Mode Natural Frequencies Research Articles

Ambient Vibration Testing of a Pedestrian Bridge Using Low-Cost Accelerometers for SHM Applications

Damage detection and structural health monitoring have always been of great importance to civil engineers and researchers. Vibration-based damage detection has several advantages compared to traditional methods of non-destructive evaluation, such as ground penetrating radar (GPR) or ultrasonic testing, since they give a global response and are feasible for large structures. Damage detection requires a comparison between two systems states, the baseline or “healthy state”, i.e., the initial modal parameters, and the damaged state. In this study, system identification (SI) was carried out on a pedestrian bridge by measuring the dynamic response using six low-cost triaxial accelerometers. These low-cost accelerometers use a micro-electro-mechanical system (MEMS), which is cheaper compared to a piezoelectric sensor. The frequency domain decomposition algorithm, which is an output-only method of modal analysis, was used to obtain the modal properties, i.e., natural frequencies and mode shapes. Three mode shapes and frequencies were found out using system identification and were compared with the finite element model (FEM) of the bridge, developed using the commercial finite element software, Abaqus. A good comparison was found between the FEM and SI results. The frequency difference was nearly 10%, and the modal assurance criterion (MAC) of experimental and analytical mode shapes was greater than 0.80, which proved to be a good comparison despite the small number of accelerometers available and the simplifications and idealizations in FEM.

Multiphysics numerical investigation on the aeroelastic stability of a Le Mans Prototype car

In the analysis and design of racing competition cars, numerical tools allow to investigate a wide range of solutions in short time and with high confidence in results. The great available computational power permits to combine simulation software so that different physics involved can be tackled at the same time. An important class of multi-physics simulations for motor sport addresses the fluid-structure interactions happening between the aerodynamic components of the car and the surrounding flow: this interaction can induce structural deformations and vibrations which, in turn, can influence the surrounding fluxes. In this paper, the flutter analysis of the front wing splitter mounted on the 2001 Le Mans Prototype car by Dallara (LMP1) is presented. The study was set up adopting high fidelity CAE models: a 400k shell elements FEM represents the full front wing assembly including the mounting frame, a 240M cells CFD represents the full car immersed in a box shaped wind tunnel. FEM extracted structural modal shapes are mapped onto the CFD mesh adopting Radial Basis Functions (RBF) mesh morphing so that the surfaces of the CFD model can be deformed according to retained modes. Such deformation is then propagated so that the volume mesh is adapted accordingly. The elastic CFD model with modes embedded was then loaded by applying a transient signal individually to each retained mode with a smoothed step function. A Reduced Order Model (ROM) for the aerodynamics of the coupled system was then extracted combining the results of the individual transient run. The critical speed experimentally observed to be in the operating range of the car was captured by the model quite well. The same workflow was then adopted to investigate a different design in which a stiffener has been introduced to increase the first mode natural frequency from 40Hz to 49.4Hz. Flutter speed was increased and moved outside the vehicle range. The car equipped with the improved part proved to perform on the track without previously detected instabilities.

Analysis of structures subjected to crowd loads

The movement of people on any structure induces dynamic crowd load. The enthusiastic potential behavior of people from overwhelming happiness in concert, shows etc. on structures such as stadiums, auditorium, grandstands, bridges, malls and convention centers causes synchronized rhythmic movements. Resonance between forcing frequency and one or more natural frequencies of the structure resulting from human-structure synchronization leads to strong vibrations. Such vibrations not only affect structural stability, but also create discomfort among people. Pedestrian induced lateral vibration of Millennium Bridge, London is a classic example for the same. Crowd loads impose vertical as well as horizontal loads on the structure. Both these loads induce vibrations in corresponding directions. Beyond an acceptable limit of vibration level, people may feel uncomfortable. If there is a mode of low natural frequency, even a significantly low forcing frequency can lead to strong vibrations, which in turn may cause panic. The present research focuses on analysis of a simply supported slab strip subjected to crowd load. The crowd-structure interaction is analytically modelled and the modal parameters and the response of the occupied structure are determined. Furthermore, the effect of various parameters such as crowd size, crowd location and crowd activity on the behavior of occupied structure is studied. The comfort level of the people on the structure is also estimated. It is observed that crowd parameters affect the behavior of the system as well as the comfort level of the occupants. It is further seen that the trend of variation of natural frequency of the occupied structure with variation in crowd properties changes with change in the empty structure properties.

Structural and modal Analysis of Scooter Frame for Design Improvement

This paper discusses the stress and deformation developed in chassis during the different load cases and identifying the failure modes by the modal analysis. It starts from the benchmark study of different scooter frame in the aspect of material selection, mechanical properties and the sections used in it (usually circle section is preferred because of its easiness of manufacturing, even load distribution for different load cases and some other geometrical reasons). Then Structural and modal analysis of frame were carried out under the various load considerations. It involves 3D modeling in Pro-E, meshing in HyperMesh and analysis by ANSYS. Hence the following works are completed. Viz (i) Validation of the Frame design i.e. stress and deformation calculation using FEA and suggest the design recommendations, (ii) Bench mark study of the frame structure, load characteristics, metallurgical and mechanical properties of the scooter frame members and (iii) Identification of critical stress areas and suggest for design improvement from the Modal analysis by identifying the different mode shapes and Natural frequency of the frame.

Modal Analysis of Ultrasonic Horn using Finite Element Method

Abstract Ultrasonic Machining (USM) is a preferred advanced machining method for hard and brittle material. This process can be conveniently combined with other machining processes to develop different hybrid machining processes. The machining capability of the USM process largely depends on the amplification of the amplitude of vibration produced by transducer. The ultrasonic horns vibrate in longitudinal direction and transfer the vibrational energy from transducer to workpiece. The design of ultrasonic horn is utmost important because incorrect design not only deteriorate the machining performance but also the cause damage to the vibration system and generator. In this study, modal analysis of two different horn profiles which are comparatively difficult to manufacture i.e. steeped and exponential have been performed using finite element based ANSYS software. Mode shape and natural frequencies of the above two profiles made of Titanium and Aluminium have been taken into consideration. From the result it is observed that for stepped profile Titanium horn produces higher natural frequency for all the six modes but in case of exponential profile Aluminium horn produce more frequency than Titanium alloy.

Tip-replaceable Horn with Full Wavelength for Ultrasonic Welding

Ultrasonic welding is faster, environmental friendly, and more efficient than conventional welding. Ultrasonic welding stack, the key part in ultrasonic welding equipment, is composed of transducer, booster, and horn. In the case of ultrasonic welding, wear in the welding tips or breakage of horn occurs because ultrasonic vibration of tips is transmitted directly to the welding material. If grinding of the tips is repeated several times, the mass of horn is reduced and the frequency characteristic is changed. So, there is a limit to refurbishment. In additions, as materials of horn are relatively expensive, some cost problems could be occurred for replacing horns. This study, in order to reduce the manufacturing cost of horn, devised a tip-replaceable ultrasonic horn so that its tip can be easily replaced whenever it is worn. For the designed shape, natural frequency and vibration mode are analyzed using FEA. Through the FEA, the optimal tip-replaceable horn with resonance frequency of 40 kHz is proposed.

Effects of soil-structure interaction in seismic analysis of buildings with multiple pressurized tuned liquid column dampers

Abstract In this paper soil-structure interaction (SSI) effects are investigated while an array of Pressurized Tuned Liquid Column Dampers (PTLCD) is employed for seismic vibration control of buildings. This device represents the most general case of a passive damper, with different reduction options to other control devices obtained by simplifying the involved parameters. Soil conditions considerably affect the control device functioning, because dynamic parameters such as natural frequency, damping factor, and natural modes depend on the soil properties. A simplified mathematical model is developed for the building with multiple degrees of freedom connected to a flexible base. For the time-domain analysis, a computational routine is developed for the linearization of the equilibrium equations of the PTLCD, as well as details for the reduction to the other types of passive dampers. Several numerical examples are selected for the analysis of the damper efficiency in reducing seismic vibration considering SSI. These simulations include Kobe earthquake data, which is applied to the model to evaluate the device performance under different scenarios. It is verified the influence of SSI in the natural frequency and structural response, which is related to the earthquake frequency components. Results confirm that the array of PTLCD’s can reduce the vibration amplitudes, being more effective for soils with higher stiffness values.

Experimental and numerical analysis on vibration features of typical external pipe in aero-engine

The aero-engine pipe vibration phenomenon is a serious complicated problem in engine structure design and application. In this paper, an experimental and computational study was implemented on the aviation straight and L-shape pipe vibration characteristics. The pipe vibration shape and natural frequency were obtained by both hammering and Finite Element Methods (FEM). Effects of fluid type, pressure and temperature were examined on pipe vibration characteristic parameters. The results show that the pipe vibrates along transverse and vertical directions. There are slight differences in pipe vibrating natural frequency in the two directions. The pipe experimentally natural frequency and vibration modes agree well with those obtained in FEM computation. The fluid type, pressure and temperature can change the pipe vibrating amplitude values, but cannot influence the pipe vibration modal characteristics. Varying fluid pressure and temperature can to some extent change the pipe natural frequencies.

Analysis of flutter vibration response of large wind turbine blades under resonant loads

Based on the finite element method, the structural model of large wind turbine blades is established and the natural frequency and natural vibration mode of the structure are studied. The vibration response of the structure under the resonant load is calculated. The displacement amplitude and phase angle at the tip are obtained with frequency. It is found that under the given resonant load conditions, the maximum displacement amplitude and the maximum phase angle at the tip are within the allowable range of the structure, and the structure does not undergo resonance damage. Through the harmonic response vibration analysis of the wind turbine blade, it can provide an effective theoretical basis for the safe design of the blade.

Effect of Head Types on the Free Vibration and Fatigue for Horizontal LPG Pressure Vessels

Pressure vessels are the heart of plants and oil refineries stations. In many engineering applications such vessels can be subjected to periodic loading either internally due to the charging and discharging process or externally due to the excitation from other nearby components such as pumps, compressors or from seismic. So that in spite of a good design according static assumption it may be critical in dynamics. In this work a horizontal pressure vessel with accessories subjected to liquefied petroleum gas pressure LPG is considered. Three models of different head types are investigated herein namely; Deep torispherical, Elliptical 2:1 and Hemispherical. The design and material selections are chosen as per ASME. For practical service many accessories are attached to the vessel such as manhole, supports, inlet and outlet opining. Finite Element method via ANSYS R18.2 is introduced for the numerical analysis. The fatigue life in case of fully reversed cyclic loading are estimated and located. Vibration characteristics such as mode shapes and natural frequencies for the lowest five modes are evaluated and compared. It is found that the fatigue life can be increased as higher as 180% for hemi- spherical head as compared with deep torispherical head pressure vessel and the lowest four natural frequencies are nearly identical for all models, however significant change observed in the fifth natural frequency.

Structural Model Calibration of Vierendeel Bridge Based on the Vibration Properties

In this study the Vierendeel bridge structural model is adopted as a complex structure case study scaled from a real structure located near Čačak city in Serbia. Experimental analysis is conducted under simulation of ambient vibration using shaker device for exciting the model. Frequency Domain Decomposition (FDD) technique is applied using ARTeMIS software extractor to extract the modal properties, natural frequencies and mode shapes. As a comparative study, Enhanced Frequency Domain Decomposition (EFDD) is used to verify the extracted results from FDD. A finite element model is created in ANSYS software to simulate the adopted model to estimate modal properties numerically. Calibration process is implemented to converge the numerically estimated with the experimentally extracted modal properties. Two procedures written in MATLAB environment, for calibration and damage identification, are proposed using heuristics optimization, Simulated Annealing (SA) and Tabu Search (TS). Both of proposed calibration procedures exhibit high accuracy and efficiency due to good convergence between experimentally extracted and numerically updated values of natural frequencies extracted based on ambient vibration measurements.

Electromagnetic Mechanical Coupling Analysis of Linear Motor Used in Machine Tools

The finite element model of the linear motor machine tool was established by the finite element software, and the multi-field coupling analysis and modal analysis of the linear motor for the machine tool were carried out. The deformation amount of the machine tool driven by linear motor under multi-field coupling was obtained. At the same time, the force cloud diagram, the first 6th modal analysis of the important components (machine base), the natural frequency and vibration mode of the base are all obtained. The result shows that the natural frequency is much lower than the excitation frequency, so it can effectively avoid the resonance phenomenon. This article can provide reference for the application of linear motor on machine tools.

Development of Marker-Free Night-Vision Displacement Sensor System by Using Image Convex Hull Optimization.

Vision-based displacement sensors (VDSs) have the potential to be widely used in the structural health monitoring field, because the VDSs are generally easier to install and have higher applicability to the existing structures compared to the other conventional displacement sensors. However, the VDS also has disadvantages, in that ancillary markers are needed for extracting displacement data and data reliability is significantly lowered at night. In this study, a night vision displacement sensor (NVDS) was proposed to overcome the aforementioned two limitations. First, a non-contact NVDS system is developed with the installation of the infrared (IR) pass filter. Since it utilizes the wavelength of the infrared region and it is not sensitive to the change of a visible ray, it can precisely extract the shape information of the structure even at night. Second, a technique to extract the feature points from the images without any ancillary marker was formulated through an image convex hull optimization. Finally, the experimental tests of a three-story scaled model were performed to investigate the effectiveness of proposed NVDS at night. The results demonstrate that the NVDS has sufficiently high accuracy even at night and it can precisely measure the dynamic characteristics such as mode shapes and natural frequencies of the structure. The proposed system and formulation would extend the applicability of vision sensor not only into night-time measure but also marker-free measure.

Dynamic characteristics and seismic response of frame–core tube structures, considering soil–structure interactions

SummaryIn order to study the dynamic characteristics and seismic response of high‐rise buildings with a frame–core tube structure, while considering the effect of soil–structure interactions (SSIs), a series of shaking table tests were conducted on test models with two foundation types: fixed‐base (FB), in which the superstructure was directly affixed to the shaking table, and SSI, consisting of a superstructure, pile foundation, and soil. To increase the applicability of the model to the dynamic characteristics of real‐world tall buildings, the superstructure of test models was built at a scale of 1/50. This simulated a 41‐floor high‐rise building with a frame–core tube structure. The mode shape, natural frequency, damping ratio, acceleration and displacement response, story shear, and dynamic strain were determined in each of the test models under the excitation of simulated minor, moderate, and large earthquakes. The SSI effect on frame–core tubes was analyzed by comparing the results of the two test models. The results show that the dynamic characteristics and seismic response of the two systems were significantly different. Finally, these results were verified by performing a numerical analysis on the differences in the seismic responses of the FB and SSI numerical models under various simulated seismic conditions.

The effects of S-glass fiber hybridization on vibration-damping behavior of intraply woven carbon/aramid hybrid composites for different lay-up configurations

In this study, the vibration and damping characteristics of the hybrid composites reinforced with plain woven S-glass and intraply woven carbon/Kevlar fiber fabrics are investigated. Vibration tests on the samples have been conducted only for measuring the first mode of natural frequency with application of experimental modal analysis procedures. Symmetric and asymmetric layering structures have been prepared for the hybrid composite configurations in order to study the stacking sequence effects. Damping ratios have been evaluated from the logarithmic decrement method by using acceleration–time envelope curves. Results have shown that position and percentage of the fibers in the composites are the most effective parameters for natural frequency and damping characteristics of hybrid samples, and some samples have shown the synergistic effects leading to a significant enhancement in damping and natural frequency.

A study on vibration of Setar: stringed Persian musical instrument

Knowing how a musical instrument vibrates can benefit the tonal characteristics shaping of the instrument. In this research, an approach for investigating the mode shapes and natural frequencies of Setar body is addressed. First, mechanical properties of wood used in the production of Setar are analyzed experimentally. Then a numerical modal test is performed to find the mode shapes and natural frequencies of Setar structure. To validate the results obtained by the numerical method, experimental modal testing is also done for the structure, and it is found that the results of both the methods are in good consistency. As the vibration pattern of plates is of utmost importance in the production of musical instruments, vibration patterns of a Setar plate are experimentally extracted and the results are compared with finite element analysis.

A Damage Identification Approach for Offshore Jacket Platforms Using Partial Modal Results and Artificial Neural Networks

This paper presents a damage identification method for offshore jacket platforms using partially measured modal results and based on artificial intelligence neural networks. Damage identification indices are first proposed combining information of six modal results and natural frequencies. Then, finite element models are established, and damages in structural members are assumed by reducing the structural elastic modulus. From the finite element analysis for a training sample, both the damage identification indices and the damages are obtained, and neural networks are trained. These trained networks are further tested and used for damage prediction of structural members. The calculation results show that the proposed method is quite accurate. As the considered measurement points of the jacket platform are near the waterline, the prediction errors keep below 8% when the damaged members are close to the waterline, but may rise to 16.5% when the damaged members are located in deeper waters.

Vibration analysis of non-uniform tapered beams with nonlinear FGM properties

This paper presents the free vibration analysis of a non-uniform cone beam with nonlinearly varying axial functionally graded material (FGM) properties. Based on the Adomian decomposition method and a proposed modified mathematical procedure, the vibration mode shapes and natural frequencies of a nonlinearly tapered FGM beam are analytically derived. Several vibration analyses for uniform and non-uniform FGM structures are presented and the results are compared with the existing ones to prove the effectiveness and accuracy of the proposed methodology. Additionally, vibration analysis of exponentially and trigonometrically tapered beams with nonlinearly axial varying FGM properties considering different geometry and material taper ratios was studied and presented. Based on this analytical model, ideal structural design can be efficiently achieved for many engineering applications, such as stability enhancement and energy harvesting.

Effects of elastic supports and flexural cracking on low and high order modal properties of a reinforced concrete girder

A number of nondestructive evaluation (NDE) methods are available to detect cracks and damage in reinforced concrete structures. Methods such as ultrasonic, impact echo, or X-ray testing have high resolution but are time consuming to perform and therefore only used locally. Since the early 1970s, researchers have also studied the modal properties of structures for damage detection and identification. In this paper, we discuss the effects of elastic supports and flexural cracking on the dynamic response of a large-scale laboratory reinforced concrete girder. For this purpose, an instrumented hammer used for impulse response testing was employed to initiate vibrations and to subsequently estimate the natural frequencies and modes of a large-scale laboratory concrete girder. Natural frequencies up to the 13th mode were successfully extracted from the frequency response function (FRF). In addition, the mode shapes were extracted up to the 6th mode due to the limitation of the linearity of the FRF response. These modal properties were determined from the measured accelerations of two points on the girder using a roving hammer. The test procedure was performed on the uncracked beam and repeated after the beam had been cracked. The experimental measurements were verified with a finite element (FE) model consisting of one-dimensional beam elements that consider both flexural and shear deformations. Support flexibility was modeled as linear-elastic springs, and was found critical in order to explain experimentally-obtained measurements. The effects of cracking were found to be most obvious in the higher modes. Additionally, utilizing the modal flexibility method on the first mode (natural vibration frequency and mode shape) was an accurate predictor of flexural crack locations.

Data-driven methods for operational modal parameters identification: A comparison and application

The operational modal parameters identification under ambient excitation has been widely applied in structural dynamics analysis, where the input force is difficult to measure. This paper makes comprehensive and systematic comparisons of four statistical learning algorithms (PCA, ICA, SOBI, LLE) on analyzing their performance for resolving operational modal parameters identification. It mainly focuses on the comparison and evaluation of the four data-driven methods based for operational modal analysis and explores the use of Hilbert Transform and Random Decrement Technique for the identification of modal damping ratios. The further tests, the robustness of four algorithms, are conducted for investigating the influences of external noise to the performance of the algorithms. On the basis of the modal expansion theory, the vibration response signals could be decomposed into the inner product of modal shapes matrix and modal responses vector in the modal coordinate, from which the modal shapes, modal natural frequencies and modal damping ratios can be well estimated. Hence, a one-to-one mapping between the mathematical model of four statistical learning algorithms and physical model of dynamic systems is established. To validate the effectiveness of the proposed methods, performance and comparison of the proposed methods are studied using a discrete three degree-of-freedom (DOF) system and continuous cantilever steel plate. The simulation and experimental results show that, for the same experimental data, the SOBI algorithm has better performance than other algorithms, and it is more suitable for operational modal identification. Finally, the characteristics of four algorithms and further directions are concluded and discussed in this paper.