Mode Natural Frequencies Research Articles

Dynamic characteristic analysis of micro-hole gun drill based on ANSYS

This paper takes different material properties of gun drill as the research object. ANSYS software is used in the dynamic characteristic analysis of gun drills of different materials. According to modal analysis theory and experiment, the natural frequency and vibration mode of the drill are obtained. The analysis results show that the cemented carbide gun drill after the cubic boron nitride treatment can better withstand bending vibration and torsion during the working process. It is found that the natural frequency of the treated cemented carbide gun drill is very different from that of other materials. The performance micro-hole gun drill provides a certain theoretical basis, and at the same time provides a reference for reducing the vibration and deformation of the gun drill.

A nonlocal Layerwise theory for free vibration analysis of nanobeams with various boundary conditions on Winkler-Pasternak foundation

In this study, a nonlocal Layerwise theory is presented for free vibration analysis of nanobeams resting on an elastic foundation. Eringen's nonlocal elasticity theory is used to consider the small-scale effect on behavior of nanobeam. The governing equations are obtained by employing Hamilton's principle and Layerwise theory of beams and Eringen's nonlocal constitutive equation. The presented theory takes into account the in-plane and transverse normal and shear strain in the modeling of the nanobeam and can predict more accurate results. The governing equations of the beam are solved by Navier's method for Simple-Simple boundary conditions and semi-analytical methods to obtain the natural frequency for various boundary conditions including Clamped-Simple (C-S), Clamped-Clamped (C-C) and Free-Free (F-F) boundary conditions. Predictions of the present theory are compared with benchmark results in the literature. Effects of nonlocal parameter, Pasternak shear coefficient, Winkler spring coefficient, boundary conditions, and the aspect ratio on the free vibration of nanobeams are studied. The flexural mode and thickness mode natural frequencies of the nanobeam are predicted. It is shown that the predictions of present method are more accurate than the equivalent single layer theories. The theoretical developments and formulation presented herein should also be served to analyze the mechanical behavior of various nanostructures with various loading and boundary conditions.

Statistical correlation between environmental time series and data from long-term monitoring of buildings

Within the context of civil structures, a monitoring system supported by an intelligent diagnostic features extraction allows to keep under observation the overall health state of a building. In most cases, the diagnostic features are influenced by Environmental and Operational Variations (EOVs) which cause fluctuations that can be confused with the appearance of damage, or worse, hide it. A useful strategy to get rid of those confounding effects consists in modelling the structural behaviour of the system, considering and predicting these harmless and reversible fluctuations. However, a model approximates a much more complex reality and therefore it is based on a reasonable number of components whose selection might turn out complicated. In this research, a large amount of heterogeneous field data is systematically analysed to investigate which have the greatest influence on structural behavior and therefore, could contribute for modelling the behaviour of a historic building for Structural Health Monitoring (SHM) purpose. Environmental data, measurements of static sensors and modal natural frequencies collected in more than 10 years are scanned and crossed in order to discover any correlations. The analysis of these time series, treated with mathematical and statistical tools, has led to some mechanical interpretations of the observed behaviour of the system, i.e. the Sanctuary of Vicoforte, a monumental Italian church which houses the largest masonry oval dome in the world. The results obtained, especially in terms of correlations between different factors affecting measurements, are deemed relevant in the practice of long-term monitoring of cultural heritage and existing buildings in general.

Vibration Modelling and Control Experiments for a Thin-Walled Cylindrical Rotor with Piezo Patch Actuation and Sensing

This paper describes a dynamic model formulation and control experiments concerning the vibration behaviour of a thin-walled cylindrical rotor with internal piezoelectric patch transducers. Model development, validation and controller design procedures were undertaken for an experimental rotordynamic system comprising a tubular steel rotor (length 0.8 m, diameter 0.166 m and wall-thickness 3.06 mm) supported by two radial active magnetic bearings. Analytical solutions for mode shapes and natural frequencies for free vibration were first derived using a shell theory model, and these used to construct a speed-dependent parametric model for the rotor structure, including piezo patch actuators and sensors. The results confirm that the developed shell theory model can accurately capture the rotating frame dynamics and accounts correctly for frequency splitting from Coriolis effects. The model is also shown to be suitable for active controller design and optimization. Model-based H2 feedback control using the rotor-mounted actuators and sensors is shown to achieve vibration suppression of targeted flexural modes, both with and without rotation.

Analytical study on free vertical and torsional vibrations of two- and three-pylon suspension bridges via d'Alembert's principle

This study derives the differential equations of free vertical bending and torsional vibrations for two- and three-pylon suspension bridges using d'Alembert's principle. The respective algorithms for natural vibration frequency and vibration mode are established through the separation of variables. In the case of the three-pylon suspension bridge, the effect of the along-bridge bending vibration of the middle pylon on the vertical bending vibration of the entire bridge is considered. The impact of torsional vibration of the middle pylon about the vertical axis on the torsional vibration of the entire bridge is also analyzed in detail. The feasibility of the proposed method is verified by two engineering examples. A comparative analysis of the results obtained via the proposed and more intricate finite element methods confirmed the former feasibility. Finally, the middle pylon stiffness effect on the vibration frequency of the three-pylon suspension bridge is discussed. It is found that the vibration frequencies of the first- and third-order vertical bending and torsional modes both increase with the middle pylon stiffness. However, the increase amplitudes of third-order bending and torsional modes are relatively small with the middle pylon stiffness increase. Moreover, the second-order bending and torsional frequencies do not change with the middle pylon stiffness.

Assessment of Seismic Retrofitting Interventions of a Masonry Palace Using Operational Modal Analysis

ABSTRACT The paper delivers a short report about the modal identification carried out on a historical masonry palace in the city centre of L’Aquila, Palazzo Pica Alfieri, retrofitted after the 2009 earthquake. A concise description of the damage pattern and the retrofitting interventions heads the presentation of the results of the dynamic identification using Operational Modal Analysis. The identified mode shapes and natural frequencies drive a discussion about the detectability and the assessment of the modifications induced by the structural interventions using low-vibration measurements. Differently from more uncomplicated structures, the production of a Finite Element model representative of an existing masonry complex requires considerable efforts: the masonry structure may not behave like a continuum, due to the presence of cracks and unknown structural discontinuities. Still, the results of the dynamic identification bestow valuable information about the structural behaviour from a qualitative viewpoint, even if not backed by a faithful FE model. The paper addresses the aspects possibly related to the dynamic identification of a monumental masonry building, based on the shreds of evidence arisen from the presented case study.

Design and Analysis of 4LZ-8 Wheat Harvester Head

In this paper, the parameter design of the header of the 4LZ-8 wheat harvester is established, and the three-dimensional model of the header is established. The header frame is selected as the main analysis object. The force analysis and static analysis of the header frame are carried out to detect whether it meets the stiffness requirements. In order to reduce the loss caused by vibration during harvesting, the pre-stressed modal analysis is performed on the designed header on the basis of statics to obtain the natural frequency and main vibration mode of the header frame, and then the vibration frequency is analyzed. The results show that the probability of resonance of other parts of the header with the header frame is relatively low, which meets the requirements for use.

Dynamic characteristics and influencing factors of azimuth axis of a new antenna pedestal

Based on the finite element method, the dynamic characteristics of the azimuth axis of an antenna pedestal were studied. With the help of modal analysis module of finite element software, the modal natural frequency and modal shape of the structure were obtained, and the influence of structural size parameters on its dynamic characteristics was also investigated. Through the research, it can be concluded that the first six natural frequency values of the azimuth axis are 220.21, 220.24, 1178.2, 1519.9, 1531.3, 1531.3 Hz. And the first six modes are shown as follows: the first and second order is the swing mode of the axis, the third order is the up and down stretching mode of the azimuth axis, the fourth order is the torsional vibration mode of the azimuth axis, and the fifth and sixth order are the first bending vibration mode of the azimuth axis. The first and second order natural frequencies of the axis decrease with the increase of size parameters d2 , l1 and l2 , and increase with the increase of size parameters d1 , d3 and d4 . The analysis results provide a theoretical basis for the optimization of the dynamic performance of the azimuth axis.

Energy Method to Compute the Maximum Amplitudes of Oscillation Due to Galloping of Iced Bundled Conductors

The paper presents a modal model to describe the interaction between a 4-conductor bundle and wind. A finite-element model of the bundle is used to perform a linear analysis, to extract mode shapes and natural frequencies of the system. The motion of the expanded bundle is then described through mode coordinates representing the first horizontal, vertical and torsional modes. Wind tunnel tests were performed adding templates over the cables to mimic the presence of ice over the same conductor bundle; tests allowed to characterize the aerodynamic coefficients of the entire bundle and provided data for the model validation. The model was then applied to a case study to predict the maximum oscillations produced by iced conductor galloping. Time-domain simulations were used for the purpose, together with an alternative approach named energy method; this last directly estimates the amplitude of limit cycles avoiding the integration of the equations of motion and can be much more useful from the engineering point of view.

Multi-objective optimal design of hybrid composite laminates under eccentric loading

Laminated composites are being used in many engineering applications since they provide significant weight reduction, better fatigue and corrosion resistance. In this study, design optimization of a hybrid composite laminate subjected to eccentric loading was carried out using multi-objective genetic algorithm (MOGA). The ply material (carbon fiber or E glass) and fiber orientations (−90 ≤ θ ≤ 90) were considered as design variables. The objective function was to minimize cost and weight with the maximization of the stiffness. The design constraints were the maximum Tsai-Wu failure index, first mode natural frequency. The numerical analyses were carried out by using ANSYS software package. Genetic aggregation model was used to generate the response surfaces which were used to obtain the optimum design variables. The optimum lay-up sequence and ply materials were determined for weight saving and cost reduction of hybrid composite plates. It was shown that the hybridization of carbon fiber and E glass fiber provided the optimal designs offers lower cost and higher mechanical performance. MOGA method was very effective to optimize the structural performance of the hybrid composite plates under eccentric loading.

Vibrational detection of delamination in composites using a combined finite element analysis and machine learning approach

One common challenge of using composite materials is detecting delamination failure in a non-destructive and cost-effective way. Past studies have proven the feasibility of using vibrational measurements to detect damage but have not explored the full capabilities and limitations of vibrational testing. Here, we use a finite element model of a composite plate to characterize the natural frequency, mode shape, and mode curvature tests for a variety of delamination scenarios. We find that the mode curvature test is resource-intensive to conduct but provides the best resolution in both identifying and localizing delamination. On the other hand, the natural frequency test is simple and inexpensive to conduct but can only reliably identify the presence of delamination. Additionally, a machine learning model is implemented to augment the natural frequency test, allowing both localization of damage and quantification of its severity with only the natural frequencies of modes 1–6. We are able to interpret our model and discover a phase transition for natural frequencies with different sized delaminations. This testing framework allows rapid non-destructive analysis for the iterative design of composites, accelerating the development of novel delamination-resistant materials.

An experimental study on wave forces on a vertical cylinder due to spilling breaking and near-breaking wave groups

This paper highlights the importance of spilling breaking waves in the design of offshore structures. Although wave loading on offshore structures due to non-breaking waves has been extensively studied, wave loading due to breaking waves is uncertain and not very well understood. Plunging breaking waves in deep water are very unusual, whereas spilling breaking waves are very common in extreme seas. Nevertheless, no significant research efforts have been made to study the effects of spilling breaking waves. The present study addresses this, comparing the wave loading from highly nonlinear non-breaking waves and spilling breaking waves. Focused wave groups have been used to generate the non-breaking and spilling breaking wave conditions in a wave tank. The experiments have shown that spilling breaking waves generate significantly larger forces on the cylindrical model than highly non-linear non-breaking waves of equivalent size. This is shown to be due to the direct excitation at high frequency as well as the resonant and impact excitation of higher natural frequency modes. It is concluded that spilling breaking waves can generate very significant forces and should therefore be considered in the design of offshore structures.

Modal Parameters Identification Based on Equalization Principal Component Analysis

Aiming at the magnitude influence of different discrete points in modal parameters identifications with traditional principal component analysis (PCA), a method of modal parameters identifications by equalization PCA is proposed in this paper. The basic idea is using the mean of time domain response data before identifying modal parameters with PCA. On the premise of not losing the main information of the original data, the influence of magnitude on the data is weakened. Taking a doubly-clamped beam as an example, modal parameters of the beam are identified by traditional PCA and equalization PCA with the same constraints of principal component cumulative contribution rate. The results show that compared with the traditional PCA, equalization PCA can effectively identify more orders of modal parameters. The errors of vibration modal shapes and natural frequencies identified by equalization PCA are allowable.

Modal analysis of monorail rocket sled and its cabin connections

Structural stiffness is an important dynamic parameter for the rocket sled. In this paper, both modal test and finite element modal analysis are carried out on the certain monorail sled and its two different cabin connection kinds which are bolt and thread. By comparing the natural frequencies and modal shapes obtained by test and simulation methods respectively, it is found that the stiffness of bolted cabins is consistent with the simulation results, while the threaded cabins performs a severe stiffness degradation due to the thread clearance, which also causes the natural frequencies of the completed sled to be reduced and the modal shapes to be inconsistent with the simulation results. The finite element model of threaded connections is modified by giving anisotropic material properties to the connected elements, and the simulation deviation is reduced. According to the analysis results of two different kinds of cabin connections, threaded cabins on the final assembled rocket sled are strengthened by welding. The modal test results of the reinforced threaded cabin connection indicate that negative influence of the threaded connections is eliminated and the natural frequency and vibration mode are very close to the simulation results.

Application of Transfer Matrix Method in Calculating Flexible Deployment Mechanisms Modes

Flexible deployment mechanisms are widely used in the aerospace field. During the satellite antenna’s attitude adjustment and deployment process, vibration will greatly affect the accuracy of the satellite antenna profile after deployment. The finite element method (FEM) has the disadvantages of high calculation order, slow calculation speed and difficult optimization in the process of establishing the dynamic model of the flexible deployment mechanism. This paper uses the principle of the transfer matrix method to propose a calculation method for the natural frequency and vibration mode of a flexible deployment mechanism, which is used to calculate the vibration characteristics of a radial rib deployment antenna. Finally, its accuracy is verified by the finite element method (FEM).

DIAGNOSTICS OF STRUCTURAL DAMAGE BASED ON THE NATURAL FREQUENCIES RATIO CHANGE

The problems of vibration diagnostics based on the change of natural frequencies of structures are connected with the influence of ambient and operational factors (temperature, humidity, wind, heavy traffic etc.) on the natural frequencies. In some cases, this effect is comparable with the effect of damage itself and reliable diagnostics of damage becomes problematic. To solve this problem, the use of the ratio change between natural frequencies of different mode shapes is proposed as a characteristic of damage. The study has demonstrated that this ratio is unaffected by the environmental and operational factors. Application of the proposed method is illustrated using the example of Z24 reinforced concrete bridge. As the characteristic feature of the reinforced concrete structures damage is the occurrence of multiple cracks, in the analytical model, apart from the size and location of the cracks, the possibility of several locally located cracks was taken into account.The analytical study was performed to calculate the mode shapes and natural frequencies of damaged multi-span beam-like structure. The results reveal that, in order to identify local damage of subcritical size, natural frequency data of at least four modes of vibration are necessary. The eigenfrequencies obtained experimentally in the study of the Z24 bridge were used to confirm that the change in the eigenfrequency ratio can be used to diagnose relatively small local defects in complex structures. At this the reliability of such vibration diagnostics is much higher than based on the change of natural frequencies and mode shapes, since the change in the ratio of natural frequencies does not depend on the environmental conditions and operating conditions of the structure.

Vibration characteristics of two DOF system designed by modal vectors

The dynamic absorber must have the desired natural frequency which is determined by the condition of vibration suppression. For example, the Frahm damper has the natural frequency which is just same as the target frequency for vibration suppression. For two DOF system, we have shown that there are two combination of the parameters for specified natural frequencies. In the vibration theory of MDOF system, natural frequency and modal vector are a set and inseparable. Then, there is the question whether modal vector determines the parameters of two DOF system. In this study, we pick up mass ratio and stiffness ratio as parameters of two DOF system. and examine the relationship between these parameters and their modal vectors. It is shown that each of the mass ratio and the stiffness ratio mainly affects the second and the first modal vector, respectively. The transition of natural frequencies by the mass ratio and the stiffness ratio is also considered. Moreover, the mass ratio and the stiffness ratio from modal vectors are successfully derived. The modal vectors affect the mass ratio and the stiffness ratio in the almost similar way. In addition, the relationship between the modal vectors and natural frequencies are almost same as the mass ratio and the stiffness ratio.

Free vibration analysis of a porous rotor integrated with regular patterns of circumferentially distributed functionally graded piezoelectric patches on inner and outer surfaces

This article studies dynamic characteristics of a novel porous cylindrical hollow rotor based on the first-order shear deformation theory and Hamilton’s principle. The proposed model is made from a core including aluminum with porosity integrated with an arrangement of functionally graded piezoelectric patches placed on its inner and outer surfaces with a customized circumferential orientation. The piezoelectric patches are subjected to applied electric potential as sensor and actuator. The kinematic relations are developed based on the first-order shear deformation theory. Hamilton’s principle is used to derive governing equations of motion with calculation of strain and kinetic energies and external work. Solution procedure of the partial differential equations of motion is developed using Galerkin technique for simple boundary conditions. The accuracy and trueness of this work is justified using a comprehensive comparison with previous valid references. A large parametric study is presented to show influence of significant parameters such as dimensionless geometric parameters, porosity coefficient, angular speed, inhomogeneous index, and characteristics of patches on the mode shapes, natural frequencies, and critical speeds of the structure.

An Improved Analytical Method for Vibration Analysis of Variable Section Beam

The variable section structure could be the physical model of many vibration problems, and its analysis becomes more complicated either. It is very important to know how to obtain the exact solution of the modal function and the natural frequency effectively. In this paper, a general analytical method, based on segmentation view and iteration calculation, is proposed to obtain the modal function and natural frequency of the beam with an arbitrary variable section. In the calculation, the section function of the beam is considered as an arbitrary function directly, and then the result is obtained by the proposed method that could have high precision. In addition, the total amount of calculation caused by high-order Taylor expansion is reduced greatly by comparing with the original Adomian decomposition method (ADM). Several examples of the typical beam with different variable sections are calculated to show the excellent calculation accuracy and convergence of the proposed method. The correctness and effectiveness of the proposed method are verified also by comparing the results of the several kinds of the theoretical method, finite element simulation, and experimental method.

Analysis of Vibration Fatigue of A Subway Shunting Train

In order to research the fatigue life of a subway shunting train, the power spectrum density (PSD) is used to calculate the vibration fatigue based on frequency domain analysis. Through pre-stressed modal analysis in finite element simulation, the natural frequency and vibration mode are obtained. Then harmonic response is used to get the frequency response function (FRF) based on the modal superposition method. Then the solution is imported into Ncode Designlife. After using the Lalanne method to process PSD curve and the Goodman method to correct the mean stress of the estimated S-N curve, the vibration fatigue damage of the shunting train is obtained, so as to evaluate its vibration fatigue. The result will provide a certain theoretical basis for the fatigue study of shunting train.