Experimental Natural Frequencies Research Articles

Ambient vibration based-simplified frequency formulas for historical masonry stone mosques with timber truss roofs

ABSTRACT Historical masonry stone mosques with timber truss roofs were widely constructed all over the world. Due to the complex structural behaviors of this type of building, it is difficult to determine natural frequencies during the seismic safety evaluations numerically. The article aims to develop simplified natural frequency formulas based on ambient vibrations for the historical masonry stone mosques with timber truss roofs. Fourteen masonry stone mosques with timber truss roofs built in the Eastern Black Sea Region of Turkey are selected for the study. Experimental natural frequencies, mode shapes and damping ratios of the selected mosques under ambient vibrations are determined using the Operational Modal Analyses. Ambient vibration-based simplified natural frequency formulas based on the geometrical dimensions for the masonry stone mosques with timber truss roofs are obtained by using the statistical regression analysis. The proposed formulas for the first three frequencies are verified with the control data.

Translational and rotational resonance frequencies of a disk in a single-axis acoustic levitator

In this study, we investigate the acoustic levitation of a disk in a single-axis acoustic levitator operating at 21.53 kHz. First, two acoustic models based on the finite element method are employed for calculating the acoustic radiation force and torque on a levitating disk. The models are also used for calculating the vertical, horizontal, and torsional trapping stiffness and its corresponding natural frequencies. Furthermore, translational and angular oscillations of the disk are captured by a high-speed camera, and a tracking algorithm is employed for extracting the natural frequencies of the oscillations. The experimental natural frequencies present good agreement with those predicted by the models. Although the numerical model was employed for simulating the forces and torques on a disk, the presented method is general and it can be employed for simulating the acoustic levitation of objects of arbitrary shapes and sizes.

Dynamic properties of a steel–UHPC composite deck with large U-ribs: Experimental measurement and numerical analysis

Steel–ultra-high-performance concrete (UHPC) composite decks, which are composed of thin steel– UHPC layers and large U-ribs, are an innovative bridge deck system. In this study, experimental and numerical approaches were combined to investigate the dynamic properties of a steel–UHPC composite deck. A large-scale steel–UHPC composite deck specimen was fabricated and tested under hammer impacting. The effects of the impact force characteristics on structural vibrations and noise were evaluated, and the vibration transmission characteristics in the deck were explored. The experimental results revealed that the steel–UHPC composite deck with large U-ribs exhibited complicated dynamic properties in different frequency bands. A finite element (FE) model was built and validated through comparison with the experimental natural frequencies and frequency responses. FE analysis was then used to compare the steel–UHPC composite deck with two other bridge deck systems (a conventional orthotropic steel deck and a steel–concrete composite deck). The numerical results indicated that the thin UHPC layer guaranteed the stiffness of the steel deck plate in the low-frequency range. At frequencies above 200 Hz, the vibration energy of the conventional orthotropic steel deck was approximately 0.45 times that of the steel–UHPC composite deck. Two countermeasures for reducing vibration (i.e., adjusting the crossbeam spacing and filling the large U-ribs with plain concrete) were found to be effective. Based on the simulation results, filling the U-ribs with plain concrete was the most effective approach and reduced the vibration energy by an average of 285% in the center frequency range of 63–1600 Hz.

Model updating of a reduced-scaled masonry bridge by using response surface method

Historical structures reflect the historical and cultural properties of countries and also contributes to the economy in terms of cultural tourism. Therefore, it is important to understand the structural behavior of these kinds of structures under dynamics loads such as earthquakes, etc. to protect and transfer them safely to future generations. For this reason, this study aims to investigate the dynamic behavior of a reduced-scale one-span masonry arch bridge constructed in laboratory conditions by performing experimental and numerical analysis. Operational Modal Analysis (OMA) Technique was performed under ambient vibrations for experimental study to determine modal parameters of the reduced-scaled bridge model. Sensitive three-axial accelerometers were located on critical points on the bridge span and signals originated by accelerometers were collected to quantify the vibratory response of the scale bridge model. The experimental natural frequencies, mode shapes and damping ratios resulting from these measurements were figured out by using Enhanced Frequency Domain Decomposition (EFDD) technique. ANSYS software was utilized to carry out 3D finite element (FE) modeling of the reduced-scale masonry bridge and determine the natural frequencies and mode shapes of the bridge numerically. Experimental results were compared with FE analysis results of the bridge. Significant differences appeared when comparing the results of the experimental and numerical with the initial conditions. Therefore, the finite element model is calibrated by using the response surface (RS) method according to the experimental results to minimize the uncertain finite element modeling parameters of the reduced-scale bridge model such as material properties.

Empirical formulation for estimating the fundamental frequency of historical stone mosques with masonry domes

SummaryHistorical stone mosques with masonry dome are complex structures due to their different structural elements, material properties, boundary conditions, connections, etc. It is very difficult to develop the numerical models representing the real behaviour of these structures. Therefore, their numerical models should be checked with ambient vibration tests for the reliable safety evaluations before the restoration applications. However, it is known that the ambient vibration tests of historical mosques are very difficult and costly and need permissions from the owners and relevant government agencies. The paper aims to develop an empirical formulation for estimating the fundamental frequency of historical stone mosques with masonry dome to check the initial finite element models. Nine stone mosques with masonry dome in different dimensions in the eastern Black Sea Region of Turkey were selected as examples for this purpose. By performing ambient vibration tests of the selected mosques, experimental natural frequencies, mode shapes, and damping ratios have been determined and evaluated together. An empirical formulation for the fundamental frequency and coefficients for the second and third frequencies of stone mosques with masonry dome based on vibration data are obtained by using the statistical regression analysis and verified with the control data. The comparative results confirm that the proposed formulation has a reliable predictive performance.

The Application of Non-deterministic Model Updating method of a Complex Jointed Structure using Central Composite Design based meta-model

Finite element (FE) model of a structure is highly depended on idealising and simplification of model, however, the model may not truly represent the physical structure. The application of FE model updating is advocated to modify FE model of structure in order to acquired better correlation between the predicted and measured structure response. Nevertheless, for complex jointed structure, a FE model is containing a very large degree of freedoms that may contribute to high computational time. Therefore, this paper presents the application of response surface method in non-deterministic model updating using central composite design (CCD) sampling for improving the efficiency of a finite element model of a laser stitch welded structure. In this study, FE model of the structure is developed using CQUAD4 shell elements and ACM2 element connectors been used to representing the laser stitch weld joints. For the measured data, experimental modal analysis was performed using LMS SCADAS and conducted under free-free boundary conditions. In the model updating, the minimisation of uncertainties parameters in the FE model is based on the objective function that is formed from the residuals between the FE and experimental natural frequencies. The results show that the response surface method using CCD sampling is efficient to be used in FE model updating because it is capable of improving the accuracy of the initial FE model.

Seismic Assessment of Footbridges under Spatial Variation of Earthquake Ground Motion (SVEGM): Experimental Testing and Finite Element Analyses.

In this paper, the seismic assessments of two footbridges, i.e., a single-span steel frame footbridge and a three-span cable-stayed structure, to the spatial variation of earthquake ground motion (SVEGM) are presented. A model of nonuniform kinematic excitation was used for the dynamic analyses of the footbridges. The influence of SVEGM on the dynamic performance of structures was assessed on both experimental and numerical ways. The comprehensive tests were planned and carried out on both structures. The investigation was divided into two parts: in situ experiment and numerical analyses. The first experimental part served for the validation of both the finite element (FE) modal models of structures and the theoretical model of nonuniform excitation as well as the appropriateness of the FE procedures used for dynamic analyses. First, the modal properties were validated. The differences between the numerical and the experimental natural frequencies, obtained using the operational modal analysis, were less than 10%. The comparison of the experimental and numerical mode shapes also proved a good agreement since the modal assurance criterion values were satisfactory for both structures. Secondly, nonuniform kinematic excitation was experimentally imposed using vibroseis tests. The apparent wave velocities, evaluated from the cross-correlation functions of the acceleration-time histories registered at two consecutive structures supports, equaled 203 and 214 m/s for both structures, respectively. Also, the coherence functions proved the similarity of the signals, especially for the frequency range 5 to 15 Hz. Then, artificial kinematic excitation was generated on the basis of the adopted model of nonuniform excitation. The obtained power spectral density functions of acceleration-time histories registered at all supports as well as the cross-spectral density functions between registered and artificial acceleration-time histories confirmed the strong similarity of the measured and artificial signals. Finally, the experimental and numerical assessments of the footbridges performance under the known dynamic excitation generated by the vibroseis were carried out. The FE models and procedures were positively validated by linking full-scale tests and numerical calculations. In the numerical part of the research, seismic analyses of the footbridges were conducted. The dynamic responses of structures to a representative seismic shock were calculated. Both the uniform and nonuniform models of excitation were applied to demonstrate and quantify the influence of SVEGM on the seismic assessment of footbridges. It occurred that SVEGM may generate non-conservative results in comparison with classic uniform seismic excitation. For the stiff steel frame footbridge the maximum dynamic response was obtained for the model of nonuniform excitation with the lowest wave velocity. Especially zones located closely to stiff frame nodes were significantly more disturbed. For the flexible cable-stayed footbridge, in case of nonuniform excitation, the dynamic response was enhanced only at the points located in the extreme spans and in the midspan closely to the pillars.

A theoretical computational model of a plate in hypersonic flow

A theoretical model of an elastic panel in hypersonic flow is derived to be used for design and analysis. The nonlinear von Kármán plate equations are coupled with 1st order Piston Theory and linearized at the nonlinear steady-state deformation due to static pressure differential and thermal loads. Eigenvalue analysis is applied to determine the system’s stability, natural frequencies and mode shapes. Numerically time marching the equations provides transient response prediction which can be used to estimate limit cycle oscillation amplitude, frequency and time to onset. The model’s predictive capability is assessed by comparison to an experiment conducted at a free stream flow of Mach 6. Good agreement is shown between the theoretical and experimental natural frequencies and mode shapes of the fluid–structure system. Stability analysis is performed using linear and nonlinear methods to plot stability, flutter and buckling zones on a free stream static pressure vs temperature differential plane.

Effects of prestressing force on natural frequency of prestressed concrete beams considering self-weight

This study investigated the effects of prestressing force on the natural frequency of concrete beams considering changes in the self-weight of the beam. For this, a finite element formulation was derived to account for the increase in the stiffness of a beam-tendon system due to the axial force and deformation induced by prestressing of the tendon. The developed finite element formulation was validated with the data obtained in laboratory experiments. The experimental natural frequencies of the small prestressed concrete (PSC) beam specimens were consistent with those obtained using the proposed method. The first natural frequency increased almost linearly as the prestressing force increased. The proposed method was then applied to four actual PSC bridges typically employed in the field. Different from the laboratory specimens, the first natural frequencies of the actual PSC bridges barely changed or increased with increasing prestressing force. The results of an analytical parametric study showed that the increase in the natural frequency strongly depended on the magnitude of the prestressing force relative to the total weight of the structure. Thus, the variation in the natural frequencies of the actual PSC bridges with high total weight relative to the prestressing force was negligible due to the application of the prestressing force.

Updating the finite element model of a Colombian Bridge with Ansys

Updating structural model is a knowledge field that have been studied in the last decades to guarantee the reliability on the model defined to represent the behavior of a structure, but generally implies the use of different software to carry out the different parts of the process. This paper presents the updating of the finite element model of a curve-alignment reinforced concrete bridge located near to the city of Ubaté in Colombia by using the optimization tool available in software Ansys and ambient vibration measurements. The use of such type of information avoids to carry out forced-vibration test, which affect the normal operation of the bridge. The objective function corresponds to the minimization of the error between analytical and experimental natural frequencies of the bridge. The design variables correspond to the material properties of the concrete and the elastomeric bearings. Results show that the error was decreased to less than 2%. The sensibility analysis allowed to determine which variables are more sensible to affect the natural frequencies in the structure.

Experimental and numerical vibration analysis of plates with curvilinear sub-stiffeners

Curvilinear stiffened panels are being developed for aerospace structures and other applications. This paper presents an experimental and numerical study into the vibration response of three curvilinear stiffened square plates clamped at the edges. The experimental modal analysis was performed using laser Doppler vibrometry (LDV) and an impact hammer test. Two of the three plates was constructed with curvilinear stiffener geometry, while the third was a straight stiffened plate with the stiffeners oriented at an angle to the edge of the plate. Even though the natural frequencies of the plates are similar, the different stiffening patterns was sufficient in providing unique directional properties and therefore distinct mode shapes. The numerical modal analysis of the plates was performed using finite element analysis (FEA). A comparison of the experimental and numerical results was carried out in terms of natural frequencies and mode shapes, using relative differences and modal assurance criterion (MAC), respectively. The experimental and numerical results were in good agreement for all the three plates. The difference between experimental and numerical natural frequencies was typically less than 5% and the diagonal MAC values typically ranged from 0.8 to 1. This is in line with previously published results in the literature. The reasons for differences between the experimental and numerical results, and the practical significance of the findings, are also discussed.

Temperature-dependent thermo-elastic parameter identification for composites using thermal modal data

To accurately determine the temperature-dependent parameters of composites, a thermo-elastic parameter identification approach using thermal modal data is proposed in this article. The investigation is based on two hypotheses: (1) the structure is at steady-state temperature field, which means the temperature distribution is time independent; (2) temperature distribution can be determined in advance of thermo-elastic parameter identification, and thermal-related large deformation is not considered. The thermal-dependent elastic constants and thermal expansion coefficients are expressed as intermediate functions with the independent variable of temperature, perturbation method is adapted to calculate the sensitivity of thermal modal frequencies with respect to the intermediate variables, and variables with high sensitivity are selected as the identifying parameters. By constructing the intermediate function and calculating the relative sensitivity, thermo-elastic parameters are identified by minimizing the residual between experimental and analytical natural frequencies under thermal circumstance. Two different types of composite models are employed to verify the strategies of parameter identification. Results show that on the basis of the intermediate function, the proposed approach can be applied to identify the thermo-elastic parameters effectively.

Seismic performance evaluation of a fire-exposed historical structure using an updated finite element model

This paper presents a seismic performance evaluation of a historical masonry structure. The process involves geometrical checking and seismic performance controls and also requires consideration of relevant codes and guidelines. Geometric checking was carried out in accordance with previous and newly-introduced Turkish Earthquake Codes. In order to obtain reliable results for seismic evaluation, the numerical model of the building was updated by means of non-destructive experimental measurement methods. The experimental measurement process was carried out using the Operational Modal Analysis method. The maximum error between the numerical and experimental natural frequencies, calculated as 37.11%, was reduced to 2.39% through the use of updating procedure. Time history seismic analysis was conducted on the updated finite element model using the Kocaeli 1999 earthquake record. Evaluation of the seismic performance of the structure was carried out with reference to a new guideline published specifically for assessment of historical structures. At the end of the analyses, maximum displacements and principal stresses were obtained and presented in detail using contour diagrams. In terms of displacement control, the structure showed only limited damage during the applied earthquake record: 0.0001 < 0.003. In other words, in terms of the new guideline, the structure behaved in a linear way when exposed to the selected earthquake.

Nondeterministic Model Updating of Laser Spot Welded Structure via Response Surface Methodology

This paper presents the application of response surface method in finite element model updating, as an approach for improving the accuracy and efficiency of the finite element model of a laser spot welded structure, to reflect the physical responses of the structure. The procedures of implementation for response surface in model updating such as sampling method, selecting the significant updating parameters and constructing a quadratic polynomial response surface are discussed. Initially, the finite element model of the structure was developed using CQUAD4 shell element alongside CWELD element connectors to represent laser spot weld joints. Then, NASTRAN SOL 103 was used to calculate the dynamic behaviour of the model (natural frequencies and mode shapes). The experimental modal analysis was then conducted under free-free boundary conditions via LMS SCADAS to obtain experimental data. The minimisation of the discrepancies of the finite element model was based on objective function that was formed by the residuals between finite element and experimental natural frequencies. Results show that response surface method was efficient to be used in finite element model updating since it is capable to improve the accuracy of the finite element model.

Experimental Verification and Comparative Analysis of Equivalent Methods on Metal's Fixed Joint Interface.

In order to effectively improve the dynamic characteristics of the fixed metal joint interface, it is important to establish a correct equivalent model of the metal joint interface. In this paper, three equivalent methods for simulating the metal joint interface are analyzed, including the virtual material method, spring damping method, finite element method, and verification by modal experiment. First, according to the contact mechanics model of the constructed metal joint interface, the physical properties of the three-dimensional models of the fixed joint interface are assigned in the ANSYS software. Then, three methods are used for the modal analysis and compared with a modal experiment. The results show that the modal shapes of the three theoretical methods are consistent with those of the experimental modes. The first five natural frequencies obtained by the virtual material method are closest to the experimental natural frequencies, and the errors are within 10%. The errors of the other two methods are between 9% and 39%. Therefore, the virtual material method is a better equivalent method of the metal joint interface.

Non-destructive modal parameter identification of historical timber bridges using ambient vibration tests after restoration

Historical structures are important cultural relics which illustrate the progress of engineering development. They are a valuable source of information on construction techniques and materials selection over the centuries. However, many factors, including environmental conditions and natural disasters, contribute to damage and destruction of historical structures. Today, the aim of restoration is to carry out necessary works with care and sensitivity while ensuring historical buildings are restored as near as possible to their original structural strength. However, the extent of the contribution of the restoration to the structure and the determination of the restoration success is carried out by various non-destructive experimental studies. This aim of this paper was to obtain structural modal parameters for the historical timber Buzlupınar Bridge using non-destructive ambient vibration tests after restoration. From calculations of natural frequencies and mode shapes, it can be seen that the six natural frequencies obtained are between 2.0 and 20.0 Hz. To minimize the 34.55% differences in experimental and numerical natural frequencies, a FE model of the timber bridge was updated using manual model updating procedures. The maximum differences were reduced to below 1% except for the fourth mode.

A novel strategy for effectively implementing a typical AVC scheme using finite element model updating

Finite element (FE) model of a square cantilevered plate instrumented with a piezoelectric sensor and an actuator is created using Hamilton’s principle. Rotational degrees of freedom (dofs) of the FE model are eliminated using system equivalent reduction expansion process (SEREP). Experimental mode shapes and natural frequencies are extracted from the structure using high speed cameras and digital image correlation (DIC) technique. Initial FE model is updated using experimental mode shapes and natural frequencies by well-known Berman and Nagy approach. Updated FE model thus derived is further reduced to first three modes using orthonormal modal reduction technique. Modal model of the smart plate is then used to derive state space model of the smart plate. Two Kalman observers are constructed: one using initial FE model and other using updated FE model. Active vibration control experiments are conducted on the cantilevered using these two Kalman observers in the control law. It is observed that much better vibration suppression occurs when Kalman observer based on updated FE model is used in the control law. Strategy suggested in this work to implement a typical active vibration control scheme on a structure is simple and yet very effective.

Application of Response Surface Method in Modification of Virtual Material Model

Virtual material model is an effective equivalent modelling technique to simplify and characterize the stiffness weakening effect of mechanical joints. In order to further improve the accuracy of virtual material model, the density and thickness parameters of virtual material model were optimized and modified by response surface method. The advantage of this method is that under the condition of maintaining the original surface characteristics of the joint, the micro-characteristics of the joint under certain pre-tightening conditions can be quantitatively characterized macroscopically, which makes the analysis results more close to the actual situation. The natural frequencies of the virtual material model before and after modification are compared with the experimental natural frequencies, and the validity of the method and the modified model are verified.

Identification of the tension force in cables with insulators

The present paper explores two approaches which, based on the measurement of the two first natural frequencies, allow the identification of the tension force in cables with insulators. For this purpose, the nonlinear mathematical model of the mechanical system and its Finite Element discretization are firstly stated. Besides, free-vibrations experiments on both a laboratory and a real-scale simulated configuration of cables with insulators are performed in order to derive their frequency response. During the laboratory experiments, a vision-based methodology is implemented for the register of the time series displacements of the cable. On this basis, a Bayesian approach is first addressed. In this framework, the cable tension is regarded as a random variable and the Bayes rule is applied to combine the experimental natural frequencies with the prior information about the random variable to derive the posterior distribution of the tension force. The Markov Chain Monte Carlo-Metropolis Hastings algorithm is implemented for the evaluation of the posterior distribution. On the other hand, a heuristic approach is proposed through the implementation of an Artificial Neural Network (ANN) as an inverse model between the parameters of the cable—including the natural frequencies—and its tension force. The training patterns are obtained from computational simulations of different cable configurations. The experimental natural frequencies are then applied to the trained ANNs to infer the tension force of the laboratory and real-scale configurations. Both approaches provide estimates of the tension force within admissible error margins.

Identification of material properties of a laminated plate from measurements of natural frequencies and modal rotations

This paper presents a method for identification of material constants of a laminated composite plate. An optimization problem, with an objective function relating experimental and numerical natural frequencies, is formulated and solved. Three optimization algorithms were applied in this study for comparison purposes: (1) particle swarm, (2) genetic, and (3) pattern search algorithms. The identified material constants were validated by comparing modal rotations measured with shearography with those computed by finite element analysis.