Whole-body vibration training: metabolic cost of synchronous, side-alternating or no vibrations.

Whole-body vibration training improves strength and can increase maximal oxygen consumption ([·V]O(2max)). No study has compared the metabolic demand of synchronous and side-alternating whole-body vibration. We measured [·V]O₂ and heart rate during a typical synchronous or side-alternating whole-body vibration session in 10 young female sedentary participants. The 20-min session consisted of three sets of six 45-s exercises, with 15 s recovery between exercises. Three conditions were randomly tested on separate days: synchronous at 35 Hz and 4 mm amplitude, side-alternating at 26 Hz and 7.5 mm amplitude (peak acceleration matched at 20 g in both vibration conditions), and no vibrations. Mean [·V]O₂ (expressed as %[·V]O(2max)) did not differ between conditions: 29.7 ± 4.2%, 32.4 ± 6.5%, and 28.7 ± 6.7% for synchronous, side-alternating, and no vibrations respectively (P = 0.103). Mean heart rate (% maximal heart rate) was 65.6 ± 7.3%, 69.8 ± 7.9%, and 64.7 ± 5.6% for synchronous, side-alternating, and no vibrations respectively, with the side-alternating vibrations being significantly higher (P = 0.019). When analysing changes over exercise sessions, mean [·V]O₂ was higher for side-alternating (P < 0.001) than for synchronous and no vibrations. In conclusion, side-alternating whole-body vibration elicits higher heart rate responses than synchronous or no vibrations, and could elevate [·V]O₂, provided the session lasts more than 20 min.

The effect of mountain bike suspensions on vibrations and off-road uphill performance.

AIM: This study evaluates the effect of front suspension (FS) and dual suspension (DS) mountain-bike on performance and vibrations during off-road uphill riding. METHODS: Thirteen male cyclists (27+/-5 years, 70+/-6 kg, VO(2max)59+/-6 mL.kg(-1).min(-1), mean+/-SD) performed, in a random sequence, at their lactate threshold, an off-road uphill course (1.69 km, 212 m elevation gain) with both type of bicycles. Variable measured: a) VO(2) consumption (K4b2 analyzer, Cosmed), b) power output (SRM) c) gain in altitude and d) 3-D accelerations under the saddle and at the wheel (Physilog, EPFL, Switzerland). Power spectral analy- sis (Fourier) was performed from the vertical acceleration data. RESULTS: Respectively for the FS and DS mountain bike: speed amounted to 7.5+/-0.7 km.h(-1) and 7.4+/-0.8 km.h(-1), (NS), energy expenditure 1.39+/-0.16 kW and 1.38+/-0.18, (NS), gross efficiency 0.161+/-0.013 and 0.159+/-0.013, (NS), peak frequency of vibration under the saddle 4.78+/-2.85 Hz and 2.27+/-0.2 Hz (P<0.01) and median-frequency of vertical displacements of the saddle 9.41+/-1.47 Hz and 5.78+/-2.27 Hz (P<0.01). CONCLUSION: Vibrations at the saddle level of the DS bike are of low frequencies whereas those of the FS bike are mostly of high frequencies. In the DS bike, the torque produced by the cyclist at the pedal level may generate low frequency vibrations. We conclude that the DS bike absorbs more high frequency vibrations, is more comfortable and performs as well as the FS bicycle.

Non-Linear Journal Bearing Model for Analysis of Superharmonic Vibrations of Rotor Systems

A rotating machine usually consists of a rotor and bearings that supports it. The nonidealities in these components may excite vibration of the rotating system. The uncontrolled vibrations may lead to excessive wearing of the components of the rotating machine or reduce the process quality. Vibrations may be harmful even when amplitudes are seemingly low, as is usually the case in superharmonic vibration that takes place below the first critical speed of the rotating machine. Superharmonic vibration is excited when the rotational velocity of the machine is a fraction of the natural frequency of the system. In such a situation, a part of the machine’s rotational energy is transformed into vibration energy. The amount of vibration energy should be minimised in the design of rotating machines. The superharmonic vibration phenomena can be studied by analysing the coupled rotor-bearing system employing a multibody simulation approach. This research is focused on the modelling of hydrodynamic journal bearings and rotorbearing systems supported by journal bearings. In particular, the non-idealities affecting the rotor-bearing system and their effect on the superharmonic vibration of the rotating system are analysed. A comparison of computationally efficient journal bearing models is carried out in order to validate one model for further development. The selected bearing model is improved in order to take the waviness of the shaft journal into account. The improved model is implemented and analyzed in a multibody simulation code. A rotor-bearing system that consists of a flexible tube roll, two journal bearings and a supporting structure is analysed employing the multibody simulation technique. The modelled non-idealities are the shell thickness variation in the tube roll and the waviness of the shaft journal in the bearing assembly. Both modelled non-idealities may cause subharmonic resonance in the system. In multibody simulation, the coupled effect of the non-idealities can be captured in the analysis. Additionally one non-ideality is presented that does not excite the vibrations itself but affects the response of the rotorbearing system, namely the waviness of the bearing bushing which is the non-rotating part of the bearing system. The modelled system is verified with measurements performed on a test rig. In the measurements the waviness of bearing bushing was not measured and therefore it’s affect on the response was not verified. In conclusion, the selected modelling approach is an appropriate method when analysing the response of the rotor-bearing system. When comparing the simulated results to the measured ones, the overall agreement between the results is concluded to be good.

Vibrations in Rotating Machinery Arising from Minor Imperfections in Component Geometries

Vibrations in machines can cause noise, decrease the performance, or even damage the machine. Vibrations appear if there is a source of vibration that excites the system. In the worst case scenario, the excitation frequency coincides with the natural frequency of the machine causing resonance. Rotating machines are a machine type, where the excitation arises from the machine itself. The excitation originates from the mass imbalance in the rotating shaft, which always exists in machines that are manufactured using conventional methods. The excitation has a frequency that is dependent on the rotational speed of the machine. The rotating machines in industrial use are usually designed to rotate at a constant rotational speed, the case where the resonances can be easily avoided. However, the machines that have a varying operational speed are more problematic due to a wider range of frequencies that have to be avoided. Vibrations, which frequencies equal to rotational speed frequency of the machine are widely studied and considered in the typical machine design process. This study concentrates on vibrations, which arise from the excitations having frequencies that are multiples of the rotational speed frequency. These vibrations take place when there are two or more excitation components in a revolution of a rotating shaft. The dissertation introduces four studies where three kinds of machines are experiencing vibrations caused by different excitations. The first studied case is a directly driven permanent magnet generator used in a wind power plant. The electromagnetic properties of the generator cause harmonic excitations in the system. The dynamic responses of the generator are studied using the multibody dynamics formulation. In another study, the finite element method is used to study the vibrations of a magnetic gear due to excitations, which frequencies equal to the rotational speed frequency. The objective is to study the effects of manufacturing and assembling inaccuracies. Particularly, the eccentricity of the rotating part with respect to non-rotating part is studied since the eccentric operation causes a force component in the direction of the shortest air gap. The third machine type is a tube roll of a paper machine, which is studied while the tube roll is supported using two different structures. These cases are studied using different formulations. In the first case, the tube roll is supported by spherical roller bearings, which have some wavinesses on the rolling surfaces. Wavinesses cause excitations to the tube roll, which starts to resonate at the frequency that is a half of the first natural frequency. The frequency is in the range where the machine normally operates. The tube roll is modeled using the finite element method and the bearings are modeled as nonlinear forces between the tube roll and the pedestals. In the second case studied, the tube roll is supported by freely rotating discs, which wavinesses are also measured. The above described phenomenon is captured as well in this case, but the simulation methodology is based on the flexible multibody dynamics formulation. The simulation models that are used in both of the last two cases studied are verified by measuring the actual devices and comparing the simulated and measured results. The results show good agreement.

Finite field treatment of vibrational polarizabilities and hyperpolarizabilities: on the role of the Eckart conditions, their implementation, and their use in characterizing key vibrations

In the finite field (FF) treatment of vibrational polarizabilities and hyperpolarizabilities, the field-free Eckart conditions must be enforced in order to prevent molecular reorientation during geometry optimization. These conditions are implemented for the first time. Our procedure facilities identification of field-induced internal coordinates that make the major contribution to the vibrational properties. Using only two of these coordinates, quantitative accuracy for nuclear relaxation polarizabilities and hyperpolarizabilities is achieved in π-conjugated systems. From these two coordinates a single most efficient natural conjugation coordinate (NCC) can be extracted. The limitations of this one coordinate approach are discussed. It is shown that the Eckart conditions can lead to an isotope effect that is comparable to the isotope effect on zero-point vibrational averaging, but with a different mass-dependence

Are the maximum hardness and minimum polarizability principles always obeyed in nontotally symmetric vibrations?

An overview is given on a study which showed that not only in chemical reactions but also in the favorable case of nontotally symmetric vibrations where the chemical and external potentials keep approximately constant, the generalized maximum hardness principle (GMHP) and generalized minimum polarizability principle (GMPP) may not be obeyed. A method that allows an accurate determination of the nontotally symmetric molecular distortions with more marked GMPP or anti-GMPP character through diagonalization of the polarizability Hessian matrix is introduced

On the relationship of normal modes to local modes in molecular vibrations

A simple model for the effective vibrational hamiltonian of the XH stretching vibrations in H2O, NH3 and CH4 is considered, based on a morse potential function for the bond stretches plus potential and kinetic energy coupling between pairs of bond oscillators. It is shown that this model can be set up as a matrix in local mode basis functions, or as a matrix in normal mode basis functions, leading to identical results. The energy levels obtained exhibit normal mode patterns at low vibrational excitation, and local mode patterns at high excitation. When the hamiltonian is set up in the normal mode basis it is shown that Darling-Dennison resonances must be included, and simple relations are found to exist between the xrs, gtt, and Krrss anharmonic constants (where the Darling-Dennison coefficients are denoted K) due to their contributions from morse anharmonicity in the bond stretches. The importance of the Darling-Dennison resonances is stressed. The relationship of the two alternative representations of this local mode/normal mode model are investigated, and the potential uses and limitations of the model are discussed.