Sommerfeld effect in rotationally symmetric planar dynamical systems
ثبت نشده
چکیده
Sommerfeld effect concerns the non-linear jump phenomena induced due to the influence of the unbalance response on a non-ideal drive around the critical speed of the excited structure. In this work, we study the influence of external and internal dampings and gyroscopic forces on the Sommerfeld effect in rotationally symmetric planar dynamical systems. The rotational symmetry assumption allows us to obtain neat analytical results for the steady state dynamics. We show that the rotating material or internal damping and the gyroscopic forces influence the spin rate of the non-ideal system and the former changes the system dynamics in an unexpected manner. In particular, we show that the stability threshold may restrict the jump phenomena due to the Sommerfeld effect for larger values of internal damping. Moreover, it is also shown that the Sommerfeld effect would cease to exist under certain conditions. A stability condition for various steady-state equilibriums (branches of steady-state solutions) is derived. A rotor dynamics problem and a structural dynamics problem where the systems interact with a non-ideal source are considered as illustrative examples. A few numerical results are given to validate the analytical solutions.
منابع مشابه
Quantization of the planar affinely-rigid body
This paper is a continuation of [1] where the classical model was analyzed. Discussed are some quantization problems of two-dimensional affinely rigid body with the double dynamical isotropy. Considered are highly symmetric models for which the variables can be separated. Some explicit solutions are found using the Sommerfeld polynomial method.
متن کاملComplete Systems of Inequalities
In this paper we summarize the known results and the main tools concerning complete systems of inequalities for families of convex sets. We discuss also the possibility of using these systems to determine particular subfamilies of planar convex sets with specific geometric significance. We also analyze complete systems of inequalities for 3-rotationally symmetric planar convex sets concerning t...
متن کاملCapturing Outlines of Planar Generic Images by Simultaneous Curve Fitting and Sub-division
In this paper, a new technique has been designed to capture the outline of 2D shapes using cubic B´ezier curves. The proposed technique avoids the traditional method of optimizing the global squared fitting error and emphasizes the local control of data points. A maximum error has been determined to preserve the absolute fitting error less than a criterion and it administers the process of curv...
متن کاملExtremality conditions for isolated and dynamical horizons
A maximally rotating Kerr black hole is said to be extremal. In this paper we introduce the corresponding restrictions for isolated and dynamical horizons. These reduce to the standard notions for Kerr but in general do not require the horizon to be either stationary or rotationally symmetric. We consider physical implications and applications of these results. In particular we introduce a para...
متن کاملOrr Sommerfeld Solver Using Mapped Finite Di?erence Scheme for Plane Wake Flow
Linear stability analysis of the three dimensional plane wake flow is performed using a mapped finite di?erence scheme in a domain which is doubly infinite in the cross–stream direction of wake flow. The physical domain in cross–stream direction is mapped to the computational domain using a cotangent mapping of the form y = ?cot(??). The Squire transformation [2], proposed by Squire, is also us...
متن کامل