Flexural Resonant Frequencies of Thin Rectangular Cantilever Plates

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Jason R. Looker ◽  
John E. Sader
Keyword(s):  
Singular Perturbation ◽  
Resonant Frequency ◽  
Analytical Formula ◽  
Flexural Vibration ◽  
Maximum Error ◽  
Vibration Frequencies ◽  
Resonant Frequencies ◽  
Aspect Ratios ◽  
Simple Analytical Formula ◽  
Simple Nature

Knowledge of the flexural vibration frequencies of thin rectangular cantilever plates forms the basis for numerous applications in sensing and instrumentation. Despite the seemingly simple nature of the problem, an accurate formula for the fundamental resonant frequency that is valid for all aspect ratios and Poisson’s ratios is notably lacking in the literature. In this article, we present such a result using a variational and singular perturbation formulation. This yields a simple analytical formula that exhibits a maximum error of 2%.

Pre-Impact Configuration Designing of a Robot Manipulator for Impact Minimization

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Jingchen Hu ◽  
Tianshu Wang
Keyword(s):  
Impact Force ◽  
Robot Manipulator ◽  
Analytical Formula ◽  
Joint Space ◽  
Collision Problem ◽  
Spatial Operator ◽  
Inertia Ellipsoid ◽  
The Impact ◽  
Maximum Minimum ◽  
Simple Analytical Formula

This paper studies the collision problem of a robot manipulator and presents a method to minimize the impact force by pre-impact configuration designing. First, a general dynamic model of a robot manipulator capturing a target is established by spatial operator algebra (SOA) and a simple analytical formula of the impact force is obtained. Compared with former models proposed in literatures, this model has simpler form, wider range of applications, O(n) computation complexity, and the system Jacobian matrix can be provided as a production of the configuration matrix and the joint matrix. Second, this work utilizes the impulse ellipsoid to analyze the influence of the pre-impact configuration and the impact direction on the impact force. To illustrate the inertia message of each body in the joint space, a new concept of inertia quasi-ellipsoid (IQE) is introduced. We find that the impulse ellipsoid is constituted of the inertia ellipsoids of the robot manipulator and the target, while each inertia ellipsoid is composed of a series of inertia quasi-ellipsoids. When all inertia quasi-ellipsoids exhibit maximum (minimum) coupling, the impulse ellipsoid should be the flattest (roundest). Finally, this paper provides the analytical expression of the impulse ellipsoid, and the eigenvalues and eigenvectors are used as measurements to illustrate the size and direction of the impulse ellipsoid. With this measurement, the desired pre-impact configuration and the impact direction with minimum impact force can be easily solved. The validity and efficiency of this method are verified by a PUMA robot and a spatial robot.

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.

scholarly journals Analysis of an Approximated Model for the Depletion Region Width of Planar Junctionless Transistors

Electronics ◽  
2019 ◽  
Vol 8 (12) ◽  
pp. 1436
Author(s):  
Arian Nowbahari ◽  
Avisek Roy ◽  
Muhammad Nadeem Akram ◽  
Luca Marchetti
Keyword(s):  
Numerical Simulations ◽  
Analytical Model ◽  
Threshold Voltage ◽  
Analytical Formula ◽  
Numerical Data ◽  
Maximum Error ◽  
Depletion Region ◽  
Comsol Multiphysics ◽  
Flat Band ◽  
Junctionless Transistors

In this paper, we investigate the accuracy of the approximated analytical model currently utilized, by many researchers, to describe the depletion region width in planar junctionless transistors (PJLT). The proposed analysis was supported by numerical simulations performed in COMSOL Multiphysics software. By comparing the numerical results and the approximated analytical model of the depletion region width, we calculated that the model introduces a maximum RMS error equal to 90 % of the donor concentration in the substrate. The maximum error is achieved when the gate voltage approaches the threshold voltage ( V t h ) or when it approaches the flat band voltage ( V F B ) of the transistor. From these results, we concluded that this model cannot be used to determine accurately the flat-band and the threshold voltage of the transistor, although it represents a straightforward method to estimate the depletion region width in PJLT. By using the approximated analytical model, we extracted an analytical formula, which describes the electron concentration at the ideal boundary of the depletion region. This formula approximates the numerical data extracted from COMSOL with a relative error lower than 1 % . The proposed formula is in our opinion, as useful as the formula of the approximated analytical model because it allows for estimating the position of the depletion region also when the drain and source terminals are not grounded. We concluded that the analytical formula proposed at the end of this work could be useful to determine the position of the depletion region boundary in numerical simulations and in graphical representations provided by COMSOL Multiphysics software.

A simple experiment for measuring bar longitudinal and flexural vibration frequencies

2010 ◽  
Vol 78 (12) ◽  
pp. 1429-1432 ◽  
Author(s):  
S. Velasco ◽  
F. L. Román ◽  
J. A. White
Keyword(s):  
Flexural Vibration ◽  
Vibration Frequencies ◽  
Simple Experiment

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.

Effect of Temperature on Electrical Resonance in Leopard Frog Saccular Hair Cells

1998 ◽  
Vol 79 (1) ◽  
pp. 312-321 ◽  
Author(s):  
M. S. Smotherman ◽  
P. M. Narins
Keyword(s):  
Steady State ◽  
Resonant Frequency ◽  
Hair Cells ◽  
Outward Current ◽  
Leopard Frog ◽  
Effect Of Temperature ◽  
Channel Kinetics ◽  
Resonant Frequencies ◽  
Voltage Dependent ◽  
Electrical Resonance

Smotherman, M. S. and P. M. Narins. Effect of temperature on electrical resonance in leopard frog saccular hair cells. J. Neurophysiol. 79: 312–321, 1998. Leopard frog saccular hair cells exhibit an electrical resonance in response to a depolarizing stimulus that has been proposed to contribute to the tuning properties of the frog sacculus by acting as an electrical band-pass filter. With the whole cell patch-clamp technique, we have investigated the effect of temperature on electrical resonances in isolated saccular hair cells, and we have described the effects of temperature on the currents and channel kinetics underlying electrical resonance. A hair cell's onset resonant frequency in response to a constant depolarizing current pulse increases linearly with temperature at a rate of 11 Hz/1°C, exhibiting a mean Q 10 of 1.7 between 15 and 35°C. However, offset resonant frequencies continue to double every 10°C, exhibiting a mean Q 10 of 2.1. If steady-state voltage during the stimulus is held constant, all oscillatory frequencies increase with a mean Q 10 of 2.1. The average level of steady-state depolarization during a +150-pA depolarizing current pulse decreases with increasing temperature (−6 mV from 15 to 25°C). This temperature-dependent reduction of the steady-state membrane potential causes a shift in the voltage-dependent channel kinetics to slower rates, thus reducing the apparent Q 10 for onset resonant frequencies. The peak outward tail current and net steady-state outward current, which is the sum of a voltage-dependent inward calcium current ( I Ca) and an outward calcium-dependent potassium current ( I K(Ca)), increase with temperature, exhibiting a mean Q 10 of 1.7 between 15 and 25°C. The activation rate ( T 1/2) of the outward current exhibits a mean Q 10 of 2.3 between 15 and 25°C, while the deactivation rate (τrel) exhibits a mean Q 10 of 2.9 over the same temperature range. These results support previous models of the molecular determination of resonant frequency, which have proposed that a combination of I K(Ca) channel kinetics and the overall magnitude of the outward current are primarily responsible for determining the resonant frequency of an isolated hair cell. The robust temperature sensitivity of the hair cell receptor potential contrasts sharply with the temperature-insensitive tuning properties of in vivo saccular nerve fiber recordings. Possible explanations for this discrepancy are discussed.

Group Theoretic Approach to the Exponential Cosine Screened Coulomb Potential

1985 ◽  
Vol 40 (5) ◽  
pp. 453-455 ◽  
Author(s):  
Barnana Roy
Keyword(s):  
Perturbation Method ◽  
Coulomb Potential ◽  
Analytical Formula ◽  
Theoretic Approach ◽  
Energy Eigenvalues ◽  
Screened Coulomb Potential ◽  
Simple Analytical Formula

Perturbation method, using the properties of SO (2,1) algebra is applied to get a simple analytical formula for energy eigenvalues of the exponential cosine screened Coulomb potential.

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