Showing papers on "Modal testing published in 2021"

Modal characterization of additively manufactured TPMS structures: comparison between different modeling methods

Abstract: The use of lattice structures has received increasing interest in various engineering applications owing to their high strength to weight ratio. Advances in additive manufacturing technologies enabled the manufacturing of highly complex lattice structures such as triply periodic minimal surface (TPMS) models in recent years. The application of simulation tools is expected to enhance the performance of these designs further. Therefore, it is vital to understand their accuracy and computational efficiency. In this paper, modal characterization of additively manufactured TPMS structures is studied using five different modeling methods for a beam, which is composed of primitive, diamond, IWP, and gyroid unit cells. These methods include (1) shell modeling, (2) solid modeling, (3) homogenization, (4) super-element modeling, and (5) voxelization. The modal characterization is performed by using modal analysis, and the aforementioned models are compared in terms of their computational efficiency and accuracy. The results are experimentally validated by performing an experimental modal testing on a test specimen, made of HS188, and manufactured by direct metal laser melting. Finally, the relationship between the modal characteristics and volume fraction is derived by carrying out a parametric study for all types of TMPS structures considered in this paper. The complex modal characteristics of different TPMS types suggest that they can be jointly used to meet the ever-challenging design requirements using the modeling guidelines proposed in this study.

Model updating of seven-storey cross-laminated timber building designed on frequency-response-functions-based modal testing

Abstract: Based on the experimental estimation of the key dynamic properties of a seven-storey building made entirely of cross-laminated timber (CLT) panels, the finite element (FE) model updating was perfor...

Performance of Optical Structural Vibration Monitoring Systems in Experimental Modal Analysis.

Abstract: Image-based optical vibration measurement is an attractive alternative to the conventional measurement of structural dynamics predominantly relying on accelerometry. Although various optical vibration monitoring systems are now readily available, their performance is currently not well defined, especially in the context of experimental modal analysis. To this end, this study provides some of the first evidence of the capability of optical vibration monitoring systems in modal identification using input–output measurements. A comparative study is conducted on a scaled model of a 3D building frame set in a laboratory environment. The dynamic response of the model to an impulse excitation from an instrumented hammer, and an initial displacement, is measured by means of five optical motion capture systems. These include commercial and open-source systems based on laser Doppler velocimetry, fiducial markers and marker-less pattern recognition. The performance of these systems is analysed against the data obtained with a set of high-precision accelerometers. It is shown that the modal parameters identified from each system are not always equivalent, and that each system has limitations inherent to its design. Informed by these findings, a guidance for the deployment of the considered optical motion capture systems is given, aiding in their choice and implementation for structural vibration monitoring.

Parametric studies on vibration characteristics of triply periodic minimum surface sandwich lattice structures

Abstract: Additive manufacturing has opened new avenues for the manufacturing of structures to achieve challenging engineering tasks. Gyroid, a unique example of such structures, exhibits many attractive properties, such as high stiffness-to-weight ratio and impact characteristics. This study aimed to evaluate the dynamic performance of gyroid structures made from HS188 using direct metal laser melting. The frequency response predictions of a finite element-based model of the gyroid sandwich structure were first validated against the modal testing in terms of its natural frequencies and mode shapes using the Dewesoft software. Subsequently, the effects of the plate and gyroid wall thickness on the dynamic characteristics of the structure were investigated by varying these across their expected limit ranges as part of a parametric study using the validated finite element model. The findings from the parametric study were validated against modal testing. Moreover, the performance of the aforementioned structure was compared with that of a solid structure with the same mass. The simulation results indicated that the dynamic characteristics of the gyroid structure can be improved considering the structure’s frequency response by using parametric models. It was concluded that simulation and optimization tools will play a crucial role in additive manufacturing techniques to attain optimal mechanical properties of complex structures.

Digital Image Correlation as an Experimental Modal Analysis Capability

Abstract: Digital image correlation (DIC) is an established test technique in several fields including quasi-static displacement measurements. Recently there has been growing interest in using DIC to measure structural dynamic response and even extract modal parameters from that information. While high-speed cameras have become more ubiquitous, there are no commercial end-to-end packages for modal analysis based on image data, particularly when combined with traditional data acquisition systems. As such, the practitioner is left to develop several key data processing capabilities, hardware interface equipment, and testing practices themselves. This work highlights several practical aspects that have been encountered while establishing DIC as a viable modal testing capability in a laboratory environment.

Optimal Sensor Placement for Laminated Composite and Steel Cantilever Beams by the Effective Independence Method

Abstract: In modal testing, the quality of vibration signals and clarity of peak points to extract the natural frequencies, corresponding mode shapes and damping ratio depend on the number and location of th...

Experimental Quantification and Validation of Modal Properties of Geometrically Nonlinear Structures by Using Response-Controlled Stepped-Sine Testing

Abstract: Various nonlinear system identification methods applicable to distributed nonlinearities have been developed over the last decade. However, many of them are not eligible to accurately quantify a high degree of nonlinearity. Furthermore, there exist few studies that actually validate the identified nonlinear properties. The main objective of this paper is the validation of a novel nonlinear system identification framework recently developed by the authors on a double-clamped thin beam structure that exhibits continuously distributed strong geometrical nonlinearity due to large amplitude oscillations and considerable damping nonlinearity due to micro-slip in the beam-base connections. The identification framework consists of response-controlled stepped-sine testing (RCT) and the harmonic force surface (HFS) concept. The framework is implemented by using standard hardware and software in modal testing. The RCT approach is based on keeping the displacement amplitude of the driving point constant throughout the frequency sweep and its basic assumptions are well-separated modes and no internal resonance. Constant-force frequency response curves and backbone curves of the first nonlinear normal mode (NNM) are identified at multiple measurement points from HFSs constructed by using measured harmonic excitation force spectra. The NNM shapes of the first mode at various vibration levels are then constructed from the identified NNM backbone curves. On the other side, the response level-dependent modal parameters are identified by applying standard linear modal analysis techniques to frequency response functions (FRFs) measured at constant displacement amplitude levels throughout RCT. The RCT-HFS framework quantifies about a 20% shift of the natural frequency and an order of magnitude change of the modal damping ratio (from 0.5% to 4%) for the first mode of the double-clamped beam, which indicates a considerably high degree of stiffness and damping nonlinearities in the vibration range of interest. The identified nonlinear modal parameters are successfully validated by comparing near-resonant constant-force frequency response curves synthesized from these parameters with the ones measured by constant-force stepped-sine testing and with the ones extracted from the HFSs. The HFSs are determined for the first time in an experiment at multiple measurement points other than the driving point. The NNM shapes determined from HFSs are also validated by comparing them with the ones obtained from the identified nonlinear modal constants. The RCT-HFS framework is successfully validated for the first time on a structure that exhibits continuously distributed geometrical nonlinearity. This study is a humble contribution towards making nonlinear experimental modal analysis a standard engineering practice.

A Compact Linear Ultrasonic Motor Composed by Double Flexural Vibrator.

Abstract: A minimized linear ultrasonic motor was proposed, and two flexural bimorph vibrators were utilized to form its stator. The construction of the linear ultrasonic motor and its operation principle was introduced. Two working modes with the same local deformation distribution were chosen on the basis of Finite Element Analysis (FEA). To obtain its optimized structural parameters, sensitivities on frequency difference were calculated, and a way of decreasing the frequency difference of two working modes was introduced. A prototype of the optimized model was made. The modal testing of the stator and its performance evaluation was conducted. The modal testing results were in good agreement with that of the simulation. The maximum speed of the prototype is 245 mm/s, and its maximum thrust is 1.6 N.

Sensor Placement and Structural Damage Evaluation by Improved Generalized Flexibility

Abstract: The technology of damage evaluation based on data collected by sensors has become an important topic in the field of structural engineering This paper presents an improved generalized flexibility method for sensor placement and damage evaluation. Compared with the existing methods, the main improvements of the proposed method lie in three aspects. The first one is to replace mass-normalized mode shapes with arbitrary-scaled mode shapes since that only the latter can be obtained in modal testing under ambient excitation. The second one is to combine the generalized flexibility sensitivity with the frequency sensitivity to obtain more equations. The third one is to use a new regularized generalized inverse technique for computing the unknowns more accurately. Sensor placement based on the improved generalized flexibility method can be divided into three steps. Firstly, the number of sensors can be predicted by a simple formula derived by the principle of the number of equations should close to the number of unknowns as far as possible. Secondly, the key components of the whole structure are determined based on their contributions to the global generalized flexibility change. Thirdly, the sensor positions can be obtained according to the common nodes of those key components. Overall, the proposed method is simple and convenient since it only needs environment excitation and a few sensors. The results of numerical and experimental examples show that the proposed method can successfully evaluate structural damage with a few sensor signals.

PMSM Current Shaping for Minimum Joule Losses While Reducing Torque Ripple and Vibrations

Abstract: This paper presents a current shaping method for torque ripple and mean air-gap radial force-shape harmonics reduction, under minimum Joule losses, used for air-born and structure-born vibration reduction in 3-phase PMSM electric drives. The main source for structure-born noise in electric powertrains is the torque ripple, while the main source for air-born noise are the radial air-gap forces. The proposed method uses a Fourier-decomposed LUT model obtained from updating the 2D electromagnetic FE model using test-bench results. Modal testing is used to update the structural model, and the vibration response on the machine full RPM range is determined using the vibration-synthesis method. The proposed current shaping algorithm is deterministic and can be used on any topology of 3-phase PMSMs. The torque and mean air-gap force harmonics that are intended for reduction can be arbitrary selected and their minimization can be fully completed if the maximum current and voltage constraint are respected. On the machine under test, vibration reduction is accomplished, especially for the mechanical orders that interact with the second mode-shape.

A Full-Field Non-Contact Thermal Modal Testing Technique Under Ambient Excitation

Abstract: Temperature has significant effects on modal parameters of a structure. However, it is difficult to do a full-field dynamic measurement and identify modal parameters of the structure under high temperature and working conditions. In this work, three-dimensional digital image correlation combined with Bayesian operational modal analysis is used to yield a full-field non-contact thermal modal testing technique under ambient excitation. Thermal modal verification experiments are carried out on a titanium plate with free boundary conditions under ambient excitation by a low-cost high-temperature dynamic measurement system. Natural frequencies and mode shapes of the plate under different average high temperatures are studied in detail. From the experimental process, it is believed that the thermal modal testing technique proposed in this work is an effective alternative testing technique to traditional contact testing techniques, and after some improvements, one can achieve thermal modal analysis of a structure under high temperature and working conditions.

Assignment of Natural Frequencies and Mode Shapes Based on FRFs

Abstract: This paper proposes a method of structural modification for the assignment of natural frequencies and mode shapes based on frequency response functions (FRFs). The method involves the addition of masses or stiffness (supporting stiffness or connection stiffness), the simultaneous addition of masses and stiffness, or the addition of mass-spring substructures to the original structure. Firstly, the proposed technique was formulated as an optimization problem based on the FRFs of the original structure and the masses or stiffness that needed to be added. Next, the required added masses and stiffness were obtained by solving the optimization problem using a genetic algorithm. Finally, numerical verification was performed for the different structural modification schemes. The results show that, compared to only adding either stiffness or masses, adding both simultaneously or adding spring-mass substructures obtained better optimization results. The advantage of this FRFs-based method is that the FRFs can be directly measured by modal testing, without knowledge of analytical or modal models. Furthermore, multiple structural modifications were considered in the assignment of natural frequencies and mode shapes, making the application of this method more applicable to engineering.

Single Output and Algebraic Modal Parameters Identification of a Wind Turbine Blade: Experimental Results

Abstract: This paper describes the evaluation of a single output, online, and time domain modal parameters identification technique based on differential algebra and operational calculus. In addition, an analysis of the frequency response function (FRF) of the system is conducted in a specific set up, emulating its nominal or operational conditions to determine the influence of the non-linearities over the dynamic behavior of the system in those particular magnitudes of deformations; thus, this influence is quantified by a numerical index. This methodology is applied to a wind turbine blade submitted to wind tunnel experiments. The natural frequencies and modal damping ratios of six bending modes associated with the blade are estimated using real-time velocity measurements from one single point of the blade. A comparison with the usual impact hammer modal testing is performed to evaluate and establish the proposed approach’s main contributions. The developed modal parameter identification algorithms are implemented to run into a standard personal computer (PC) where the data acquisition system’s measurements are conditioned and processed. The results show the performance and the fast parametric estimation of the proposed algebraic identification approach.

Dynamic Characterization of a Pop-Up Folding Flat Explorer Robot (PUFFER) for Planetary Exploration

Abstract: NASA’s Jet Propulsion Laboratory is currently in the design phases of the new Pop-Up Flat Folding Explorer Robot (PUFFER) for planetary exploration. Inspired by origami, PUFFER is constructed of a printed circuit board (PCB) body which utilizes Nomex fabric as foldable joints. The structure can fold flat to stow for launch and to change shape according to the obstacles encountered. Of primary interest is how PUFFER will perform under impacts caused by drops into large pits on a planet’s surface. In order to simulate PUFFER’s dynamic performance, Finite Element Models (FEM) need to be constructed in an informed manner using the material properties and damping characteristics of the joints. This paper presents the first step in this process, the dynamic characterization of PUFFER via modal testing. The frequencies, associated mode shapes, and modal damping extracted by modal analysis will be correlated with the FEM to ensure that the dynamic behavior of the structure is properly captured.

Spatially Resolved Experimental Modal Analysis on High-Speed Composite Rotors Using a Non-Contact, Non-Rotating Sensor.

Abstract: Due to their lightweight properties, fiber-reinforced composites are well suited for large and fast rotating structures, such as fan blades in turbomachines. To investigate rotor safety and performance, in situ measurements of the structural dynamic behaviour must be performed during rotating conditions. An approach to measuring spatially resolved vibration responses of a rotating structure with a non-contact, non-rotating sensor is investigated here. The resulting spectra can be assigned to specific locations on the structure and have similar properties to the spectra measured with co-rotating sensors, such as strain gauges. The sampling frequency is increased by performing consecutive measurements with a constant excitation function and varying time delays. The method allows for a paradigm shift to unambiguous identification of natural frequencies and mode shapes with arbitrary rotor shapes and excitation functions without the need for co-rotating sensors. Deflection measurements on a glass fiber-reinforced polymer disk were performed with a diffraction grating-based sensor system at 40 measurement points with an uncertainty below 15 μrad and a commercial triangulation sensor at 200 measurement points at surface speeds up to 300 m/s. A rotation-induced increase of two natural frequencies was measured, and their mode shapes were derived at the corresponding rotational speeds. A strain gauge was used for validation.

Model Updating and Global Eigenvalue Analysis of a Tie-Bolt Rotor Using Zero-Length Contact Elements under Different Preloads

Abstract: Tie-bolt rotors are composed of several disks fastened by tie bolts where contact properties have a great influence on the modal behavior. In this work, a linear spring-damper element is used to consider the contact stiffness and damping in a tie-bolt rotor. A tie-bolt rotor model is developed using the beam element and the zero-length contact element. Experimental modal testing is performed under different preloads of tie bolts. Model updating is carried out to tune the contact parameters using the Particle Swarm Optimization algorithm. Furthermore, a global eigenvalue evaluation is carried out to demonstrate the impact of the lumped spring-damper element on the modal results. Results show that a larger pretension reduces the influence of contact damping on modal parameters. Compared to antisymmetric modes, symmetric modes are more sensitive to the change of contact damping.

Vision-Based Modal Testing of Hyper-Nyquist Frequency Range Using Time-Phase Transformation

Abstract: Mechanical structures such as automobiles, building structures, ships, etc., are exposed to vibration under operating conditions. Especially under resonance, small excitations cause large deformation of structures, which is directly related to human safety. Modal testing is a method by which the dynamic properties of structures under vibrational excitation can be determined. A modal testing system can be utilized in a variety of applications and ways, depending on the sensor that measures vibration. Recently, numerous studies in the field of noncontact measurement techniques have been carried out. Among the developed approaches, vision-based vibration measurement has the important advantage that the displacement response of a whole region, not a point or a line, can be measured at one time. However, the measurement using a camera has a problem in that the sampling rate is insufficient as compared with the conventional contact-type sensor. The sampling rate is determined by the limited frame rate of the camera hardware, and modes above the Nyquist frequency cannot be measured according to the Nyquist theorem. In response, in this research, we propose a phase axis-based vibration measurement method instead of the conventional time axis-based vibration measurement method using time-phase transformation. In order to apply the proposed method, among the various excitation methods used in modal testing, we utilize the excitation method of changing the single excitation frequency stepwise. The single frequency excitation method has a feature that the response frequency is equal to the frequency of the excitation signal when the response of the excited system reaches a steady state. Using this feature together with time-to-phase transformation, we can perform modal testing in the hyper-Nyquist frequency range, which was previously impossible to measure. Finally, a simple experiment on a beam confirmed the validity of the proposed method.

Dynamics of Miniature and High-Compliance Structures: Experimental Characterization and Modeling

Abstract: The dynamic behavior of miniature and high-compliance structures is critical for their performance. However, their low stiffness and inertia bring significant challenges to the experimental characterization and modeling of their dynamics. Traditional modal testing techniques cannot produce the required low noise, high-bandwidth dynamic models with sufficiently low forces to prevent damage to the fragile structures. The objective of this work is to develop a new iterative approach that enables effective dynamic characterization of miniature and high-compliance structures. The iterative approach consists of a combination of model-based simulations and experimentation. An impact excitation system (IES) with a flexure-jointed cantilever controls the motions of an instrumented impact tip to enable specifying the bandwidth and force magnitude of the impact excitations. Successful application of the IES requires determination of the IES-parameters that produce the desired (broad) bandwidth and (limited) force magnitudes. However, for high-compliance and miniature structures, this requires the knowledge of the dynamics of the sample (the structure), which is not known a priori. To address this, the simulations use both the dynamic model of the IES and an approximate model of the sample dynamics obtained from the previous iteration in order to identify a set of favorable IES parameters for the current iteration. Two case studies involving a miniature blade of a jet engine turbine and a high-compliance load cell are presented to demonstrate the approach. Only a few iterations were sufficient for converging to a favorable set of parameters that produce high-bandwidth (e.g., 31 kHz) and reproducible dynamic models in the form of frequency response functions (FRFs). As compared to manual impact testing, the use of the new approach expands the bandwidth by as much as 50 times while reducing the test repetitions by more than ten times. The presented iterative framework based on the impact excitation system addresses the shortcomings of traditional modal testing techniques and enables effective dynamic characterization and modeling of miniature and high-compliance structures.

Analysis of the frame rate limit for the estimation of the natural frequency of vibration in a mechanical system using optical techniques

Abstract: In this work, we analyze the advantages and limitations of the systems of low speeds of frames per second (fps) for the estimation of the vibrations measurements in systems where optical techniques are used. The acquisition systems with low fps are interesting because they are not expensive. In this way, the aim of this work is to compute the limit speed to obtain good resolutions in data collection. Laser triangulation technique is implemented to determine the natural frequency of vibration of a system using a cantilever beam, as a standard example. The results are compared, with a commercial accelerometer.

Utilizing Modal Testing for Monitoring the Structural Health of Wind Tunnel Facility Hardware

Abstract: The 10- by 10-Foot Abe Silverstein Supersonic Wind Tunnel (10 × 10) is the largest and fastest wind tunnel facility at NASA’s Glenn Research Center(GRC) and is specifically designed to test supersonic propulsion components from inlets and nozzles to full-scale jet and rocket engines (10 × 10 Abe Silverstein Supersonic Wind Tunnel, https://www1.grc.nasa.gov/facilities/10x10/). Recently, a critical part of the wind tunnel failed and required a redesign before reintegrating into the facility. The design requirements of this new component required that clearances between large metallic components exist, which have the potential for undesirable nonlinear dynamics to occur, in particular rattling. Rattling is feared to occur when the wind tunnel is being operated in certain flow regimes that induce cyclic aero loads on the new component near its natural frequencies. This paper describes the approach taken to better understand and resolve this vibration problem using modal testing. A modal test was developed and executed by GRC’s Structural Dynamics Lab to quantify the modal parameters of the structure, namely which specific excitation frequencies caused the structure to rattle. These results were shared with facility operators as frequency ranges that should be avoided to ensure maximum lifespan of the new structure. Additional means of structural health monitoring (SHM) as well as Vortex shedding are briefly discussed in this paper.

Encapsulation Based Method for Natural Frequency Identification of Deployable Solar Arrays with Multiple Plates

Abstract: The ground modal test is an important approach to the natural frequency of solar arrays to support the attitude control of spacecraft. However, for the batch production of small satellites, the accuracy and efficiency of traditional ground modal testing methods are limited. This shortcoming restricts the development of satellite constellations. Based on the encapsulation method widely used in the computer field, this paper proposed a natural frequency identification method of deployable solar arrays with multiple plates. This method is of high accuracy and efficiency that meets the demand of attitude control and makes sense to accelerate the batch production of small satellites. First, a suspended modal test system with gravity compensation function is designed. Second, the mathematical model of the test system is established. Abstracting parts of the parameters of the test object into an encapsulated entity, the mathematical model is simplified by equivalent variables. Thus, the direct mapping relationship between the ground test result and the true natural frequency is proposed. Finally, to verify the identification accuracy, finite element analysis (FEA) and the ground modal test of a two-folder solar array simulant are carried out. The results show that the relative error of the first-order natural frequency after correction and the theoretical value is less than 3%. Meanwhile, the identification accuracy of the ground modal test is improved by more than 50%. This method improves the availability of ground test results and reduces the calculation amount, so that it is convenient for engineering applications.