Free Vibration Technique Research Articles

Evaluation of System Identification Methods for Free Vibration Flutter Derivatives of Long-Span Bridges

The significance of long-span bridges being susceptible to wind-induced vibrations and the need for evaluating their aerodynamic performance is the focus of this study. The main emphasis is on experimental methods for assessing the bridges’ aerodynamic stability, using sectional model tests with the free vibration technique. The dynamic properties of the model are determined from the measured response, using various system identification methods, including the modified Ibrahim time domain (MITD) and iterative least squares (ILS) for two-degree-of-freedom systems and the logarithmic decrement method (LDM) and the Hilbert transform method (HTM) for single-degree-of-freedom (SDOF) systems. A new dynamic testing setup was designed to facilitate single-degree-of-freedom (heave and pitch) and coupled two-degree-of-freedom (2DOF) motion in a wind tunnel section model. The vertical and torsional stiffnesses of the model were adjusted with elastic springs. A Great Belt Bridge section model was selected for testing due to its streamlined aerodynamic shape. The direct and crossflow derivatives were extracted from the measured response using the system identification methods mentioned. Additionally, analytical studies and numerical computational fluid dynamics simulations were conducted to validate the experimental results. The study found that HTM is most effective in SDOF due to its ability to extract both damping and frequency from the nonlinear response, whereas the MITD method is faster in converging system parameters in 2DOF system tests. The experimental and numerical results are comparable to the flat plate, which confirms the streamlined behavior of the Great Belt section from an aerodynamic perspective.

Experimental investigation of self-damping characteristics of the ACSR Beresford and TERN transmission line conductors using log-decrement and quality factor methods

This work considered the experimental investigation of self-damping characteristics of ACSR Beresford and TERN transmission line conductors using the free and forced vibration techniques. When subjected to a load, self-damping is the power dissipated per unit length of the conductor as it vibrates. ACSR Beresford and TERN conductors are the two most commonly used conductors in the South African transmission network. The paper has revealed that for all the tests, the damping factors for the forced vibration on the TERN conductor was ζ ≤ 0.0307, and for the free vibration was, ζ ≤ 0.057, whereas the damping factors for the ACSR Beresford (forced vibration) were found to be ζ ≤ 0.0103, and for the ACSR Beresford (free vibration) were found to be ζ ≤ 0.056.The damping factors obtained in both conductor-tests were not sufficient to suppress Aeolian vibrations. Results obtained by Mokeretla (2011), that the internal self-damping of TERN transmission lines could not suppress Aeolian vibrations, have been confirmed, due to the damping values being much less than critical damping (ζ ≪ 1). An additional conductor was tested, the ACSR Beresford conductor, whose self-damping factor was also not sufficient to suppress Aeolian vibration.

Room and high temperature mechanical properties of Mg2Si, Mg2Sn and their solid solutions

Knowledge of the mechanical properties of thermoelectric materials at high temperature is required for the modelling and optimization of a thermoelectric generator under application conditions. We present room and high temperature characterization of Young’s modulus for Mg2Si, Mg2Sn and their solid solutions establishing a linear dependence, both on composition and on temperature.Through the comparison of Resonant Ultrasound Spectroscopy and free vibration techniques, we measure the elastic moduli with high precision. The comparison of our results (E = 110 GPa for Mg2Si and 78 GPa for Mg2Sn) to first principles calculations and experimentally reported data shows good agreement. Additionally, by estimating the Poisson ratio, we calculate the temperature-dependent shear modulus G and finally provide a simple bilinear function for Young’s and shear moduli as a function of temperature and composition.

Mechanical and free vibration properties of skin and core designed basalt woven intertwined with flax layered polymeric laminates

Design of fiber-reinforced polymer damping laminates has been attracting great interest in industrial sectors for lightweight structural damping applications. The present work investigates the impact of skin, core, neutral, and alternate intertwined basalt/flax fabric on the mechanical and vibrational properties of the newly designed polymeric laminate. The designed sequence structure was fabricated using a wet hand lay-up technique with hydraulic compression. Tensile and flexural strength of intertwined multilayer basalt/flax woven composite were studied. An effect of the intertwining on the tensile and flexural strength fractured surface of the composites has been further evaluated. Free vibration technique was used for recording vibration response and the related damping frequencies of intertwining composites. A cantilever mode impact hammer was used for generating periodic signals of the designed composite systems. Damping ratios and damped natural frequencies were calculated with several plies and sequence of flax/basalt woven in the composite. The experimental results revealed that the damped natural frequencies of class II, skin basalt layer intertwined seven core flax layered composite (B2F7) was high, followed by two skin basalt layers intertwined core flax layered composite (B4F5). The addition of the flax layer enhanced the natural frequency to the higher value. It was found that the skin basalt layer with intertwined flax layered B2F7 design structure exhibits maximum damping value with acceptable mechanical properties.

Experimental Uncertainty Quantification of Flutter Derivatives for a PK Section Girder and Its Application on Probabilistic Flutter Analysis

Aerodynamic flutter instability could lead to the catastrophic collapse of flexible long-span bridges and needs to be prevented. This study investigated the variability of eight experimentally measured flutter derivatives (FDs) for a commonly used a Pasco–Kennewick (PK) section girder using a free vibration technique in a wind tunnel, which provided some new insights into the identification of FDs and supplemented the reliability analysis for buffeting and flutter performance. The aerodynamic uncertainties in terms of the dispersion of flutter coefficients were studied and two implications behind the extraction of FDs were discussed. The statistical and probabilistic behaviors of FDs at different reduced wind speeds were examined before generating sufficient independent random samples using the Monte Carlo (MC) approach. The intercorrelations between experimental FDs quantified by correlation coefficients were also examined and were employed to randomly sample the correlated FDs. The probabilistic flutter solutions in terms of critical wind speed propagated from the FDs uncertainties were studied utilizing step-by-step analysis, which resulted in several multimodal probability distributions of flutter onset. In addition, the role played by each FD on the variation of critical wind speed was discussed.

Investigation of Wind-induced Behavior and Aerodynamic Stability of a Long-span Flat Roof Based on Wind Tunnel Experiment and FSI Simulation with Free-vibration Technique

Investigation of Wind-induced Behavior and Aerodynamic Stability of a Long-span Flat Roof Based on Wind Tunnel Experiment and FSI Simulation with Free-vibration Technique

Comparison study of mechanical and dynamic vibration properties of hole defect introduced in hybrid polymer composite

The need for hybrid composites has increased because it includes the advantages both of synthetic glass and natural fibers. In this research work, a hybrid composite has been developed using a glass and coir fiber which has been subjected to moisture, tensile with and without the hole, flexural and dynamic properties. The glass fiber-coconut coir-glass fiber (G-C-G) hybrid composite was made by hand layup technique. The dynamical properties of tensile and open-hole tensile composites were measured by a free vibration technique. SEM analysis on fractured surfaces of the composite was also performed. The results showed that there was an appreciable rise in the moisture absorption capacity of the composites. Tensile testing showed that there was a decrease in tensile strength and modulus with increases in center hole diameter. Results of the fracture study indicated that the fiber-matrix interface improved with fiber treatment. The mechanical properties of hybrid composites were abruptly decreased with a hole diameter of 6 mm. The damping ratio and natural frequency of composite without tensile hole show higher value due to undisturbed in fiber strength.

Experimental studies on the vortex-induced forces of a 4:1 rectangular cylinder and two typical bridge girders

Wind tunnel tests were performed on a 4:1 rectangular (REC) cylinder, a trapezoidal (TRA) girder, and a typical streamlined (STR) box girder to investigate the vortex-induced forces and their spanwise correlations. First, using the free vibration technique, the vortex-induced vibration responses and the Strouhal number were investigated at different Scruton numbers and attack angles. Then, the mean and standard deviations of the vortex-induced pressure coefficients of the three models were analyzed through simultaneous pressure measurements. The power spectral density and the spanwise correlation of vortex-induced pressures at some typical points were also studied. Finally, the spanwise correlations of vortex-induced forces acting on the three models in the cases of different vibration amplitudes and attack angles were investigated. The results show that the attack angle has a significant effect on the vortex-induced pressure distributions for the three types of girders. The second frequency components of the vortex-induced pressure occur near the trailing edge of the upper surface for the three types of sections. The correlation of vortex-induced force decreases with the increase in the oscillation amplitude for the REC model, but becomes larger for the TRA and STR models. With the increase in the attack angle, the spanwise correlations of vortex-induced forces on the three sections become weaker, especially for the REC model.

Spanwise correlation of vortex-induced forces on typical bluff bodies

The spanwise correlation of vortex-induced forces (VIFs) on rectangular cylinders has been studied extensively. However, little knowledge exists regarding the differences and the evolution of the spanwise correlations of VIFs on blunt and streamlined bluff bodies. In this paper, wind tunnel tests were performed using the free vibration technique on three types of models in smooth flow. The models included a 4:1 rectangular (REC) cylinder, a trapezoidal (TRA) girder and a typical streamlined (STR) deck. Firstly, the vortex-induced pressure distribution was investigated at different attack angles for three models. The spanwise correlations of VIFs in different VIV stages were then studied in detail, along with the effects of VIV amplitude and attack angle. An interesting phenomenon was found in the REC and TRA models: the largest spanwise correlation appeared at the rising stage of VIV rather than at the peak oscillation amplitude. In addition, the spanwise correlations were preliminarily explained by the spectral analysis. The test results indicate that the spanwise correlations of the total VIFs may vary with the VIV stage, oscillation amplitude and changes in the cross-section configuration of bluff bodies.

A study of the reproducibility and reliability of the musculo-articular stiffness of the ankle joint.

The objective of this work was to evaluate the reproducibility, reliability and usefulness of the musculo-articular stiffness (MAS) of the ankle joint, measuring it by the free vibration technique. Seventeen (nine males and eight females) healthy university students were included in the study. Force (f), MAS (k) and unitary MAS (ku) (defined as the ratio between the value of stiffness k obtained in the test (absolute terms) and the value of force (f)) were obtained. A test-retest protocol was designed and performed on the same day to determine the short-term reproducibility of f, k and ku. Short-term reproducibility of k and ku on 1 day in absolute terms (< 7% Coefficient of Variation (CV)) and relative reproducibility (Intraclass Correlation Coefficient (ICC) and Pearson ≥ 0.97) for both feet were obtained. The reliability of k and ku in absolute terms (< 9% CV) and in relative terms (ICC and Pearson ≥0.93) based on repeating the protocol for 1 week was analysed for both feet. To analyse the usefulness, the Effect Size (ES) ratio = "Trivial" for all variables (for 1 day and 1 week) and the Smallest Worthwhile Change (SWC) ratio (Typical Error (TE)< SWC) = "GOOD" for k and ku (1 day and 1 week) were considered. The Minimal Difference needed to be considered "real" (MD) for ku ≅ 3.5% (1 day); ku≅ 8.5% (1 week) (p < 0.05) was obtained. The statistical analysis carried out displayed the high reproducibility, reliability and usefulness of the MAS test, which was more consistent with ku than k. Therefore, the unitary stiffness (ku) proven to be representative of the mechanical response of the ankle joint obtained by free vibration techniques, which allows comparison between different subjects.

Flutter Derivatives of the Kao-Pin Hsi Cable-Supported Bridge

Long-span cable-supported bridges, characterized with low natural frequencies and mechanical damping, are very sensitive to wind effects. Therefore, investigation of the aeroelastic behaviour of bridges is particularly important when designing these complex engineering structures. The focus is on evaluation of dimensionless aeroelastic coefficients, i.e. flutter derivatives, which are considered as indicators of the aeroelastic stability of bridges. A comprehensive experimental study on dynamic wind-induced behaviour of the Kao-Pin Hsi Bridge in Taiwan is carried out in the Climatic Wind Tunnel of the Centre of Excellence Telč (CET), Czech Republic. The bridge-deck section is tested at a multipurpose experimental setup originally developed in the CET. Flutter derivatives are obtained by the means of the free-vibration technique for the double-degree-of-freedom (DDOF) system. The results are compared to those of a thin flat plate with large width to height ratio, which previously proved to be stable with respect to the flutter phenomenon. While the torsional instability is observed for the Kao-Pin Hsi bridge-deck section, the flat plate proves to be aeroelastically stable.

Some new insights into the identification of bridge deck flutter derivatives

In the identification of flutter derivatives using coupled free vibration technique, the influences of implied approximations are assessed in this study. For a thin flat plate section and three representative deck sections of long-span bridges, KH1∗, KH2∗, KA1∗, KA2∗, K2H3∗, K2H4∗, K2A3∗, and K2A4∗ are demonstrated to be dependent on reduced wind velocity, especially at lower reduced wind velocities. This is contrary to the commonly used assumption of these parameters being constants. Kh is conventionally used to quantify H1∗, H4∗, A1∗, A4∗, and Kα for H2∗, A2∗, H3∗, A3∗. This means the direct components of aeroelastic motions (h1,α2) are comparatively predominant than the incentive cross components (h2,α1). However, this approximation is only valid for weak modal coupling cases at lower wind velocities. Novel perspectives are provided regarding the subtle underlying complexities in extracting flutter derivatives using coupled free vibration technique. The accuracy in identifying flutter derivatives can be effectively improved by setting close frequencies of coupled modes. The mechanical damping ratio, mass, and mass moment of inertia can be artificially increased to postpone the occurrence of flutter and extend the reduced wind velocity region to acquire sufficient flutter derivatives for flutter analysis. This study may serve as a building block for improving the understanding of flutter derivative identification from coupled free vibration responses, and practical strategies are proposed to improve the identification accuracy.

Damping Evaluation of Linseed Oil-Based Engineering Elastomers by Vibration Response Method

A low cost experimental setup has been fabricated for evaluation of vibration damping properties of a variety of elastomers developed from linseed oil. Free and forced vibration principles were utilized in this experimental setup. Under forced vibration, the shear loss factor varies from 0.37 to 1.03 at 2nd bending vibration mode and 0.43 to 0.99 at 3rd bending vibration mode for different elastomers. The loss factor varies from 0.52 to 0.94 under free vibration. The loss factors determined by both forced and free vibration techniques are in good agreement with the loss factors obtained from dynamic mechanical analysis. The ultimate tensile strength and Young’s modulus of the elastomers vary from 0.37 to 3.71 MPa and 0.27 to 10.27 MPa, respectively, whereas these properties in compression are in the range of 3.1 to 72.9 MPa and 1.5 to 30.1 MPa, respectively. Thus, these elastomers are mechanically stable for vibration damping applications.

A critical study on the experimental determination of stiffness and viscosity of the human triceps surae by free vibration methods

Muscles and tendons play an important role in human performance. Their mechanical behaviour can be described by analytical/numerical models including springs and dampers. Free vibration techniques are a widely used approach to the in vivo determination of stiffness and viscosity of muscle-tendon complexes involved in sport movements. By considering the data reported in the literature, it appears that the visco-elastic properties of the triceps surae muscle-tendon complexes are independent of the modality in which free vibration is induced as well as they do not depend on the composition of the population of subjects submitted to the experiments. This research will critically discuss this important aspect focussing in particular on two studies documented in the literature. For this purpose, two equipments will be developed to reproduce literature experiments under the assumption that the oscillating part of the body behaves as a single-degree-of-freedom system: The governing degree of freedom is associated with the vertical displacement of the lower leg or with the rotation of the foot around the ankle articulation. Unlike literature, measurements are now conducted on the same population of subjects in order to draw more general conclusions on the real equivalence of results and validity of the mechanical properties determined experimentally. Free vibration tests are accurately simulated by analytical models describing the response of each vibrating system. It is found that if the two measurement protocols are applied to the same population of individuals as it is done in this study, values of visco-elastic properties of muscle-tendon complexes extracted from experimental data are significantly different, the differences presenting a convincing consistency. This result is in contrast with the literature and confirms the need to evaluate results of free vibration techniques by taking homogeneous bases of comparison.

Identification of Rational Functions using two-degree-of-freedom model by forced vibration method

In prediction of self-excited forces and flutter instability of flexible structures, time domain method has distinct advantages. Rational Functions that are used to formulate self-excited aerodynamic forces in time domain were indirectly extracted from experimentally obtained flutter derivatives in the past. Recently, an algorithm was published to directly extract the Rational Functions from wind tunnel section model tests in free vibration. To overcome the limitations of free vibration technique, a new algorithm that is developed for direct extraction of the Rational Functions from section model tests using a forced vibration technique is presented here. The new algorithm can be used to extract all the Rational Functions associated with one, two or three degree-of-freedom motion (vertical, lateral and torsional) of a section model. To validate the new algorithm, forced vibration wind tunnel tests in two degrees of freedom (vertical and torsional) were performed on a streamlined bridge deck section model with width-to-depth ratio B/D=15:1 and also a bluff rectangular section model with B/D=5:1. This is a significant improvement from other forced vibration methods that require separate one-degree-of-freedom model tests which are dependent on phase angle difference between aerodynamic loads and displacements.

Identification of flutter derivatives of bridge decks with free vibration technique

The flutter derivatives of bridge decks can be determined in a unique manner on condition that the complex modal parameters of the system at one reduced frequency are obtained. Based on the idea, a new method of identifying the flutter derivatives of bridge decks is proposed and it can overcome some shortcoming of the existing method and extend the applicability of the free vibration technique at high wind velocity. The identified results have agreements with the target ones of an ideal thin-plate section and those of a thin-plate section measured by the forced vibration technique. The proposed method is reliable and effective to extract the flutter derivatives from coupled free vibration.

Effect of Mouthguards on the Transmission of Force Across the Human Jaw

To determine if impact responses (stiffness and damping values) of the jaw and neck are significantly different between mouthguards of varying material and manufacturing properties, in controlled conditions involving specified upper limb orientation and applied loading. Quasi-experimental design. Simon Fraser University biomechanical laboratory. Twelve male subjects between the ages of 19 to 28 participated in this study. All subjects were healthy, had no missing teeth, and had no mechanical (orthodontic) appliances. For each condition, the system stiffness and damping values were estimated using the free vibration technique. Stiffness and damping values are relevant because they are the major determinants of impact force and, potentially, injury risk. It is the first study to show experimentally the quantitative effects of mouthguard in situ. All the mouthguards lowered the system stiffness as compared with the no mouthguard condition (P < 0.001). There was no observed effect on stiffness between the 2 limb orientation positions. Excitation weight had an unexpected effect on system stiffness (P = 0.041), with increasing weight leading to increased stiffness. The findings suggest that wearing any mouthguard is better than wearing none at all due to their ability to reduce system stiffness and damping values after a blow to the chin.

Design guidelines for tuned liquid column damper for structures responding to wind

In this paper, some useful guidelines for designing tuned liquid column dampers (TLCDs) for damped single-degree-of-freedom structures under a white noise type of wind excitation are proposed as quick guidance for industrial practice. These guidelines contain two major parts that serve two respective purposes. One is the design table that provides the list of necessary optimal parameters as well as the corresponding response reduction to be used as the design reference. The other is the empirical formula for reliably predicting the basic properties of TLCDs, especially for head loss coefficients, to ensure the design objectives can be achieved. In the first part, the solutions of optimal parameters in the design table are obtained through numerical optimization, by which it is also found that for a given mass ratio and horizontal length ratio, using a uniform cross-section for all columns can always achieve the best performance. To construct the prediction formula in the second part, TLCD property tests using free vibration and harmonic forced vibration techniques via a shake table are performed and the experimental results thus calibrated are used. Consequently, a modified formula to predict head loss coefficients for TLCDs with sharp-edged elbows is proposed as a guideline for designers. Finally, an example of the TLCD design is demonstrated by following the guidelines presented.

Simulation of Muscle-Tendon Complex During Human Movements

The purpose of this paper was to review the research findings regarding the biomechanical behavior of the muscle-tendon complex (MTC) during dynamic human movements, especially those obtained using computer simulation. Specific studies conducted by the authors using the free vibration technique and MTC modeling have been discussed in detail. For determining individual viscoelastic characteristics of the human triceps surae MTC groups, a race difference between Black and White college athletes was investigated using the free vibration technique. It was found that the muscle stiffness was greater among Black athletes. Through computer simulation using a Hill-type MTC model, the benefit of making a countermovement was investigated in relation to the length ratio between the contractile element (CE) and the series elastic element (SEE) and the compliance of the MTC. The integral roles of the SEE were simulated in a cyclic human heel-raise exercise. It was revealed that it is beneficial to make a countermovement for explosive activities like vertical jumping, and the benefit of making a countermovement increases as the compliance of the MTC increases. Also, using a MTC model, the effects of moment arm length on kinetic outputs of the musculoskeletal system were evaluated. It was found that longer moment arm resulted in smaller joint moment development, smaller joint power output and smaller joint work output in the larger plantarflexion angular velocity region. It can be said that computer simulation is a powerful tool for determining and evaluating MTC behavior during dynamic human movements.

Degradation of niobium in molten aluminium: A. Robin, H.R.Z. Sandim. (Faculty of Chemical Engineering (Materials), Lorena, Brazil.) Int. J. Refract. Metals/Hard Mater., Vol 20, No 3, 2002, 221–225

Knowledge of the mechanical properties of thermoelectric materials at high temperature is required for the modelling and optimization of a thermoelectric generator under application conditions. We present room and high temperature characterization of Young’s modulus for Mg2Si, Mg2Sn and their solid solutions establishing a linear dependence, both on composition and on temperature.Through the comparison of Resonant Ultrasound Spectroscopy and free vibration techniques, we measure the elastic moduli with high precision. The comparison of our results (E = 110 GPa for Mg2Si and 78 GPa for Mg2Sn) to first principles calculations and experimentally reported data shows good agreement. Additionally, by estimating the Poisson ratio, we calculate the temperature-dependent shear modulus G and finally provide a simple bilinear function for Young’s and shear moduli as a function of temperature and composition.