Stability-Related Unsteady Phenomena

When a rotor, excited by unbalance, is operating eccentrically within a clearance and in local contact with the stator it behaves as a bilinear oscillator with a natural periodic motion that resembles bouncing. When excited by unbalance at a subcritical rotative speed which is exactly or nearly 1/Nsuper times its natural frequency, the nonlinear system will respond by bouncing at or nearly at its natural frequency, or superharmonically at a frequency exactly Nsuper times the operating speed or forcing frequency. As in supercritical subharmonic response, there is a zone with characteristics of chaotic behavior in the transition zone between any order of superharmonic response and the next highest order of superharmonic response. There is also an intricate pattern of progressive bifurcations of the orbit on entry into this characteristically chaotic region and a reverse progression on exit from this region. The response is a mirror image or reciprocal set of the more thoughly studied supercritical subharmonic response of the same bilinear oscillator system which, when excited by unbalance at a supercritical rotative speed which is exactly or nearly a whole number Nsub times its natural frequency, the nonlinear system will respond by bouncing at exactly or nearly its natural frequency at a frequency exactly 1/Nsub times the operating speed or forcing frequency. Such supercritical subharmonic response is also characterized by the appearance of characteristically chaotic behavior in the transition zone between successive orders of subharmonic response and by patterns of progressive bifurcations of the orbit on entry into and exit from each region of characteristically chaotic response. Various aspects of subcritical superharmonic response are studied in a numerical model of the nonlinear system, and are compared to data taken on the core spool of an aircraft engine gas turbine. The engine data show many of the unique characteristics of response, wave form, and spectral content predicted by the numerical model of the bilinear oscillator when operating at subcritical rotative speed.

The ability of hydrodynamically self-excited jets to lock into strong external forcing is well known. Their dynamics before lock-in and the specific bifurcations through which they lock in, however, are less well known. In this experimental study, we acoustically force a low-density jet around its natural global frequency. We examine its response leading up to lock-in and compare this to that of a forced van der Pol oscillator. We find that, when forced at increasing amplitudes, the jet undergoes a sequence of two nonlinear transitions: (i) from periodicity to${ \mathbb{T} }^{2} $quasiperiodicity via a torus-birth bifurcation; and then (ii) from${ \mathbb{T} }^{2} $quasiperiodicity to 1:1 lock-in via either a saddle-node bifurcation with frequency pulling, if the forcing and natural frequencies are close together, or a torus-death bifurcation without frequency pulling, but with a gradual suppression of the natural mode, if the two frequencies are far apart. We also find that the jet locks in most readily when forced close to its natural frequency, but that the details contain two asymmetries: the jet (i) locks in more readily and (ii) oscillates more strongly when it is forced below its natural frequency than when it is forced above it. Except for the second asymmetry, all of these transitions, bifurcations and dynamics are accurately reproduced by the forced van der Pol oscillator. This shows that this complex (infinite-dimensional) forced self-excited jet can be modelled reasonably well as a simple (three-dimensional) forced self-excited oscillator. This result adds to the growing evidence that open self-excited flows behave essentially like low-dimensional nonlinear dynamical systems. It also strengthens the universality of such flows, raising the possibility that more of them, including some industrially relevant flames, can be similarly modelled.

This paper presents a Pulse Width Modulation (PWM) based method for Active Power (AP) and Reactive Power (RP) measurements in electric sinusoidal and Non-sinusoidal power systems. The method takes advantage of the fact that frequencies present in a power line are of a specific fundamental frequency range (a range centred around the 50Hz or 60Hz) and that in case of the presence of harmonics the frequencies of those dominating in the power line spectrum can be specified on the basis of the fundamental. In order to estimate the power components in a generalised power line, in the first stage the elimination of any harmonics present and the identification of the power line fundamental frequency are cascaded by the application, in the next step, of a PWM stage at which a Pulse Wave is generated based on the frequency of the fundamental. In the final stage of the method the power components are calculated. In the major advantages of the proposed method are included: a) in contrast to a number of existing methods a time delay or shifting of the input signal is not required, b) the method does not involve a time delay by ?/2 of the Current signal with respect to the Voltage signal, c) the fundamental frequency of the power line is considered as an unknown parameter, simultaneously estimated with the signal's spectrum using the Fast Fourier Technique (FFT) and so the method is insensitive to fundamental power line frequency changes, and d) complex computations that include multiplication of the Voltage and Current sample values by trigonometric functions are avoided.

In this study, a weighted sum, consisting two non-dimensionalized quantities critical buckling force and natural frequency, is employed to maximize the objective function for a laminated composite circular cylindrical shell. The function is considered to find the optimum solutions as the goal. Orientation angels of fibers are mentioned in a well-known configuration as candidate design, and critical buckling force and natural frequency values are derived with the first order shear deformation theory. The composite shell is considered with 8 layers, also the boundary conditions are assumed to be fully simply support and to satisfy boundary conditions displacement and slope components are defined in form of double Fourier series. After combination of differential operators and Fourier series, eventually the matrix L is found and Galerkin method gains function values. For this purpose, a program based on MATLAB is employed for the process. Validations of numerical results show that the used method is moderately satisfactory and acceptable in predicting the critical buckling force and the natural frequency of the shell in comparison with other works. As the conclusion, the effect of different weighting ratios, shell length-to-radius ratios, and shell thickness-to-radius ratios on the optimal designs are investigated and the results are compared.

One method to reduce the vibration of a structure is to shift its natural frequencies away from frequency of the excitation force. This paper investigates shifting and optimizing the natural frequencies of a plate-like structure. The method is based on local modification of plate surface by creating spherical dimples or cylindrical beads. These dimples/beads alter the local stiffness in the plate while keeping the overall plate mass the same. The optimal designs of dimpled and beaded plates are presented. The approach couples a finite element method with an optimization technique based on the genetic algorithm (GA). The objective of optimization is either the maximization of the fundamental frequency or the maximization of the gap between two adjacent natural frequencies. The optimization results show that dimpling and beading techniques are effective for altering the plate natural frequencies.

We have performed experiments in a turbulent mixing layer with periodic forcing introduced by a Piezo Film Actuator (PFA). Three different lengths of PFAs have been used, and the effects of various combinations of forcing amplitudes and frequencies are investigated. The forcing at the first and second sub-harmonic frequencies against the natural frequency enhances the development of the thickness of the mixing layer: the mixing layer spreads due to the forcing. On the other hand, the forcing near the natural frequency suppresses the development: the mean velocity gradient becomes steeper than the no control case. The vector pattern of the periodic velocity components indicated the formation of the vortical structure. By forcing at the natural and its first sub-harmonic frequencies, two counter-rotating vortices are clearly observed in one period of forcing. By forcing at second sub-harmonic frequency, the vortical structure is found only in the downstream region. The distribution of the periodic Reynolds shear stress significantly varies with the forcing frequency and it takes a positive value when forcing occurs near the natural frequency. However, the total value of the Reynolds shear stress remains negative due to the contribution of the turbulent components.

<p>This report consists of experimental and Finite element-based numerical modal analysis of a 3D printed PLA cantilever beam with a nonuniform delamination of 0.5mm, carried out as part of an MEng project. Experimental modal analysis is performed on four different samples of different delamination thicknesses, including the one with a delamination of 0.5mm, to obtain the system's bending fundamental frequency. Numerical analysis, however, is focused and conducted on only the defective specimen with a non-uniform delamination of 0.5mm. In this case, the delamination is sketched with the help of an electronic microscope which takes the images of the delamination zone. These images are then used to plot the non-uniform delamination on the 3D model, focusing on obtaining the model that is as close as possible to the manufactured specimen. The experimental frequencies are subsequently compared with the numerical values obtained from the Finite Element Analysis (FEA) of the 3D model. In numerical analysis, a progressive approach was used to create two sophisticated models referred to as refined and further refined models. The numerical fundamental frequency obtained from these last models are compared with that of the PLA beam with uniform delamination of 0.5mm. It is observed that by applying progressive refinement in the FEM model, the numerical fundamental bending frequency increasingly converges to the experimental one. Appendix A consists of the images taken by the microscope, which show the non-uniform geometry of the delamination zone.</p>

In order to clarify the influence of water on the natural vibration of bridge with complex piers, based on a continuous beam with 4-column pier, the numerical analysis model is established. Single column circular pier is taken to discuss the range of waters. Then the influences of water on the natural vibration are analyzed. The research shows that waters reduce the natural frequency. When waters area width is less than 10 m, the natural frequency of the pier decreases. And the first-order longitudinal bending frequency is reduced by 3.36%. When waters area width is more than 10 m, the vibration frequencies tend to be stable gradually. Therefore, the waters 10 m can be regarded as an infinite boundary. The natural frequencies of single column pier and 4-column pier decrease with the increase of water depth. When the water depth is less than 10 m, the changes of natural frequency of the first four orders of single column pier are relatively small, and the changes of 5–10 order natural frequency are large. The maximum effect of the first ten orders is 14.84%. The natural vibration frequency of the bridge decreases gradually with the increase of water depth. The maximum effect of the first five orders is 3.33%.

Kawasaki has developed a methodology for estimating car body low mode bending and torsion mode natural frequency. These natural frequencies have a significant influence on ride quality. Although it has been believed that the natural frequencies become lower when passengers are present, Kawasaki established that the natural frequency does not change with the number of standing and sitting passengers, and the vibration acceleration amplitude becomes smaller when passengers are present. This has been shown by implementing numerical analyses and experiments using a mock up car. The increased knowledge will enable designing for better ride quality in the future through optimization of more accurate models.

In the last several years, there has been a discernible increase in research devoted to developing innovative and complex composite materials. Because of their superior performance, especially in the aircraft industry, Fibre Metal Laminates (FML) and hybrid structures made of glass, aramid fibre, carbon, or aluminium are the most commonly used of these new technological commodities. Thus, free vibration analysis is the first step in the design of these structures. The current work examines the vibration behavior of a fiber-metal-laminate (FML) composite beam using numerical and experimental methods, a novel material for aircraft. This research series evaluated the bending natural vibration frequencies of the multi-walled carbon nanotube FML composite cantilevered beam. The Bruel and Kjaer (B and K) Fast Fourier Transform (FFT) analyzer with a PULSE platform was used in this study to find the intrinsic vibration frequencies of glass FML beams. Two parameters that investigated the dynamic behavior of the FML composite beam were the amount of MWCNT filler material and the beam's length. There was a reasonable agreement between the experimental and numerical results and the natural frequencies. The amount of MWCNT filler added to the glass fiber epoxy enhances the natural frequency of the FML composite cantilevered beam, according to both experimental and computational calculations. Furthermore, it was discovered that the vibration's inherent bending frequency decreases with the beam length.

To establish an acceptable extension tube length (ETL) to measure direct blood pressure (BP) in dogs. Prospective, experimental study. University-based small animal research facility. Eight healthy Beagle dogs: 6 males and 2 females. Each extension tube with lengths of 25, 50, 75, 115, 145, 205, and 275cm were connected after the catheterization with a 22-Ga catheter in the dorsal pedal artery in sternal recumbency. A square wave from the fast-flush test was consecutively recorded 5 times to analyze the system's dynamic response characteristics according to the ETL. After recording the square wave, the ETL was converted to a Latin square. The dynamic response was analyzed using natural frequency (NF) and the damping coefficient (DC), both of which affect the damping factor. The average values of NF and DC were plotted against a graph showing the damping factor. Linear regression was used to evaluate the between-group changes in NF and DC. The DC gradually increased from 0.21 to 0.29ξ, and the NF gradually decreased from 38 to 14Hz according to the increase in ETL (P<0.05). The dynamic response showed adequate damping with all ETLs. With an increase in ETL, the NF decreased significantly, while the DC demonstrated a less significant change. Therefore, NF had a greater influence on the damping factor of arterial BP measurement. There was no difference between ETLs from 25 to 275cm lines for measuring BP. An ETL of less than 275cm is recommended as the damping amount is adequate. Moreover, an ETL less than 275cm does not meaningfully affect BP measurement in dogs.

Meshfree simulation of temperature effects on the mechanical behaviors of microtubules

The dynamic response of a structural system can be described by modal analysis. In the present study, the modal analysis that adopts an Undamped Degree of Freedom (Undamped-DOF) System is implemented to describe the modal descriptors such as the natural frequency and mode shape of a bridge. Furthermore, the earthquake load acting on the bridge is also evaluated and hence the possibility of a resonance associated with this load is investigated. For this objective, the earthquake data collected during the past ten years in Indonesia is explored. This study considers the Tanjung Baru Bridge, a prestressed concrete bridge situated on the Medan-Kualanamu-Tebing Tinggi highway, as the case study. The modal analysis and the evaluation of the earthquake load confirm that the possibility of resonance for the Tanjung Baru Bridge is extremely low. The study also proves that this bridge has a sufficient capacity to withstand earthquake loads.

Influence of flow-induced bend–twist coupling on the natural vibration responses of flexible hydrofoils

Vortex-induced vibration of a flexibly-mounted circular cylinder free to oscillate in the crossflow direction with imposed rotation around its axis was studied experimentally. The rotation rate, α, defined as the ratio of the surface velocity and free stream velocity, was varied from 0 to 2.6 in small steps. The amplitudes and frequencies of oscillations as well as the flow forces were measured in a Reynolds number range of Re = 350 -1000. The maximum amplitude of oscillations was limited to values less than a diameter of the cylinder at high rotation rates. Also, the lock-in range became narrower at higher rotation rates and finally the oscillations ceased beyond α = 2.4. Vortex shedding pattern was found to be 2S (two single vortices shed per cycle of oscillations) for rotation rates up to α = 1.4 and transitioned toward an asymmetric P shedding (one pair of vortices shed in a cycle of oscillations) for rotation rates within the range of 1.4 ≤ α ≤ 1.8. Vortex shedding was found to persist up to higher rotation rates than those observed for a non-oscillating cylinder. The phase difference between the flow forces and displacement of the cylinder in the crossflow direction was influenced as the rotation rate was increased: At high reduced velocities, the phase difference decreased from 180° for a non-rotating cylinder to values close to 90° for a rotating cylinder at large rotation rates. Different shedding patterns resulted in flow forces with different frequencies. In the crossflow direction, the dominant frequency of flow forces was found to be close to the system’s natural frequency for all the rotation rates tested with either 2S or P vortex shedding pattern. In the inline direction, however, the change from 2S to P shedding at high rotation rates resulted in a shift of the ratio of the dominant frequency of the inline flow forces to the natural frequency of the system from 2:1 to 1:1.