High Frequency Vibration Analysis Research Articles

High-frequency vibration analysis of laminated composite plates using energy flow and shear deformation theories

Energy Flow Analysis (EFA) is an efficient approach for characterizing high-frequency vibrations through time-averaged energy density distributions. This study employs EFA to investigate vibroacoustic behavior in laminated composite plates subjected to high-frequency excitation. Governing equations of motion are derived using Classical Plate Theory (CPT), First Order Shear Deformation Theory (FSDT), and Higher Order Shear Deformation Theories (HSDT). Wave propagation parameters like wave number and group velocity are obtained from each theory and compared to assess accuracy. Energy density and intensity formulations are then developed based on classical solutions of the governing equations. EFA analysis indicates that HSDT provides more accurate predictions of wave parameters, especially at very high frequencies where it accounts better for shear deformation effects. Validation against classical energy density solutions shows acceptable accuracy with less than 0.5dB difference in the far-field. Comparisons further demonstrate the superiority of HSDT over FSDT for thicker plates in both classical and EFA analyses. This research establishes the effectiveness of EFA for high-frequency vibration analysis of composite laminates. The main novelty of this research lies in the integration of HSDT into the application of EFA for composite laminates, providing a more precise consideration of shear deformation effects at high frequencies. Specifically, HSDT enhances modeling of critical shear deformation effects at elevated frequencies. EFA delivers computationally efficient solutions while maintaining acceptable accuracy, improving characterization and design of composite structures under high-frequency loading.

A Symplectic-Spectral Element Method for High Frequency Vibration Analysis and Its Application in Structure-Borne Noise Prediction

The frequency-domain vibration model of the vehicle-track structure is established based on the symplectic-spectral element method (S-SEM). To this end, the vehicle is considered as 10-degree-of-freedom, and the rail is modeled by an infinite Timoshenko beam supported by discrete sprung fasteners. Further, the track slab and base plate are regarded as two-dimensional Timoshenko beams supported by uniformly distributed sprung elements. Using the pseudo excitation method (PEM), the track irregularity is viewed as the pseudo load. The vibration response and the internal force of the single-layer or multi-layer beam models are obtained by solving the corresponding S-SEM-based equations. The spectral forces are also applied in frequency bands to the finite element (FE) and statistical energy analysis (SEA) acoustic models. The steel-concrete composite bridge deck is simulated with composite plate materials. The effectiveness of the proposed method is verified by comparing the predicted results with those obtained from the field test. The achieved results reveal that multi-layer beam structures effectively consume energy, and elastic fasteners and steel springs are capable of effectively reducing bridge noise.

High-Frequency Vibration Analysis and Optimization of Irregular Wear of Pantograph Carbon Strips

The irregular wear of carbon current collector pantograph strips increases the railway maintenance costs and introduces safety hazards in the railway operation. This paper presents a method for analyzing the irregular wear of carbon strips with numerical dynamic analyses and modal tests. The carbon strips were studied in laboratory tests, and an equivalent numerical model for the investigation of their irregular wear and performance improvement was established. The results from the computational simulations were evaluated based on the laboratory results, and the correlation between the high-frequency vibration and irregular wear of the carbon strips was studied. The irregular wear contour of the carbon strips coincides with the high-frequency mode shape according to the experimental and numerical results. Moreover, the dynamic design for carbon strips was optimized with the validated computational model. The results suggest that the optimized schemes effectively mitigate the irregular wear of carbon strips.

High-frequency vibration analysis of LiTaO3 piezoelectric plates excited by lateral electric fields produced by surface electrodes under viscous liquid loadings for sensing

In this work, the coupled thickness-shear and flexural vibrations of the LiTaO3 piezoelectric plates excited by lateral electric fields produced by surface electrodes under viscous liquid loadings are modeled and analyzed based on Mindlin’s plate theory. The influences of liquid properties on the admittance characteristics and frequency shifts of the piezoelectric bulk acoustic wave devices operate in the lateral field excitation (LFE) mode are examined. In addition, the effects of the structure parameters, such as the electrode gap width, electrode/plate mass ratio and the electrode width, on the frequency sensitivity are investigated. It is shown that with the increasing electrode/plate mass ratio R, the sensitivities of the device on liquid viscosity and density increase first and then decrease, there is a maximal sensitivity when R is with a certain value. The varying trends of the frequency shifts with various liquid properties and sensitivities with various structural parameters are verified by the FEM simulations. The results are crucial to obtain good vibration characteristics and sensitivities for liquid-phase LFE piezoelectric sensors by using LiTaO3 piezoelectric crystals.

An energy flow model for high-frequency vibration analysis of two-dimensional panels in supersonic airflow

Many energy flow models have been proposed for high-frequency forced vibration analysis of structures. In this paper, a novel energy flow model is developed to predict the high-frequency vibration response of panels in supersonic airflow and quantify the effects of supersonic airflow on high-frequency forced vibration characteristics. The additional damping due to supersonic airflow is derived from the motion equation of a two-dimensional panel. The relationship between the wavenumber and the group velocity is introduced to describe the energy transmission property considering the effects of supersonic airflow. Then the energy density governing equation (i.e. energy flow model) is established and solved by the energy flow analysis (EFA) and the energy finite element method (EFEM). Finally, comparing the vibration responses obtained by the present energy flow model with the corresponding exact analytical solutions, the developed energy flow model is verified to be effective for high-frequency vibration analysis of panels in supersonic airflow. Furthermore, the numerical simulations indicate that supersonic airflow can affect the equivalent damping of the propagating elastic waves, and thus change the energy density distribution of the panel.

Distributed measurement system based on CAN data bus

PurposeThis paper aims to describe the idea behind and design of a miniaturized distributed measurement system based on a controller area network (CAN) data bus.Design/methodology/approachThe intention of the designers was to build a light and modular measurement system which can be used in remotely piloted aircraft systems and ultra-light aircraft during flight tests, as well as normal operation. The structure of this distributed measurement system is based on a CAN data bus. The CAN aerospace standard has been applied to the software as well as the hardware comprising this system. PRP-W2 software designed for PCs is an additional component of the proposed measurement system. This software supports data acquisition from a recorder unit and allows for preliminary data analysis, as well as data conversion and presentation.FindingsThe system, complete with a high-speed data recorder, was successfully installed on board of an MP-02 Czajka aircraft. A research experiment using the system and oriented on airframe high frequency vibration analysis is presented in the final part of this paper.Research limitations/implicationsThis measurement system allows analysis of high-frequency vibrations occurring at selected points of the aircraft. A data set is recorded by three-axis accelerometers and gyroscopes at frequencies up to 1 kHz.Practical implicationsThe use of a miniature and lightweight modular measurement system will, in many cases, be faster and less expensive than full-scale measurement and data acquisition systems, which often require a lengthy assembly process. The implementation of this class of lightweight flight test systems has many advantages, in particular to the operation of small aircraft. Such solutions are likely to become increasingly common in unmanned aerial vehicles and in other light aircraft in the future.Originality/valueThe adaptation of a distributed measuring system with a high frequency of measurements for purposes of small and miniature aircraft.

An energy finite element method for high frequency vibration analysis of beams with axial force

In order to predict the high frequency vibration response of beams with axial force, an energy finite element method (EFEM) is developed. An Euler–Bernoulli beam with constant axial force is considered. The energy density and energy intensity of the beam with axial force are introduced, and the relationship between the wavenumber and group velocity is derived, then the energy density governing equation is established. In addition, the impedance of beam with axial force is derived to calculate the input power, and the energy density is evaluated by solving the governing equation using finite element method. Finally, the feasibility and correctness of the present EFEM are verified by comparing the results obtained by the EFEM with the corresponding exact solutions. The effects of axial force on the energy density response and the limitations of EFEM are also discussed.

Analysis of high frequency vibrations and heat impact on human hands

This article describes combined impact of ultrasound and heat therapies on patients with rheumatoid arthritis, systemic scleroderma and Raynaud’s syndrome. Theoretical background of ultrasound and thermal effect was analyzed and described. Flexibility, strength and temperature of subjects’ wrists and hands were investigated using thermographic camera, dynamometer, and physiological indicators. Investigation results were analyzed and demonstrated in graphs.

High frequency vibration analysis in drilling of GFRP laminates using candlestick drills

The vibration signal contains a lot of information closely related to the tool performance in drilling the composite material. However, due to the limit of the frequency response characteristics of piezoelectric accelerometer, the monitored vibration signals used in researches were usually below 10kHz. Thus, the high frequency vibration signal was ignored. Drilling experiments of Glass Fiber Reinforced Plastic (GFRP) laminates were carried out utilizing candlestick drills in this article. The high frequency vibration signals of ten candlestick drills with different drill tip geometry parameters were analyzed and compared in time domain, frequency domain and in bispectrum. The results revealed that there was high frequency vibration signal above 10kHz in the process of drilling GFRP laminate. These signals were sensitive to the changes of the drill tip geometry parameters. The changes of the bispectrum energies of these signals could reflect the changes of the cutting performances and the delamination factors for the drills.

Excitation device for high frequency vibration analysis: Design and test results

In the present paper, the design and optimization of a high frequency excitation source is presented. The device was developed for a harmonic response analysis test bench, aimed at dynamic characterization and resonance prediction of mechanical structures. A wide frequency range must be covered, depending on the analyzed structure: the range 1–10 kHz was considered in the present work. The device was designed for a test bench aimed at investigating the vibrational response of centrifugal compressor bladed wheels. A really compact solution was needed since the final test bench provides one exciter for each blade (up to 20 devices on the circumference hoop). Both contact and contactless solutions were considered, but only the contact solution was found to fulfill all the specifications. Finally, different stinger solutions were proposed and compared in the paper. The investigated solutions were: a beam stinger (diameter 1 mm); a wire stinger (diameter 0.2 mm); and a ball stinger (diameter 3 mm) with two different support solutions. Experimental tests performed on a device prototype allowed to verify the specifications fulfillment and to choose the best stinger solution for the application.

High-frequency vibration analysis of thin plate based on wavelet-based FEM using B-spline wavelet on interval

The wavelet finite element methods (WFEMs) own higher calculation accuracy and efficiency for structure analysis. Unfortunately, the existing WFEMs are still limited in low-frequency domain when capturing dynamic characteristics of thin plate. This paper proposes the wavelet multi-elements method based on C1 type B-spline Kirchhoff plate (C1BKP) element to break up this limitation. The validity, numerical stability and convergence respectively are investigated systematically in numerical study. The corresponding results show that the calculation accuracy and numerical stability are very excellent when predicting the high-order natural frequency. The maximum relative errors can be rapidly reduced to 0.4% within the first 1000 modes of thin plate under simply supported. Besides, the method is suitable for predicting the dynamic characteristics of thin plate under various boundary conditions.

Analysis of high frequency vibration of tram monobloc wheel

European Environmental Agency estimates that about 120 million people in the EU (over 30% of the total population) are exposed to traffic noise above 55 Ldn dB. It is estimated that 10% of the EU population is exposed to noise associated with the rail traffic. The two main sources of traffic noise comes from vehicles engines and the noise generated in the contact between the wheel and the road. In the latter the considerable part the noise is due to phenomena occurring in a wheel tram – rail system. Therefore, the problem of reducing the noise generated by railway vehicles is the subject of many studies, both experimental and theoretical. Commonly used wheel trams so called "resilient wheels" are equipped with layer made of a resilient material, e.g. rubber, between the tread and the wheel disc. But the monobloc tram wheel is the standard design against which should be carried out the studies on reduction of noise in wheel-rail system. This paper presents the results of calculations related to eigenforms, eigenfrequencies and Frequency Response Function of a three-dimensional model of a monobloc tram wheel. The calculations were carried out using the finite element method. Vibration analysis was performed for the range to 5 kHz. Analysis carried out has shown that the wheel tread plays a more important role in the generation of high-frequency vibrations.

High frequency vibration analysis of ball bearings under radial loads

The paper investigates the role of radial load and rotating speed on the high frequency vibration of a deep groove ball bearing. Firstly, a bearing dynamic model with 6-DOF balls was established, considering the interactions between balls, races and the cage. The dynamic model was solved by fourth order varying steps Runge-Kutta integration. The frequency spectrums of dynamic response of races were analyzed with yule-walker and FFT. Secondly, a verification experiment was done with different radial loads and speeds. Finally, compared with the numerical and experimental results, the similar trend of the high frequency vibration was emerged. Higher vibration frequencies result with increasing bearing load; higher vibration amplitude cause by more quickly rotating speed. That is because the nature frequencies of the races are excited by the contact and shock between balls and races when balls leave from the non-load to the load zone. The frequency spectrums were also affected by the interaction between the balls and cage.

Forced vibrations of SC-cut quartz crystal rectangular plates with partial electrodes by the Lee plate equations

Lee plate equations for high frequency vibrations of piezoelectric plates have been established and perfected over decades with the sole objective of obtaining accurate predictions of frequency and mode shapes to aid the analysis and design of quartz crystal resonators. The latest improvement includes extra terms related to derivatives of the flexural displacement to provide much accurate solutions for vibrations of the thickness-shear mode, which is the functioning mode of resonators and has much higher frequency than the flexural mode. The improved Lee plate equations have been used in the analysis of high frequency vibrations of quartz crystal plates as an essential step for analysis of AT- and SC-cut quartz crystal resonators after validations with fully electrode quartz crystal piezoelectric plates. In this study, closed-form solutions of free and forced vibrations of SC-cut quartz plates with partial electrodes are obtained. A procedure has been established for the calculation of dispersion relations, frequency spectra, selected vibration modes, and capacitance ratios of forced vibrations. The vibration solutions obtained with the first-order Lee plate equations are proven to be close to solutions from the Mindlin plate equations. It is now clear that both the Mindlin and Lee plate equations can be used in the analysis and design of quartz crystal resonators.

Evaluation of the failure progress in the static bending of GFRP laminates reinforced with a classic plain‐woven fabric and a 3D fabric, by means of the vibrations analysis

The aim of the work is to evaluate the effectiveness of analysis of a failure progress of the glass fiber reinforced polymer laminate (classic and 3D), during static bending, with the use of high frequency vibration analysis (the order of kHz). During the tests, the instantaneous velocity of the samples' vibrations was recorded. The 3D laminate showed a more favorable course of failure (mostly fiber fracture) than the classic laminate (mostly delamination), but only in the direction transverse to the translaminar interweave strands. In the direction parallel to the interweave, it was also characterized mainly by delamination. It was stated that the vibration measurements significantly broaden and supplement the characteristics of bending, by way of revealing the local degradation changes in the examined material, especially before the initiation of the main stage of failure. The work also describes the frequency bands in which the symptoms of the occurring failures of particular laminate components were observed and where the values of the basic point parameters were estimated, which points to the occurrence of structure failure. The obtained results confirm the effectiveness of the vibration analysis as a tool for the evaluation of the course of composite material failure under static loads. POLYM. COMPOS., 38:1070–1085, 2017. © 2015 Society of Plastics Engineers

Statistical energy analysis of inhomogeneous systems with slowly varying properties

This paper is concerned with the analysis of high frequency vibrations of inhomogeneous systems with slowly varying properties subjected to harmonic excitation. A formula for the spatial scaling of the vibrational energy density of such systems is derived and is used to predict the mean and the variance of their vibrational energy response. The derivations are based on the assumption that waves propagate with negligible partial reflections in the systems, which holds when the relative variation of the properties of the systems is small over a wavelength of vibration. To validate the theoretical findings, numerical simulations of two plate systems are performed: a plate with a linearly varying thickness and a plate with a thickness bump.

Development of Energy Finite Element Analysis in Vibration Analysis of Composite Laminate Plate Structures

The high frequency vibration analysis of a composite laminate plate structure subjected to impact loads was investigated by using method of energy finite element analysis (EFEA). The time and space averaged energy density was used as the primary variable to form the governing differential equations. The multilayer laminate plate is simplified to be equivalent isotropic plate using the average concept, such as the average damping loss factor and the average group speed. The global system of EFEA equations can be solved numerically and the energy density distribution within the whole system can then be obtained. The EFEA numerical results for composite laminate plate structure were validated through comparison with those of very dense conventional finite element analysis (FEA).

A scaling approach for high-frequency vibration analysis of line-coupled plates

A scaling approach is proposed for the vibration analysis of line-coupled plates at high frequencies. It extends earlier scaling approaches for an isolated system to coupled systems. Based on the power flow balance in the plate assembly, a general scaling law is derived and a scaled model is built accordingly. Due to the dynamic similitude in a statistical sense, the scaled model is able to simulate the dynamics of the original system at high frequencies. Numerical examples validate the efficiency of the approach and suggest the application of finite element methods in the high-frequency vibration analysis.

Numerical determination of statistical energy analysis parameters of directly coupled composite plates using a modal-based approach

Statistical energy analysis (SEA) parameters such as average modal spacing, coupling loss factor and input power are numerically determined for point connected, directly coupled symmetrically laminated composite plates using a modal-based approach. The approach is an enhancement of classical wave transmission formula. Unlike most of the existing numerical or experimental techniques, the approach uses uncoupled plate modal information and treats substructure by means of averaged modal impedances. The procedure introduced here is verified using analytical definitions of infinite orthotropic plates which physically resemble to laminated plates for (under) specific conditions, and is tested by performing experimental power injection method (PIM) for an actual, right-angled composite structure. In the development process, force and moment transmissions are individually considered in order to be consistent with analytical formulations. Modal information of composite plates is statistically evaluated by the discrete singular convolution method with random boundary conditions. Proposed methodology not only provides an efficient use of SEA method in high frequency vibration analysis of composite structures, but also enhances SEA accuracy in mid frequency region in which conventional SEA fails. Furthermore, the effect of orientation angles of laminations on SEA parameters are also discussed in mid and high frequency regions.

The Dynamic Dual Vector Finite Element Method for Electromagnetic Waveguide Problem

The dynamic finite element method is widely used in vibration structural analysis of engineering, and especially advantageous in high frequency vibration analysis comparing with traditional finite element method. It is the same with the electromagnetic waveguide problem. This paper studies the cut-off frequency and the propagation constant problem of waveguide by using the dynamic finite element format which is deduced through dual variational principle and the W-W algorithm. Compared with the common dual edge element method, this one can work out the propagation constant, cut-off frequency and modal more accurately, as well as with small degree of freedom.