On the Lateral Vibrations of a Vertically Moving String With a Harmonically Varying Length

2015 ◽  
Author(s):  
Nick V. Gaiko ◽  
Wim T. van Horssen
Keyword(s):  
Resonant Frequency ◽  
Energy Analysis ◽  
Dimensional System ◽  
Time Varying ◽  
Resonant Frequencies ◽  
Lateral Vibrations ◽  
Taut String ◽  
Varying Length ◽  
Long Timescales ◽  
Elevator Cable

In this paper, the free lateral vibrations of a vertically translating continuum modeled as a taut string with variable length are studied. The time-varying length of the cable is described by a harmonically varying function about a constant mean length. This model can be used to describe the lateral vibrations of an elevator cable with changing length. A Fourier series approach is used to predict resonant frequencies arising because of the length fluctuation. The amplitudes of vibrations are represented by the infinitely dimensional system of coupled ordinary differential equations. This system is studied by Galerkin’s truncation method for the lowest resonant frequency. The obtained results are in agreement with the energy analysis, but the truncation technique leads to inaccurate approximations on long timescales. Hence, an alternative analytical method is proposed promising an accurate approximation of the response on long timescales for the general resonant frequency.

Transverse vibration of flexible hoisting rope with time-varying length

2014 ◽  
Vol 28 (2) ◽  
pp. 457-466 ◽  
Author(s):  
Ji-hu Bao ◽  
Peng Zhang ◽  
Chang-Ming Zhu ◽  
Wei Sun
Keyword(s):  
Transverse Vibration ◽  
Time Varying ◽  
Varying Length ◽  
Flexible Hoisting Rope

Free Vibration Energy and Period of a String With Time-Varying Length

2000 ◽  
Author(s):  
Seung-Yop Lee
Keyword(s):  
Free Vibration ◽  
Traveling Waves ◽  
Moving Boundary ◽  
String Tension ◽  
New Technique ◽  
Vibration Energy ◽  
Time Varying ◽  
Constant Rate ◽  
Varying Length ◽  
A New Technique

Abstract We introduce a new technique to analyze free vibration energy and natural frequencies of a string with time-varying length by dealing with traveling waves. One of boundaries is vertically fixed but it moves axially at a constant rate. When the string length is varied, the free vibration energy and period also change with time. String tension and non-zero instantaneous vertical velocity at the moving boundary results in the energy variation. When the string undergoes retraction, the vibration energy increases with time. The new technique using traveling waves gives the exact amount of energy transferred into the vibrating system at the moving boundary. The free vibration energy are compared with previous results using the perturbation method and Kotera’s approach.

Non-linear dynamic analysis of time varying length flexible body

2020 ◽  
Vol 2020 (0) ◽  
pp. 513
Author(s):  
Masato TAKEUCHI ◽  
Kensuke HARA ◽  
Hiroshi YAMAURA
Keyword(s):  
Dynamic Analysis ◽  
Flexible Body ◽  
Time Varying ◽  
Linear Dynamic ◽  
Non Linear ◽  
Varying Length

scholarly journals Piezoelectric MEMS Acoustic Transducer with Electrically-Tunable Resonant Frequency

Micromachines ◽  
2022 ◽  
Vol 13 (1) ◽  
pp. 96
Author(s):  
Alessandro Nastro ◽  
Marco Ferrari ◽  
Libor Rufer ◽  
Skandar Basrour ◽  
Vittorio Ferrari
Keyword(s):  
Acoustic Emission ◽  
Resonant Frequency ◽  
Piezoelectric Layer ◽  
Flexural Mode ◽  
Resonant Frequencies ◽  
Voltage Mode ◽  
Acoustic Transducer ◽  
Aln Film ◽  
Doped Silicon ◽  
Piezoelectric Mems

The paper presents a technique to obtain an electrically-tunable matching between the series and parallel resonant frequencies of a piezoelectric MEMS acoustic transducer to increase the effectiveness of acoustic emission/detection in voltage-mode driving and sensing. The piezoelectric MEMS transducer has been fabricated using the PiezoMUMPs technology, and it operates in a plate flexural mode exploiting a 6 × 6 mm doped silicon diaphragm with an aluminum nitride (AlN) piezoelectric layer deposited on top. The piezoelectric layer can be actuated by means of electrodes placed at the edges of the diaphragm above the AlN film. By applying an adjustable bias voltage Vb between two properly-connected electrodes and the doped silicon, the d31 mode in the AlN film has been exploited to electrically induce a planar static compressive or tensile stress in the diaphragm, depending on the sign of Vb, thus shifting its resonant frequency. The working principle has been first validated through an eigenfrequency analysis with an electrically induced prestress by means of 3D finite element modelling in COMSOL Multiphysics®. The first flexural mode of the unstressed diaphragm results at around 5.1 kHz. Then, the piezoelectric MEMS transducer has been experimentally tested in both receiver and transmitter modes. Experimental results have shown that the resonance can be electrically tuned in the range Vb = ±8 V with estimated tuning sensitivities of 8.7 ± 0.5 Hz/V and 7.8 ± 0.9 Hz/V in transmitter and receiver modes, respectively. A matching of the series and parallel resonant frequencies has been experimentally demonstrated in voltage-mode driving and sensing by applying Vb = 0 in transmission and Vb = −1.9 V in receiving, respectively, thereby obtaining the optimal acoustic emission and detection effectiveness at the same operating frequency.

scholarly journals THE STUDY OF ACOUSTIC CHARACTERISTICS OF THE PERFORATED AND HOMOGENOUS PLATES WITH SIMILAR GEOMETRICAL DIMENSIONS

Akustika ◽  
2019 ◽  
Vol 32 ◽  
pp. 79-82
Author(s):  
Valery Kirpichnikov ◽  
Lyudmila Drozdova ◽  
Alexei Koscheev ◽  
Ernst Myshinsky
Keyword(s):  
Resonant Frequency ◽  
Acoustic Radiation ◽  
Perforated Plate ◽  
Acoustic Characteristics ◽  
Resonant Frequencies ◽  
Perforated Plates ◽  
Resonance Frequencies ◽  
Flexural Vibrations ◽  
Geometrical Dimensions

The resonance frequencies of the flexural vibrations, input vibration excitability and acoustic radiation of the homogeneous and perforated plates were investigated. It is established that the average reduction range of the lower resonant frequency of flexural vibrations of the tested plates with the holes virtually coincides with the predictive estimate. The levels of the input vibration excitability of the perforated plate at the lower resonant frequencies exceeded the levels at the corresponding frequencies of the homogeneous plates greater than the calculated value. The levels of resonance acoustic radiation of the perforated plate were significantly less than of the homogeneous one.

Robust Passive-Active Mounts for Machinery and Equipment

1997 ◽  
Author(s):  
J. Hannsen Su
Keyword(s):  
Resonant Frequency ◽  
Vibration Isolation ◽  
Vibration Suppression ◽  
Low Frequency ◽  
The Other ◽  
Resonant Frequencies ◽  
Vibration Magnitude ◽  
Fixed End ◽  
Degradation Problem ◽  
Universal Application

Abstract Conventional vibration isolation mounts are not as effective as expected on a practical foundation whose resonant frequencies normally are within the bandwidth of interest. In addition, the low frequency enhancement is a characteristic of the passive mounts. Applying inertia actuators to the bottom attachment plate of the conventional mounts overcomes these shortcomings and enhances their performance significantly. This design concept has universal application since it is applicable to any dynamic system. It requires very little power and force capacity, i.e., a small percentage of the disturbance force, from the actuators to be effective for frequencies higher than the resonant frequency of the mount itself. The effectiveness of the proposed mounts for the machinery is demonstrated on the load transmissibility reduction at the foundation support (fixed end) due to disturbance from machinery above mounts. On the other hand, the vibration magnitude reduction of equipment above mounts due to disturbance from the foundation is used for evaluating the equipment isolation effectiveness. There is no stabilty or degradation problem when a number of the passive-active mounts are used on the same foundation. Furthermore, the more of this type of mounts used on a foundation the more effective the vibration suppression and the smaller actuator force requirement for each passive-active mount.

Analysis of a circular microstrip antenna on isotropic or uniaxially anisotropic substrate using neurospectral approach

2013 ◽  
Vol 33 (1/2) ◽  
pp. 567-580 ◽  
Author(s):  
Sami Bedra ◽  
Siham Benkouda ◽  
Tarek Fortaki
Keyword(s):  
Resonant Frequency ◽  
Quality Factor ◽  
Microstrip Antenna ◽  
Numerical Results ◽  
Spectral Domain ◽  
Quality Factors ◽  
Resonant Frequencies ◽  
Content Type ◽  
Anisotropic Substrate ◽  
Circular Microstrip Antenna

Purpose – The paper aims to propose an artificial neural network (ANN) in conjunction with spectral domain formulation for fast and accurate determination of the resonant frequency and quality factor of circular microstrip antenna printed on isotropic or anisotropic substrate. This neurospectral approach reduces the problem complexity. Design/methodology/approach – The moment method implemented in the spectral domain provides good accuracy but its computational cost is high due to the evaluation of the slowly decaying integrals and the iterative nature of the solution process. The paper introduces the electromagnetic knowledge combined with ANN in the analysis of circular microstrip antenna on isotropic or uniaxially anisotropic substrate to reduce the complexity of the spectral approach and to minimize the CPU time necessary to obtain the numerical results. Findings – The resonant frequency results obtained from the neural model are in very good agreement with the experimental and theoretical results available in the literature. Finally, numerical results for the substrate anisotropy effect on the resonant frequency, quality factor and radiation pattern are also presented. Originality/value – The paper develops fast and accurate model based on ANN technique to calculate the resonant frequencies and quality factors of circular microstrip antennas. ANN is used to model the relationship between the parameters of the microstrip antenna and the resonant frequencies and quality factors obtained from the spectral domain approach. This relatively simple model allows designers to predict accurately the resonant frequencies and quality factors for a given design without having to develop or run the spectral method codes themselves. The main advantages of the method are: less computing time than the spectral model, results with accuracy equivalent to that of full-wave models and cost effectiveness, since the client can use a simple PC for implementation. Another advantage of the proposed ANN model is that it takes into account the uniaxial anisotropy in the substrate without increasing the network size. This is done by combining ANN with electromagnetic knowledge.

Transfer impedances between different regions of branched excitable cells

1988 ◽  
Vol 59 (3) ◽  
pp. 689-705 ◽  
Author(s):  
L. E. Moore ◽  
K. Yoshii ◽  
B. N. Christensen
Keyword(s):  
Resonant Frequency ◽  
Voltage Clamp ◽  
Growth Cone ◽  
Transfer Functions ◽  
Excitable Cells ◽  
Resonant Frequencies ◽  
Steady State Current ◽  
Branching Patterns ◽  
Voltage Dependent ◽  
Impedance Functions

1. The excitable properties of branched cells were measured using a combination of voltage-clamp and frequency-domain techniques. Point impedance functions from either the soma or growth cone of NG-108 cells were curve fitted with a reduced cable model at different membrane potentials to establish kinetic parameters. 2. Transfer impedance functions between the soma and growth cone were measured and simulated with a morphologically determined model. In these experiments the membrane potential was controlled by a single-electrode voltage clamp thus allowing an estimate of transfer functions for any arbitrary input, such as a single synaptic current for differing degrees of tonic synaptic drive. Furthermore, the integration of different regional inputs was evaluated based on the transfer functions between different locations on an individual cell. 3. The activation of an outward steady-state current leads to resonating impedance functions that were used to evaluate the kinetic properties of ionic channels in different regions of branched excitable cells. For simple branching patterns the point and transfer impedances show lower resonant frequencies for active growth cones compared with active somas. 4. More complex branching patterns showed the unexpected result that the voltage-dependent resonant frequency was higher for the growth cone recording than the soma. The presence of a higher resonant frequency when the growth cone is activated does not require more rapid kinetics of the active potassium conductance, since the time constant of the active conductance can be the same in the growth cone and the soma membrane. 5. In conclusion, the resonant frequencies, as well as all other aspects of the impedance functions, are complicated interactions of the detailed branching patterns and active conductances. In general, these interactions are not predictable from a passive electrotonic analysis, especially when the voltage-dependent conductances are distributed throughout the dendritic tree.

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