Laplace Transform is often used in solving the free vibration problems of structural beams. In existing research, there are two types of simplified models of continuous beam placement. The first is to regard the continuous beam as a single-span beam, the middle bearing of which is replaced by the bearing reaction force; the second is to divide the continuous beam into several simply supported beams, with the bending moment of the continuous beam at the middle bearing considered as the external force. Research shows that the second simplified model is incorrect, and the frequency equation derived from the first simplified model contains multiple expressions which might not be equivalent to each other. This paper specifies the application method of Laplace Transform in solving the free vibration problems of continuous beams, having great significance in the proper use of the transform method.

A new method of optical frequency beat counting based on fast Fourier transform (FFT) analysis is described. Signals with a worse signal-to-noise ratio can be counted correctly comparing to the conventional counting method of detecting each period separately. The systematic error of FFT counting below 10 Hz is demonstrated and can be decreased. Additionally the modulation width of a frequency-stabilized laser with high frequency modulation index can be simultaneously measured during a carrier frequency measurement against an optical frequency synthesizer or other laser.

When a frequency domain sensor is under the effect of an input stimulus, there is a frequency shift at its output. One of the most important advantages of such sensors is their converting a physical input parameter into time variations. In consequence, changes of an input stimulus can be quantified very precisely, provided that a proper frequency counter/meter is used. Unfortunately, it is well known in the time-frequency metrology that if a higher accuracy in measurements is needed, a longer time for measuring is required. The principle of rational approximations is a method to measure a signal frequency. One of its main properties is that the time required for measuring decreases when the order of an unknown frequency increases. In particular, this work shows a new measurement technique, which is devoted to measuring the frequency shifts that occur in frequency domain sensors. The presented research result is a modification of the principle of rational approximations. In this work a mathematical analysis is presented, and the theory of this new measurement method is analysed in detail. As a result, a new formalism for frequency measurement is proposed, which improves resolution and reduces the measurement time.

Complaints and awareness about environmental low-frequency (LF) noise and infrasound (IS) have increased in recent years, but knowledge about perceptual mechanisms is limited. To evaluate the use of the brain’s frequency-following response (FFR) as an objective correlate of individual sensitivity to IS and LF, we recorded the FFR to monaurally presented IS (11 Hz) and LF (38 Hz) tones over a 30-phon range for 11 subjects. It was found that 11-Hz FFRs were often significant already at ~0 phon, steeply grew to 20 phon, and saturated above. In contrast, the 38-Hz FFR growth was relatively shallow and continued to 60 phon. Furthermore, at the same loudness level (30 phon), the 11-Hz FFR strength was significantly larger (4.5 dB) than for 38 Hz, possibly reflecting a higher phase synchronization across the auditory pathway. Overall, unexpected inter-individual variability as well as qualitative differences between the measured FFR growth functions and typical loudness growth make interpretation of the FFR as objective correlate of IS and LF sensitivity difficult.

The paper presents results of numerical calculations and experimental data on the directional pattern of two 38-element parametric arrays composed of ultrasound sources. Two types of antenna arrays are considered, namely with parallel and coaxial connections of ultrasonic transducers (elements). The results of selecting and functional testing of unit elements are described in this paper. It is found that in the coaxial element connection of the antenna array, the level of side lobes is higher than that in the parallel element connection.

Single Frequency Networks (SFN) of transmitters are currently used in television and digital broadcasting to effectively cover large areas using minimal spectral resources and using transmitters with much lower power than if the same area were covered using one transmitter. It is therefore a very ecological solution. In this way, much better reception conditions are obtained in large city areas, as the signal reaches the receiving antenna from different directions, reducing the risk of shading. However, in this type of network one should take into account the loss of signal caused by signal interference. Using the appropriate propagation model, it is possible, with appropriate assumptions, to check how the operation of the third transmitter affects the distribution and size of the deepest fades in relation to the network in which there are two transmitters.

Thermoacoustic refrigerator uses acoustic power to transport heat from a low-temperature source to a high-temperature source. The increasing interest in thermoacoustic technology is caused due to its simplicity, reliability as well as application of environmentally friendly working fluids. A typical thermoacoustic refrigerator consists of a resonator, a stack of parallel plates, two heat exchangers and a source of acoustic wave. The article presents the influence of the stack position in the resonance tube and the acoustic frequency on the performance of thermoacoustic refrigerator with a standing wave driven by a loudspeaker, which is measured in terms of the temperature difference between the stack edges. The results from experiments, conducted for the stack with the plate spacing 0.3 mm and the length 50 mm, acoustic frequencies varying between 100 and 400 Hz and air as a working fluid are consistent with the theory presented in this paper. The experiments confirmed that the temperature difference for the stack with determined plate spacing depends on the acoustic frequency and the stack position. The maximum values were achieved for resonance frequencies and the stack position between the pressure and velocity node.

This paper proposes a self-excited induction generator model with saturation effect for power generating mode in a remote site. The model is led through the space vector mathematical formalism and allows one to analyze the steady and dynamic states. It is developed for a squirrel cage induction machine. This model provides magnetizing inductance variation able to influence the build-up and the stabilization of voltage generation when the load changes. The final result is a realistic approach model which takes into con- sideration the dependency of the magnetizing inductance versus magnetizing current. This novel model is validated through experimental measurements to demonstrate its validity and practicability.

Microwave frequency detectors enable immediate determination of an unknown microwave signal frequency. Measurement is possible if the output characteristic of a frequency detector is unequivocal in a selected band of operation. The paper presents a method for obtaining unequivocal output characteristics for a given band of frequency detector operation.

In this paper, a discrete wavelet transform (DWT) based approach is proposed for power system frequency estimation. Unlike the existing frequency estimators mainly used for power system monitoring and control, the proposed approach is developed for fundamental frequency estimation in the field of energy metering of nonlinear loads. The characteristics of a nonlinear load is that the power signal is heavily distorted, composed of harmonics, inter-harmonics and corrupted by noise. The main idea is to predetermine a series of frequency points, and the mean value of two frequency points nearest to the power system frequency is accepted as the approximate solution. Firstly the input signal is modulated with a series of modulating signals, whose frequencies are those frequency points. Then the modulated signals are decomposed into individual frequency bands using DWT, and differences between the maximum and minimum wavelet coefficients in the lowest frequency band are calculated. Similarities among power system frequency and those frequency points are judged by the differences. Simulation results have proven high immunity to noise, harmonic and inter-harmonic interferences. The proposed method is applicable for real-time power system frequency estimation for electric energy measurement of nonlinear loads.

The paper deals with the basic set-up of single-frequency microchip laser - so called Lyot filter configuration. Description of its operation and practical realization is given. Some results obtained for Nd:YAG/KTP microchip laser are presented. The evidences of single-frequency operation and its limits are emphasized. Described construction constitutes the base for building the frequency stabilization of green 532 nm microchip laser.

Centrifugal pumps are used for different applications that include pressure boosting, wastewater, water supply, heating and cooling distribution and other industrial processes. This paper presents theoretical and experimental investigations of mechanical vibrations of a centrifugal pump. The flow in this pump, which induces pressure pulsations and mechanical vibrations, have been monitored. Vibration measurements and data collection (overall vibrations levels and frequency spectrum) were extracted from the system. In addition, one of the methods used to study vibration amplitudes for this pump is forced response analysis. To study and analyze the pump system, the finite element analysis software (ANSYS) was applied. Depending on the analysis performed and investigations outcomes, the system natural frequency coincides with the vane-pass frequency (VPF) hazardously. To attenuate the system’s vibration, a vibration control element was used. The vibration levels were reduced by a factor of 2 for a tuned element as obtained from a forced harmonic response analysis of the pump system with absorber. It is shown that the inserted element allows the centrifugal pump to work in a safe operating range without any interference with its operation.

A nanoscale beam model containing defect under the piezoelectricity considering the surface effects and flexoelectricity is established on the framework of Euler-Bernoulli theory. The governing equations of motion and related boundary conditions are derived by using Hamilton’s principle. The imperfect nanobeam is modeled by dividing the beam into two separate parts that are connected by a rotational and a longitude spring at the defect location. Analytical results on the free vibration response of the imperfect piezoelectric nanobeam exhibit that the flexoelectricity and the surface effects are sensitive to the boundary conditions, defect position, and geometry of the nanobeam. Numerical results are provided to predict the mechanical behavior of a weakened piezoelectric nanobeam considering the flexoelectric and surface effects. It is also revealed that the voltage, defect severity, and piezoelectric material have a critical role on the resonance frequency. The work is envisaged to underline the influence of surface effects and flexoelectricity on the free vibration of a cracked piezoelectric nanobeam for diverse boundary conditions. It should be mentioned, despite our R. Sourkiprevious works, an important class of piezoelectric materials used nowadays and called piezoelectric ceramics is considered in the current study.