Three‐dimensional computation for flow‐induced vibrations in in‐line and cross‐flow directions of a circular cylinder

We present numerical results for in‐line and cross‐flow vibrations of a circular cylinder, which is immersed in a uniform flow and is elastically supported by damper‐spring systems to compute vibrations of a rigid cylinder. In the case of a circular cylinder with a low Scruton number, it is well‐known that two types of self‐excited vibrations appear in the in‐line direction in the range of low reduced velocities. On the other hand, a cross‐flow vibration of the circular cylinder can be excited in the range of high reduced velocities. Therefore, we compute the flow‐induced vibrations of the circular cylinder in the wide range of the reduced velocities at low and high Scruton numbers and discuss about excitation mechanisms in the in‐line and cross‐flow directions. Copyright © 2011 John Wiley & Sons, Ltd.     

Active control of time-delay in cutting vibration

The system dynamics of turning processes can be described by a delay differential equation. How to improve the stability and suppress the vibration of cutting is of an interesting topic. In this paper, a multiple time-delay controller is developed based on discrete optimal control method for the turning vibrations control. Numerical simulations are carried out to verify the efficiency of the controller. Results indicate the designed controller can suppress the cutting vibration efficiently and improve the stability of the cutting processes. The influence of designed time-delay and sampling time on the control performance is also discussed.     

Fast sensitivity analysis of defective system

Sensitivity analysis of linear vibration system is of wide interest. In this paper, sensitivity analysis based on non-defective system and defective system is summarized in all cases. Specially, for the defective systems, a fast method for the perturbation problem of state vectors is constructed in terms of the theories of generalized eigenvectors and adjoint matrices. By this method, the state vector derivatives can be expressed by a linear combination of generalized eigenvectors. The expansion coefficients can be obtained without solving large-scale equations based on eigensolutions of original system. Numerical results demonstrate the effectiveness and the stability of the method.     

Simulation of non-selfadjoint control of thin elastic plates in the presence of conservative in-plane forces

Summary Based on the analysis presented in [1], a closed-form solution for the response of a controlled plate to a transversely applied dynamic loading is presented. Both the applied loading and the control are considered to be continuously distributed. The results and the corresponding parametric study are presented for two common boundary conditions of SSSS and SFSF in the plates. Received 11 March 1997; accepted for publication 18 March 1998     

Flow-induced vibration in two-phase flow with wire coil inserts

Information of flow-induced vibration (FIV) in two-phase flow with wire coil inserts at atmospheric pressure, is presented in this study. FIV was measured in an upward vertical tube for four different wire coil inserts using an air–water mixture as process fluid. Vibration increased along with mass flux and quality. The narrower wire coils produced more vibration. The FIV prediction correlation for two-phase flow with wire coil inserts was experimentally developed with coefficient correlation value of 0.956.     

弱粘弹性材料结构振动特性分析的摄动解法

本文提出了“弱粘弹性”概念,用以描述弱时变材料的动态性能,并构造了弱粘弹性模型进行结构振动分析。根据“弱”的特点,选择了小参数,给出弱粘弹性材料动态性能的描述形式。在此基础上,构造了两种摄动解法,第一种基于弹性解,第二种基于单粘弹性模量解。文中还特别讨论了松驰函数为指数形式时的情形。     

A modeling concept of a mechanical system having a piecewise linear spring property for its diagnosis

Machine condition monitoring and fault diagnosis of rotating machinery are very important because of the wide use of rotating machinery in industry. Couplings and gears are used in many mechanical systems to connect elements and transmit power. The system is usually modeled as a single-degree-of-freedom system with a piecewise linear spring property, where the mass of main machine is only considered. In the present study, the dynamic behavior of a system with an unsymmetrical nonlinearity and a significant mass of the connecting part was investigated both experimentally and by numerical simulation. In the experiment, a 1/3 sub-harmonic oscillation was observed, but this oscillation was not found in the simulation using a single-degree-of-freedom system, in which the mass of the connecting part was ignored. However, when a two-degrees-of-freedom system was used that considered both the mass of the connecting part and the impact property, the 1/3 sub-harmonic oscillation was observed. Thus it is recognized that an adequate mathematical model for diagnosis in the early stage of abnormality must be selected on the basis of the mass ratio between the connecting part and the main body.     

Apparent and effective drag for circular cylinders oscillating transverse to a free stream

This communication brings forward the concept of an effective drag for circular cylinders undergoing controlled or self-excited oscillation transverse to a free stream. A relationship between the effective drag and the apparent drag customarily measured by force transducers, is derived on the basis of the average rate of energy dissipation in the fluid. The effective drag is employed to gain insight into the fluid dynamics of vortex-induced vibrations using available data from the published literature. It is shown that the effective drag varies almost continuously as a function of the true reduced velocity except for a sudden decrease near conditions of maximum amplitude. The variation displays similarities but also important differences among independent experiments, which highlight the importance of various influencing parameters whose effect on the free response is currently not well understood. Some evidence is found that self-excited oscillations occur at points in the frequency–amplitude space where the effective drag is comparatively low avoiding the region where energy transfer from the fluid to the structure is most efficient. A total energy balance is employed to reveal the effect of mechanical damping on the free response which indicates that the amplitude scales with the inverse of the square root of damping in conformity with experimental data. The dimensionless damping parameters proposed by Vandiver are examined in light of the present analysis, and alternative empirical formulas are suggested for organizing the free vibration response.     

A four-node discrete singular convolution for geometric transformation and its application to numerical solution of vibration problem of arbitrary straight-sided quadrilateral plates

A four-node discrete singular convolution (DSC) method is developed for free vibration analysis of arbitrary straight-sided quadrilateral plates. The straight-sided quadrilateral domain is mapped into a square domain in the computational space using a four-node element. By using the geometric transformation, the governing equations and boundary conditions of the plate are transformed from the physical domain into a square computational domain. Numerical examples illustrating the accuracy and convergence of the DSC method for skew, trapezoidal, rhombic and arbitrary quadrilateral plates are presented. The results obtained by DSC method were compared with those obtained by the other numerical methods.     

Dynamics of a Cubic Nonlinear Vibration Absorber

We study the dynamics of a nonlinear active vibration absorber. We consider a plant model possessing curvature and inertia nonlinearities and introduce a second-order absorber that is coupled with the plant through user-defined cubic nonlinearities. When the plant is excited at primary resonance and the absorber frequency is approximately equal to the plant natural frequency, we show the existence of a saturation phenomenon. As the forcing amplitude is increased beyond a certain threshold, the response amplitude of the directly excited mode (plant) remains constant, while the response amplitude of the indirectly excited mode (absorber) increases. We obtain an approximate solution to the governing equations using the method of multiple scales and show that the system possesses two possible saturation values. Using numerical techniques, we perform stability analyses and demonstrate that the system exhibits complicated dynamics, such as Hopf bifurcations, intermittency, and chaotic responses.