Transverse Vibrations of a Centrally Clamped Rotating Circular Disk

The transverse vibrations of a circular disk of uniform thickness rotatingabout its axis with constant angular velocity are analyzed. The resultsspecialized to the linear case of disks clamped at the center and free atthe periphery are in good agreement with those reported in the literature.The natural frequencies of spinning hard and floppy disks are obtained for various nodal diameters and nodal circles. Primary resonance is shown to occur at the critical rotational speed at which, in the linear analysis, the spinning disk is unable to support arbitraryspatially fixed transverse loads. Using the method of multiple scales, wedetermine a set of four nonlinear ordinary-differential equations governingthe modulation of the amplitudes and phases of two interacting modes. Thesymmetry of the system and the loading conditions are reflected in thesymmetry of the modulation equations. They are reduced to an equivalentset of two first-order equations whose equilibrium solutions aredetermined analytically. The stability characteristics of thesesolutions is studied; the qualitative behavior of the response isindependent of the mode being considered.     

Wake-induced vibration of tandem and staggered cylinders with two degrees of freedom

The wake-induced vibration (WIV) of two staggered cylinder with two degrees of freedom (2-dof) has been investigated by experiments in a water channel for Reynolds number between 2000 and 25 000. The streamwise separation was fixed to 4 diameters and the lateral separation varied between 0 and 3 diameters for tandem and staggered configurations. Results are presented in the form of trajectories of motion and dynamic response curves of displacements, frequencies and force coefficients. Excitation caused by the WIV mechanism is found to get weaker as the initial position of the downstream cylinder is increased from the centreline of the wake (tandem arrangement) towards the sides. For a lateral separation of 3 diameters wake interference was already found to be negligible. Evidence of a type of wake-stiffness concept is also observed to occur for 2-dof WIV in tandem arrangement, especially for higher reduced velocities. A similar mechanism may also be occurring for staggered arrangements around the centreline.     

Interaction between two spheres placed in tandem arrangement in steady and pulsating flow

The interaction among two spheres in tandem formation are studied for a Reynolds number of 300 using both steady and pulsating inflow conditions. The purpose is to further investigate the force characteristics as well as the shedding patterns of the two spheres as the separation distance is changed from 1.5 to 12 sphere diameters. The method used for the simulations is the volume of solid (VOS) method, an approach based on the volume of fluid (VOF) method. Comparisons with other computational methods have shown VOS to accurately resolve the flow field around solid spheres. The results show that the separation distance plays a significant role in changing the flow patterns and shedding frequencies at moderate separation distances, whereas effect on drag is observed even at a separation distance of 12 diameters.     

Frequency response of a synthetic jet cavity

A synthetic jet results from periodic oscillations of a diaphragm in a cavity. We present the results of a detailed experimental investigation wherein the effect of excitation frequency on the synthetic jet flow is studied for cavities of different depths and for orifices of different diameters. The exit velocity averaged over an excitation cycle indicates a lower and an upper bound on the frequency for the formation of a jet, and shows resonance at two frequencies. The resonant frequencies have been identified as being close to the diaphragm and the Helmholtz frequencies, with the former being more important in the present set of experiments. We discuss approaches to manipulate these frequencies from the point of view of cavity design. Interestingly, the input power is found to be at a minimum at the diaphragm frequency. Our measurements over a relatively large parameter domain suggest that the turbulence intensity in the near field is independent of the cavity depth and excitation frequency, but depends on the orifice diameter. These results are expected to be useful for designing synthetic jet cavity.     

Transition process of cylindrical-shell vibrations under a local disturbing load

Methods for study of the transition process of induced vibrations in a cylindrical shell under a local disturbing load whose amplitude and frequency vary in accordance with given laws are developed. The amplitudes of certain vibration modes are compared with those in the transition process under a disturbing load with a constant frequency and amplitude as well as under steady vibrations. It is confirmed that, to determine the maximum amplitudes of total shell deflection, it is sufficient to consider only the vibration modes whose natural frequencies are lower than the frequencies of the disturbing load. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 67–72, April, 1999.     

Coupled vibrations of a partially fluid-filled cylindrical container with an internal body including the effect of free surface waves

Internal bodies (baffles) are used as damping devices to suppress the fluid sloshing motion in fluid-structure interaction systems. An analytical method is developed in the present article to investigate the effects of a rigid internal body on bulging and sloshing frequencies and modes of a cylindrical container partially filled with a fluid. The internal body is a thin-walled and open-ended cylindrical shell that is coaxially and partially submerged inside the container. The interaction between the fluid and the structure is taken into account to calculate the sloshing and bulging frequencies and modes of the coupled system using the Rayleigh quotient, Ritz expansion and Galerkin method. It is shown that the present formulation is an appropriate and new approach to tackle the problem with good accuracy. The effects of fluid level, number of nodal diameters, internal body radius and submergence ratio on the dynamic characteristics of the coupled system are also investigated.     

Surface and thermal effects on vibration of embedded alumina nanobeams based on novel Timoshenko beam model

This paper deals with the free vibration analysis of circular alumina （Al2O3） nanobeams in the presence of surface and thermal effects resting on a Pasternak foun- dation. The system of motion equations is derived using Hamilton＇s principle under the assumptions of the classical Timoshenko beam theory. The effects of the transverse shear deformation and rotary inertia are also considered within the framework of the mentioned theory. The separation of variables approach is employed to discretize the governing equa- tions which are then solved by an analytical method to obtain the natural frequencies of the alumina nanobeams. The results show that the surface effects lead to an increase in the natural frequency of nanobeams as compared with the classical Timoshenko beam model. In addition, for nanobeams with large diameters, the surface effects may increase the natural frequencies by increasing the thermal effects. Moreover, with regard to the Pasternak elastic foundation, the natural frequencies are increased slightly. The results of the present model are compared with the literature, showing that the present model can capture correctly the surface effects in thermal vibration of nanobeams.     

Mode identification of a rotating disk

A modal testing method permitting identification of the natural frequencies, the number of nodal diameters and wave motions in a rotating disk is presented in this paper. This method is applicable at arbitrary rotation speed without requiring a priori information about the vibration modes of the stationary disk. The influence of disk rotation speed on the prediction of mode shapes with this method is shown, and experimental predictions of modal parameters are presented for both axisymmetric and asymmetric disks.     

Studies of DDT enhancement approaches for kerosene-fueled small-scale pulse detonation engines applications

Two-phase small-scale pulse detonation engine (SPDE) offers a competitive alternative for small-scale propulsion systems from a high cycle efficiency and structural simplicity standpoint. SPDE models are designed with the aero-valve, and three different cases of obstacle combinations are used as deflagration-to-detonation transition (DDT) devices. The inner diameters of detonation tubes are 29?mm, and the lengths of three SPDEs are 995, 1,100, and 1,175?mm. Using kerosene-air as the fuel-oxidizer, a series of high-frequency detonation tests is conducted to seek efficient DDT enhancement approaches that reduce DDT distance and time and increase the frequency of kerosene-fueled SPDE. The results show that the fully developed detonation wave can be achieved at a distance of 3.4 times the minimum characteristic distance for gaseous detonation formation from the igniter and that the SPDE can steadily operate at a maximal frequency of 62.5?Hz. By adopting these DDT enhancement approaches, the detonability of kerosene is significantly improved. In addition, experiments are performed to study the effects of firing frequencies on detonation transitions. The results clearly indicate that the values of detonation wave pressures and velocities, the degree of overdriven wave, the ignition delay times, and detonation initiation times vary with frequencies. In terms of the performance, the optimal frequencies of three SPDE models are 20, 42.5, and 50?Hz, respectively.     

Obtaining fiber stress-strain curves by recording fiber vibrations during electric-field measurements

A simple method for constructing tension curves of thin fibers is proposed which consists of determining the dependence of the frequencies of small transverse vibrations of thin fibers on their tensile strain. The fiber stress at these frequencies is calculated using the classical formula of string vibrations. Instead of force and strain, it is proposed to measure frequency and strain. This method has a number of advantages, in particular, it is more accurate. Resonant frequencies are determined by recording the accompanying electric field resulting from the variation in the charge distributed over the fiber surface. The effectiveness of the method is demonstrated by constructing copolymer fibers of various diameters. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 219–223, July–August, 2009.     

Experimental Investigation of Transitional Flow in Porous Media with Usage of a Pore Doublet Model

The transition from laminar to turbulent flow in porous media is studied with a new method. To mimic interconnected pores, a simplified geometry consisting of a pipe with a relatively large diameter that is split into two parallel pipes with different diameters is studied. This is a pore-doublet setup and the pressure drops over the parallel pipes are recorded by pressure transducers for different flow rates. Results show that the flow in the parallel pipes is redistributed when turbulent slugs pass through one of them. The presence of the slugs is revealed by positive skewness in the pressure signals as well as an increase of the standard deviation of the pressure drops and correlation between the pressure drops of the pipes. A frequency analysis of the pressure drops show that lower band frequency pressure variations in one pipe are communicated to the other pipe while higher band frequencies are filtered out.     

Identification of discrete-time bilinear systems through equivalent linear models

This paper presents a novel method for identification of discrete-time, time-invariant state-space models of bilinear dynamical systems using the steady-state portion of a single input/multiple output time-history measurements. These measurements are recorded by exciting the system with a linear combination of sine and cosine functions of user-selected frequencies enriched by a subtle amount of random component. The proposed method relies on conversion of the bilinear system into an equivalent linear model (ELM) by an accurate approximation of the state in the bilinear term using a set of sine and cosine basis functions whose frequencies are obtained as combinations of the input frequencies. Observer/Kalman Filter Identification (OKID), a?linear time invariant (LTI) system identification algorithm, is used to identify the aforementioned ELM from which the original bilinear model is recovered. A?numerical example is also provided.     

Epstein transition zones in nonhomogeneous isotropic elastic media

A simple transformation in the independent variable makes it possible to obtain power series solutions of the stress equations of motion of elasticity for inhomogeneous elastic media whose refractive indices are represented by the Epstein profiles. Graphs of reflection and transmission coefficients versus angles of incidence are presented for different frequencies in the case of incident P as well as incident SV waves for some profiles.     

Wavenumber mismatch of interacting modes in a plane wake

A technique is presented to examine the level of wavenumber mismatch between nonlinearly interacting components whose frequencies obey resonant matching conditions. Cross-correlation of the auto-bispectrum is used to quantify the level of mismatch, and the concept of bispectrum coherency is introduced to determine the confidence level in the wavenumber mismatch measurements. The results show that wavenumber mismatch of the order of one tenth of the fundamental wavenumber can exist between interacting triads whose frequencies obey resonance matching.     

多孔压电分流超材料及其带隙特性研究

设计了一种新型多孔压电分流超材料构型,以单、双孔元胞构型为例,研究了其带隙特性和有限周期振动传递特性,并与未开孔压电分流超材料板进行了对比分析。计算结果表明:与未开孔压电超材料相比,两种构型在低频处的压电局域共振带隙频率更低,带宽变窄,且均会在高频范围内出现额外带隙,随着孔宽δ的增大,额外带隙数量逐渐增多;对应特定的孔宽δ的两种元胞构型均产生带宽大于1kHz的超宽带隙。该构型结合了压电分流超材料和声子晶体的特点,与传统未开孔压电分流超材料相比,具备低频和高频同时抑振的特性。     

Transitions to chaos in the spherical couette flow due to periodic variations in the rotation velocity of one of the boundaries

The results of an experimental investigation of unsteady viscous incompressible flows in a spherical gap, when the rotation velocity of one sphere varies in accordance with the harmonic law, while that of the other sphere remains constant, are presented. The modulation amplitudes and frequencies are small compared with the mean rotation velocities of the spheres. Transition to chaos is studied in a layer, whose thickness is equal to the inner sphere radius, in the case of counter rotation of the spherical boundaries. A periodic flow generated as a result of the mutual synchronization of the frequencies of a three-frequency regime preceding that under study at lower Reynolds numbers is taken as the original state. It is shown that certain properties of turbulent flows near the threshold of their formation essentially depend on the modulation frequency.     

Improved natural frequencies for plates with a free edge

A simple correction formula is developed for the square of natural frequencies of plates with a free edge. The theory is applied to torsional vibrations of a long plate strip and to vibrations of a circular plate with a free edge and a number of nodal diameters. The paper concludes with the remark that the theory may be extended mutatis mutandis to vibrations of shells with a free edge.     

Multi-axial low-cycle-fatigue test rig

A multi-axial rig for testing aircraft gasturbine compressor and turbine disks is described. The rig is based on the closed-loop electro-servo hydraulic control principle. This principle combines the use of hydraulic and electronic components not only to control the loads but to hold the true disk position. Nonrotating disks can be loaded to produce stresses which closely simulate loading experimenced by disks in service. Disks with up to 100 loading points and with diameters between 2.5 in. and 18 in. are acceptable within this framework, with loads up to 25,000 lb per loading point, at frequencies up to 7 Hz, and at temperatures in excess of 1500°F. The rig has demonstrated its effectiveness as a useful laboratory tool for compressor and turbine-disk low-cycle fatigue and cyclic stress-rupture life evaluation.     

Coupled bending and torsional vibration of nonsymmetrical axially loaded thin-walled Bernoulli–Euler beams

The dynamic transfer matrix is formulated for a straight uniform and axially loaded thin-walled Bernoulli–Euler beam element whose elastic and inertia axes are not coincident by directly solving the governing differential equations of motion of the beam element. Bernoulli–Euler beam theory is used, and the cross section of the beam does not have any symmetrical axes. The bending vibrations in two perpendicular directions are coupled with torsional vibration and the effect of warping stiffness is included. The dynamic transfer matrix method is used for calculation of exact natural frequencies and mode shapes of the nonsymmetrical thin-walled beams. Numerical results are given for a specific example of thin-walled beam under a variety of end conditions, and exact numerical solutions are tabulated for natural frequencies and solutions calculated by the other method are also tabulated for comparison. The effects of axial force and warping stiffness are also discussed.     

大范围运动细长柔性空间结构动力学特性分析

自由-自由边界无约束状态的细长柔性空间结构大范围运动时的动力学特性对整体结构运动分析和运动控制系统设计具有极其重要的作用。通过浮动坐标系建立结构的运动学关系;借助假设模态法对结构变形进行变量分离;利用Lagrange’s方程建立了结构的刚柔耦合振动方程;再通过Rayleigh-Ritz法,以无大范围运动时的振型函数作为基本解组,得到了大范围运动影响下的结构振动特征方程,求解该方程得到了结构频率和振型。通过几组数值算例的对比分析,指出了非耦合模型和耦合模型下结构频率及振型之间的差异。