of horizontally positioned plates the gas liquid system is in a state of effective weightlessness. By rotating the plates about a vertical axis, a centrifugal force field is generated, the action of which upon the bubble is studied. Bubble trajectories and travel time are determined and experimental observations are compared with numerical results. Agreement between observed data and those of numerical calculations is satisfactory in view of the approximations made in the analysis.By slight inclination of the axis of rotation towards the vertical, a weak gravitational force field is superimposed on the centrifugal field. It is shown that due to the action of reduced gravity the bubble executes a circular motion with the intersection of the spin axis and the plane of the plates as center. Further observed phenomena (e. g. the influence of tilted plates) are discussed briefly. The subject is currently of practical interest in connection with possible applications regarding materials processing in zero gravity, especially degassing of free floating liquid materials.

show abstract

“…Since all the coefficients ai, i = o, 1, 2, 3, 4 are positive, the necessary condition for stability is fulfilled [4]. Moreover, it turns out that the Hurwitz determinants…”

Section: R(t) = R O + Or(t)mentioning

confidence: 97%

On bubble motion in a rotating liquid under simulated low and zero gravity

Siekmann

Johann

1976

Ing. arch

View full text Add to dashboard Cite

show abstract

“…A general survey has been presented by Klotter [1]. But additionally to these results more examples can be found which are solved explicitly, see below.…”

Section: Introductionmentioning

confidence: 95%

“…For uniform masses and stiffnesses, m j = 1, c j = 1, the problem is solved by trigonometric functions [1]. For m j = 1 j , c j = N + 1 − j Mikota's problem has arrived which was solved by binomials coefficients [2].…”

Section: Introductionmentioning

confidence: 99%

Determination of natural modes of linear mass‐spring vibration systems by Laguerre polynomials

Müller

2009

Proc Appl Math and Mech

View full text Add to dashboard Cite

Chain structured vibration systems with N degrees of freedom with masses mj and stiffnesses kj have been discussed in detail [1]. Some of them can be solved explicitly, others only numerically. Here, an inverse problem is considered: How mj, kj, j = 1, …, N, should be chosen such that the related eigenvalue/eigenvector‐problem can be solved by Laguerre polynomials? (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

show abstract

“…We start with introducing a physically very simple model studied by Brouwer [5] that can serve as a simple illustration of destabilization by damping. Note, however that, although simple looking, the equations that arise are familiar from other applications, see for instance [12,14,17]. It is important to have mechanisms that enable us to stabilize again a gyroscopic system.…”

Section: Introductionmentioning

confidence: 99%

Brouwer’s rotating vessel I: stabilization

Verhulst

2011

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

Abstract. The paradox of destabilization of a conservative or non-conservative system by small dissipation, or Ziegler's paradox (1952), has stimulated an interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations. We discuss the motion of a particle in Brouwer's rotating vessel, a typical gyroscopic system, that has an unstable equilibrium caused by internal damping for a wide range of rotation velocities. Using quasi-periodic averagingnormalization by Mathematica, we find that modulation of the rotation frequency in the cases of single-well and saddle equilibria stabilizes the system for a number of combination resonances, thus producing quenching of the unstable motion. Mathematics Subject Classification (2000). 34D · 70J.

show abstract

Technische Schwingungslehre

Cited by 69 publications

References 0 publications

On bubble motion in a rotating liquid under simulated low and zero gravity

On bubble motion in a rotating liquid under simulated low and zero gravity

Determination of natural modes of linear mass‐spring vibration systems by Laguerre polynomials

Brouwer’s rotating vessel I: stabilization

Contact Info

Product

Resources

About