Modal Testing Method Research Articles

Modal testing of nanocomposite materials through an optimization algorithm

An efficient identification method for modal testing of viscoelastic composite materials is demonstrated in this paper, through the analytical–experimental transfer function method. The procedure for the identification of analytical–experimental transfer functions is carried out using a genetic algorithm (GA) by minimizing the difference between the measured response from tests and the calculated response, which is a function of the modal parameters. The analytical transfer functions provide a sub-structuring process to identify modes, as a function of damped natural frequencies and loss factors of a complex structure and it is insensitive to experimental noise as well as the modal coupling effect. The proposed method is verified with the calculation of the elastic modulus and modal properties of a cantilever steel beam with the FEM and compared with the identification results of the proposed algorithm. The effectiveness of the proposed method is demonstrated by investigating the static and dynamic behavior of epoxy cantilever beam specimens reinforced with silica nanoparticles. Analytical–experimental transfer functions accurately identified the viscoelastic and dynamic response of the studied specimens, while the results indicated that the inclusion of nanosilica particles increased the stiffness of the epoxy network and the damping response of the reinforced specimens is improved.

Multivariable wavelet finite element-based vibration model for quantitative crack identification by using particle swarm optimization

Crack is one of the crucial causes of structural failure. A methodology for quantitative crack identification is proposed in this paper based on multivariable wavelet finite element method and particle swarm optimization. First, the structure with crack is modeled by multivariable wavelet finite element method (MWFEM) so that the vibration parameters of the first three natural frequencies in arbitrary crack conditions can be obtained, which is named as the forward problem. Second, the structure with crack is tested to obtain the vibration parameters of first three natural frequencies by modal testing and advanced vibration signal processing method. Then, the analyzed and measured first three natural frequencies are combined together to obtain the location and size of the crack by using particle swarm optimization. Compared with traditional wavelet finite element method, MWFEM method can achieve more accurate vibration analysis results because it interpolates all the solving variables at one time, which makes the MWFEM-based method to improve the accuracy in quantitative crack identification. In the end, the validity and superiority of the proposed method are verified by experiments of both cantilever beam and simply supported beam.

An interface force measurements-based substructure identification and an analysis of the uncertainty propagation

Substructure-decoupling techniques are used to identify a substructure as a stand-alone system while it is coupled to a complex structure. These techniques can be used for various applications, e.g., when the substructure cannot be measured separately from the complex structure, when modal testing methods are not appropriate due to the limits of the measurement equipment and for vibration-control techniques. The complex structure consists of the unknown substructure and the remaining structure. A drawback of the available substructure-decoupling techniques is that they require a model of the remaining substructure. However, when the model cannot be calculated or (experimentally) identified, the substructure-decoupling techniques cannot be used. In this paper a new approach is presented that does not require a model of the remaining substructure, but is based on an experimental identification of the interface forces. The sensitivity of the approach to experimental errors was researched. Numerical and experimental test cases are researched.

Machining Mechanism of Fresnel Lens Mold

This paper analyzed the large diameter Fresnel lens mold machining mechanism based on modal test methods .The design and mold machining principle of Fresnel lens were introduced . Explored the cutting speed and feed on chip formation process. The results show that: the material strength and plastic brittle have significant impact on chip morphology in the H62 brass mold processing, an improvement of material strength with the increase of strain rate and the evolution process of the chip can be divided into: ribbon cuttings, serrated chips, cell chips.

Strain Gauges Applied to the Lightweight Structures Modal Testing

Dynamic characteristics of the structure have a significant effect on the performance of the structure. Modal test is a common method to obtain structural dynamic characteristics. However, due to the mass effect of the transducer, the measured results of lightweight structure are inaccurate. This paper proposes using strain gauges to test the mode of lightweight structures, and we take the cantilever beam as an example. The paper derived strain modal expressions. We use the strain gauges, the accelerometers and the finite element simulation to test the modal of the cantilever. To compare and analyze the experimental data, it illustrates that the strain modal test methods can measure the bending mode of the beam effectively.

Research on Chip Formation Mechanism in Mold Processing of Large Diameter Fresnel Lens

This paper describes the analysis of the chip formation mechanism in mold machining process of large diameter Fresnel lens based on the ABAQUS finite element simulation software and modal test methods. Combined with the material constitutive relation and material failure criteria etc, a two-dimensional orthogonal cutting model was established and the chip derived from the simulation was compared with the chip from modal test, with a consequent verification of the feasibility of simulation chip model. The simulation contributes to an investigation into the effects of the cutting speed on chip formation process. The results show that: the material strength and plastic brittle have significant impact on chip morphology in the H62 brass mold processing, and material strength will improve with the increase of strain rate, the evolution process of the chip of material plastic reduction can be divided into: ribbon cuttings, serrated chips, cell chips.

A modal test method using sound pressure transducers based on vibro-acoustic reciprocity

Abstract A modal test method that uses sound pressure transducers at fixed locations and an impact hammer roving over a test structure is developed in this work. Since sound pressure transducers are used, the current method deals with a coupled structural–acoustic system. Based on the vibro-acoustic reciprocity, the method is equivalent to one, where acoustic excitations at fixed locations are given and the resulting acceleration of the test structure is measured. The current method can eliminate mass loading due to use of accelerometers, which can destroy existence of repeated or close natural frequencies of a symmetric structure. It can also avoid effects of a nodal line of a mode and an inactive area of a local mode, and measure all the out-of-plane modes within a frequency range of interest, including global and local ones. The coupling between the structure and the acoustic field in a structural–acoustic system introduces asymmetry in the model formulation. An equivalent state space formulation is used for a damped structural–acoustic system and the associated eigenvalue problem is derived. The biorthonormality relations between the left and right eigenvectors and the relations between the structural and acoustic components in the left and right eigenvectors are proved. The frequency response functions associated with the current method are derived and their physical meanings are explained. The guidelines for using the current method, including the types of structures that are suitable for the method, the positions of the sound pressure transducers, and the orientation of the test structure relative to the transducers, are provided. Modal tests were carried out on an automotive disk brake using the traditional and current methods, where multiple accelerometers and microphones were used to measure its dynamic responses induced by impacts, respectively. The differences between the measured natural frequencies using the current method and those from the finite element model of the disk brake are less than 3 percent for the first 18 elastic modes, and the modal assurance criterion values of the associated mode shapes are all above 90 percent. The current method was also used to measure the natural frequencies, damping ratios, and mode shapes of a light circuit board.

Analysis and Verification of the Optimal Placement of Actuators in Modal Test on Beams

The optimal placement of actuators is studied with the combination of numerical calculation and modal test methods. The results indicate that the optimal excitation position is close to the maximum displacement of a cantilever beam, but the conclusion is not the same as a simply supported beam. The calculation results are consistent with the experimental results, which show that the approach in the present study is correct, and can be popularized.

Experimental and numerical identification of structural modes for engineering education

Development of simple classroom demonstration device and software for visualization of structural normal modes is presented. Device is made of parts of old speaker, controlled with personal computer, where the harmonic motion of solenoid is used as an excitation for beam and plate models. Simple code for finite element free vibration analysis of plates is written in Wolfram Mathematica. Good agreement of results and attractive visual patterns of normal modes attracted attention of students. Results are confirmed using modern modal testing methods. Presented approach is complementary to standard teaching of structural dynamics.

Inertia Parameters Identification of Motor Assembly for Electric Vehicles Based on Modal Test Method

Inertia parameters are essential for motor assembly mounting design, which mainly includes the mass, center of mass (CM) coordinates, moment of inertia and product of inertia. This paper explains the principle and methods of modal test method. One vehicle drive motor assembly is taken as the research object, its inertia parameters are identified using this modal test method. Finally test error analysis is also performed.

Modal Identification and Finite Element Model Updating by Adding Known Masses

This paper focus on the model updating of civil structural systems. Traditional modal test method can identify the frequency of the civil structure accurate, but it is difficult to identify the mass-normalized mode shape. By adding a series of known masses to the structure, measuring the frequency of this mass-modified system, and only using this set of frequency data, the mass-normalized mode shape of the structure can be identified. And the model updating method was developed, which constructed an objective function through the frequency of the measurement and the FE model, corrected the FE model's parameters to minimize the objective function. The example was included to show the capabilities of the technique. The finite element model of the fixed-free beam was updated by the dynamic characteristics which was identified from the modal test, the results show that updated results coincided with the experience of the analyst.

Structural identification of concrete arch dams by ambient vibration tests

Modal testing, widely accepted and applied method for determining the dynamic characteristics of structures for operational conditions, uses known or unknown vibrations in structures. The method's common applications includes estimation of dynamic characteristics and also damage detection and monitoring of structural performance. In this study, the structural identification of concrete arch dams is determined using ambient vibration tests which is one of the modal testing methods. For the purpose, several ambient vibration tests are conducted to an arch dam. Sensitive accelerometers were placed on the different points of the crest and a gallery of the dam, and signals are collected for the process. Enhanced Frequency Domain Decomposition technique is used for the extraction of natural frequencies, mode shapes and damping ratios. A total of eight natural frequencies are attained by experimentally for each test setup, which ranges between 0-12 Hz. The results obtained from each ambient vibration tests are presented and compared with each other in detail. There is a good agreement between the results for all measurements. However, the theoretical fundamental frequency of Berke Arch Dam is a little different from the experimental.

Modal Testing Based on Single Point Laser Continuous Plane Scanning Vibration Measurement

Vibration Measurement Jigang Wu, Bin Qin, Xuejun Li, Zengzeng Yang Hunan University of Science and Technology/Hunan Provincial Key Laboratory of Health Maintenance for Mechanical Equipment, jgwuhust@gmail.com Hunan University of Science and Technology/Hunan Provincial Key Laboratory of Health Maintenance for Mechanical Equipment, qinbin505@sina.com Hunan University of Science and Technology/Engineering Research Center of Advanced Mine Equipment, Ministry of Education, hnkjdxlxj@163.com, yzz430104@yahoo.cn Abstract A high precision and fast testing method for pure modal of vibration body by continuous constant speed plane scanning vibration measurement using single point laser doppler vibrometer is proposed. According to pure modal theory, the relationship between the vibration displacement signal which obtained by continuous scanning the free vibration string which both ends are fixed with single point laser vibrometer and the modal shapes of the string is established theoretically based on the investigation of free vibration of a string which both ends are fixed. The processing method for the actual vibration signal is investigated, and the calculating method for the upper and lower alternate envelope of vibration displacement signal is proposed. The modal test platform based on single point laser continuous constant speed plane scanning vibration measurement is put up, and the validity of the modal testing method is verified by the modal testing of thin sheet beam.

Identification of inertia properties from the results of output-only modal analysis

Accurate knowledge of the rigid body properties of a structure including the mass, the location of mass center and the moments of inertia is important in machine design, vibration analysis, optimization and modeling of mechanical systems. However, estimation of these properties through theoretical methods is difficult when the structure has a complicated shape. In practice, the inertia properties can be estimated using the conventional modal testing methods by extracting the rigid body modes when the structure is tested in free-free boundary condition. However, all the rigid body modes are not always detectable, due to this fact that the structure is not excited at all degrees of freedom. In order to obtain all of the rigid body modes, many activities have been conducted for selecting the type and location of excitation without much success. In operational modal analysis (OMA), the structure can be excited at any arbitrary point and in different directions. In this paper, a new approach is introduced for estimation of the inertia properties from OMA. The data from OMA are adequate to extract all the rigid body modes of structure. A modal method is used for estimating the inertia properties from the rigid body modes extracted from OMA. The suggested approach is applied to a numerical model of a two-dimensional steel beam as well as a numerical model of a 3D frame and the accuracy of results is evaluated. It is shown that OMA can provide enough data to extract the inertia properties. A real beam is also tested in order to evaluate the performance of the method in practice, needless of a complicated procedure as for conventional methods.

Non-contact modal testing by the electromagnetic acoustic principle: Applications to bending and torsional vibrations of metallic pipes

This work aims to investigate a possibility of non-contact vibration modal testing for bending and torsional motions of cylindrical bodies such as pipes. Here, a transducer operated by the electromagnetic acoustic coupling principle is newly devised. Depending on vibration modes, bending or torsional, different magnetic circuit configurations are employed to fabricate the transducer. The main characteristic of the proposed transducer is non-contact vibration generation in a test specimen without any mechanical movement of the actuating unit. It can be also used as a non-contact sensing unit if necessary. The validity and the performance of the proposed non-contact modal testing method are checked with several experiments.

Comparative Modal Tests of a Violin

In order to determine the properties that make the violins of Antonio Stradivari among the best in the world, a project is underway to reverse engineer one of the great master’s instruments. To develop the methodology, a factory violin that can be disassembled is used as the initial test case. The focus of this article is to determine the best modal test methods to use on the violin. Comparative modal tests were performed on the same violin using two of the most common types of exciters: a shaker and an impact hammer. The results show that both methods have their benefits and limitations. Overall the shaker method resulted in less noise than the impact hammer. However, the shaker method also contained error due to mass loading issues of the response sensors, as well as issues with the boundary conditions at the input location. On the basis of these results, for the purposes of this study the impact hammer is shown to be the preferred method of excitation for the modal analysis of a violin.

Investigation of Dynamic Properties of Hybrid Laminate Structure

Abstract Current research on carbon fibre reinforced plastics (CFRP) shows an evident progression not necessarily only in the field of aerospace industry. With their inherent superior specific strength and stiffness, CFRP offer an interesting option also for various machine tool components manufacturing. CFRP are generally weak in material damping. Nevertheless, this dynamic nature of CFRP parts can be successfully improved on the basis of so-called synergistic effect by the integration of particular damping layers made of rubber or cork composition. However, these additive layers can adversely influence strength and stiffness of resulting hybrid structure. This paper deals with finding of optimal lay-up of wound square tube consisting of CFRP layers with high modulus fibres and cork composition layers. For this purpose, the Pareto optimization of the square tube was performed using three-dimensional numerical simulations. The aim was to maximize the static bending stiffness, the natural frequency and the damping ratio. The theoretical studies were followed by experimental determination of dynamic characteristic of two selected specimens using impact hammer modal testing (IHMT) method and the results were compared.

Frequency response functions of shape features from full-field vibration measurements using digital image correlation

The availability of high speed digital cameras has enabled three-dimensional (3D) vibration measurement by stereography and digital image correlation (DIC). The 3D DIC technique provides non-contact full-field measurements on complex surfaces whereas conventional modal testing methods employ point-wise frequency response functions. It is proposed to identify the modal properties by utilising the domain-wise responses captured by a DIC system. This idea will be illustrated by a case study in the form a car bonnet of 3D irregular shape typical of many engineering structures. The full-field measured data are highly redundant, but the application of image processing using functional transformation enables the extraction of a small number of shape features without any significant loss of information from the raw DIC data. The complex bonnet surface on which the displacement responses are measured is essentially a 2-manifold. It is possible to apply surface parameterisation to ‘flatten’ the 3D surface to form a 2D planar domain. Well-developed image processing techniques are defined on planar domains and used to extract features from the displacement patterns on the surface of a specimen. An adaptive geometric moment descriptor (AGMD), defined on surface parametric space, is able to extract shape features from a series of full-field transient responses under random excitation. Results show the effectiveness of the AGMD and the obtained shape features are demonstrated to be succinct and efficient. Approximately 14 thousand data points of raw DIC measurement are represented by 20 shape feature terms at each time step. Shape-descriptor frequency response functions (SD-FRFs) of the response field and the loading field are derived in the shape feature space. It is seen that the SD-FRF has a similar format to the conventional receptance FRF. The usual modal identification procedure is applied to determine the natural frequencies, damping factors and eigen-shape-feature vectors from the SD-FRF. Natural frequencies and mode shapes from a finite element (FE) model are correlated with the experimental data using the cosine distance between the shape feature vectors with 20 terms. There are numerous benefits of using image decomposition to analyse 3D DIC measured data, including (1) representation of the raw measurement data with efficiency and succinctness; (2) determination of the FRF of any point on the specimen by the use of the full-field shape features; and (3) elimination of DIC measurement noise. Also, the SD-FRF is potentially ideal for cases of field excitation of structures.

Comparison on Three Computational and Experimental Schemes on Vibration Modal Frequency

This paper discussed three schemes to obtain vibration modal frequency. First, theoretical numerical method was introduced to simulate the vibration modal by ANSYS software. Second, one kind of traditional experimental modal analytical scheme was designed to obtain modal frequency by computer random signal and vibration analysis system (CRAS). Third, a new experimental modal test scheme was proposed by FBG test platform. A completed case on modal frequency of the cantilever was carried out by three different schemes, in order to evaluate their merits and drawbacks by comparison. Accordingly, computational modal numerical method in combination with experimental modal test method can meet the analytical demand of modal parameters in practice engineering.

Optimum amount of additive mass in scaling of operational mode shapes

Recently, identification of modal parameters using the response only data has attracted considerable attention particularly where the classic modal testing methods is difficult to conduct. One drawback of the response only data, also known as Operational Modal Analysis (OMA), is that only the unscaled mode shapes can be obtained which restricts the applications of OMA. The Mass change method is a usual way to scale the operational mode shapes. In this article a new method is proposed to optimize the additive mass for scaling of the unscaled mode shapes from OMA for which a priori knowledge of the Finite Element model of structure is required. It is shown that the total error of the scaled mode shapes is minimized using the proposed method. The method is validated using a numerical case study of a beam. Moreover, the experimental results of a clamped-clamped beam demonstrate the applicability of the method.