Mode Natural Frequencies Research Articles

Evaluation of Static Displacement Based on Ambient Vibration for Bridge Safety Management.

The evaluation of bridge safety is closely related to structural stiffness, with dynamic characteristics and displacement being key indicators. Displacement is a significant factor as it is a physical phenomenon that bridge users can directly perceive. However, accurately measuring displacement generally necessitates the installation of displacement meters within the bridge substructure and conducting load tests that require traffic closure, which can be cumbersome. This paper proposes a novel method that uses wireless accelerometers to measure ambient vibration data from bridges, extracts mode shapes and natural frequencies through the time domain decomposition (TDD) technique, and estimates static displacement under specific loads using the flexibility matrix. A field test on a 442.0 m cable-stayed bridge was conducted to verify the proposed method. The estimated displacement was compared with the actual displacement measured by a laser displacement sensor, resulting in an error rate of 3.58%. Additionally, an analysis of the accuracy of displacement estimation based on the number of measurement points indicated that securing at least seven measurement points keeps the error rate within 5%. This study could be effective for evaluating the safety of bridges in environments where load testing is difficult or for bridges that require periodic dynamic characteristics and displacement analysis due to repetitive vibrations, and it is expected to be applicable to various types of bridge structures.

Development of planar 9-DOF dynamic model with small damping and natural characteristics sensitivity analysis for a double-deck vibrating flip-flow screen

The current double-deck vibrating flip-flow screen (DDVFFS) exhibits swing motion due to an unreasonable structural design, which compromises vibration stability and impacts screen frame displacement response. Therefore, it is essential to investigate the dynamic characteristics of the DDVFFS. For this reason, a 9-degree-of-freedom (DOF) dynamic model of the DDVFFS is established, and a corresponding testbed for the DDVFFS is designed. A sensitivity analysis is conducted to examine the impact of design parameters on the natural frequency and vibration mode, thereby serving as valuable guidance for the design of DDVFFS. The damping matrix in the dynamic model is determined through modal testing, while the displacement response of the testbed is obtained by solving the dynamic model. The test results from the vibration testbed demonstrate that the actual amplitude of each sieve frame closely matches the theoretical amplitude.

Investigating the robustness of interface topological modes in rods

Topological phononic crystals and metamaterials are structures that can present waveguiding and energy concentration phenomena, which can be of interest in structural dynamics for energy harvesting and passive vibration and noise control. The periodicity of the typical phononic crystals and metamaterials is broken for these structures, which need to present at least two crystal lattices with different topological characteristics. Thus, the topological invariant, such as the Zak phase, which defines the topological characteristic, must be computed. A rod metastructure exhibiting two low-frequency band gaps, each with a topological interface mode, was designed. It has bolt sets whose weights generate variability, which was modeled and inferred. In order to increase variability along the rod metastructure, washers were included or removed. Experiments were performed to validate the simulations. It was observed that the variability of the topological mode in the first band gap is more robust considering its mode shape, natural frequency, and energy concentration at the interface than the second interface mode, at higher frequency. As variability increases, the robustness of the energy concentration at the interface and of the mode shape of both topological modes decreases. The same behavior was observed for the natural frequencies of the topological modes.

Thermomechanical and Viscoelastic Characterization of Continuous GF/PETG Tape for Extreme Environment Applications

The thermomechanical and viscoelastic properties of a glass fiber polyethylene terephthalate glycol (GF/PETG) continuous unidirectional (UD) tape were investigated using differential scanning calorimetry (DSC), thermomechanical analysis (TMA), and dynamic mechanical analysis (DMA). This study identified five operational conditions based on the Army Regulation 70-38 Standard. The DSC results revealed a glass transition temperature of 78.0 ± 0.3 °C, guiding the selection of temperatures for TMA and DMA tests. TMA provided the coefficient of thermal expansion in three principal directions, consistent with known values for PETG and GF materials. DMA tests, including strain sweep, temperature ramp, frequency sweep, creep, and stress relaxation, defined the material’s linear viscoelastic region and temperature-dependent properties. The frequency sweep indicated an increased modulus with rising frequency, identifying several natural frequency modes. Creep and stress relaxation tests showed time-dependent behavior, with strain increasing under higher loads and stress decreasing over time for all tested input values. Viscoelastic models fitted to the data yielded R2 values of 0.99, demonstrating good agreement. The study successfully measured thermomechanical and viscoelastic properties across various conditions, providing insights into how temperature influences the material’s mechanical response under extreme conditions.

Nonlinear dynamic analysis and vibration reduction of two sandwich beams connected by a joint with clearance

The dynamics and vibration reduction characteristics of the clamped–clamped two sandwich beams jointed with clearance is studied theoretically and experimentally. A transverse and torsional spring system with clearance is used to equivalent the joint model. The homogenization method is used to equivalent the core layer and Rayleigh-Ritz method is utilized to derive the mode function of the interconnected sandwich beam by using a sequence of orthogonal polynomials. The nonlinear motion equation of the two jointed sandwich beam structure with clearance is derived by the application of the Hamilton principle and then solved using an improved Newmark integration approach. In order to validate the accuracy of the natural frequency and vibration mode, the finite element model is established. This paper examines the impact of clearance on the amplitude frequency response and vibration transmission of the two jointed sandwich beam structure, it is found the jointed sandwich beams show obvious nonlinear characteristics and intermittent vibration transmission phenomenon due to the clearance. Moreover, the vibration transmission analysis reveals that the existed clearance demonstrates significant vibration reduction effect, for which an experiment is conducted to validate the results. In general, this work proposes a novel approach for modeling sandwich structures with clearance with improved vibration reduction performance.

Research on the distorted similitude of bolt-connected coupled cylindrical-conical shells

The model similitude technique, which employs scaled-down models to reflect the dynamic characteristics of full-scale models, has garnered significant attention in the engineering field. The inability to establish geometrically scaled models due to excessively thin shell structures has led to similitude distortion. For bolt-connected coupled cylindrical-conical shells, the dimensions of bolts (connection stiffness) vary with the radial dimension of the structure, and the coupling effects between parameters further complicate the establishment of scaling laws. To address these challenges, the distorted similitude method based on bolt equivalent stiffness modeling is proposed. For the first four bending mode natural frequencies, distorted scaling laws for the length, radius, and their coupling under double distorted reduction are established. The theoretical prediction errors of these scaling laws for the prototype are found to be within 5.43 %, 2.31 %, and 1.12 %, respectively. Experimental results demonstrate that the prediction error of the coupled distorted scaling law for length and radius is within 5.37 %. In cases of small radii, large thicknesses, and long axial lengths of bolted joint shell structures, the distortion of bolt dimensions due to radial distortion cannot be overlooked. Moreover, if the bolted joint is located at the vibration mode node, the corresponding scaling law can disregard the influence of connection stiffness. This study realizes the establishment of distorted models for complex bolted joint shell structures and enhances the prediction accuracy of coupled scaling laws, thus holding significant engineering application value.

Analytic analysis of free vibration problem of the plate with a rectangular cutout using symplectic superposition method combined with domain decomposition technique

Plates with rectangular cutouts is widely seen in the field of engineering structures. Therefore, it is crucial to examine analytical solutions for free vibration (FV) of these structures. Despite the existence of approximate/numerical methods, analytical solutions are lacking in the literature. In this study, we employ the symplectic superposition method to effectively analyze the FV problems encountered in plates with rectangular cutouts while integrating the domain decomposition technique. To address the issue of irregular geometry, the rectangular cutout plate is divided into multiple sub-plates. By dividing the problem into multiple sub-problems and solving them separately using variable separation and symplectic eigen expansion, we obtain analytical solutions. Finally, we combine the sub-problem solutions to resolve the initial issue. This solution method can be considered a logical, analytical, and systematic approach as it starts with the fundamental governing equation and is derived without assuming forms of solutions. The study presents a comprehensive set of numerical results that include mode shapes (MSs) and natural frequencies (NFs). The results are rigorously validated using the finite element method (FEM) and relevant literature. The symplectic superposition method demonstrates excellent convergence and precise accuracy, making it suitable for analytically modeling more complex mechanical problems of plates.

Two-stage structural damage detection using modal strain energy and natural frequencies: Numerical and experimental study

Two-stage structural damage detection using modal strain energy and natural frequencies: Numerical and experimental study

Investigating the relationship between natural frequency and residual strength and stiffness of cross‐ply laminate under cyclic loading

AbstractPredicting the fatigue life of wind turbine rotor blades is a challenging and crucial engineering task. This study investigates the correlation between modal parameters and the degradation of residual strength and tensile modulus in the cross‐ply glass epoxy laminate [0/90]7 used in wind turbine blades under fatigue loading. The tensile and vibration characteristics were assessed, followed by constant amplitude fatigue tests at 35%, 43% and 55% of the ultimate tensile strength, with R = 0.1 and a frequency of 8 Hz. The modal analysis was performed on the cycled specimens at life fractions from 0.05 to 0.70 and residual modulus and strength were obtained. The results establish a well‐defined correlation between these residual mechanical properties and the natural frequency. Normalized residual strength, tensile modulus and natural frequency demonstrated similar behaviors during the fatigue life. An initial rapid decrease in the first tenth of the life fraction was observed, followed by minimal changes up to a life fraction of 0.7. The strong correlation between the first mode natural frequency and both the residual strength and the tensile E‐modulus provides a promising basis for developing accurate fatigue life prediction models for fiber‐reinforced composite structures. © 2024 Society of Chemical Industry.

On the complex mode shapes and natural frequencies of clamped-clamped fluid-conveying pipe

In the present study, the closed-form expression for complex mode shapes of a fluid-conveying pipe using Timoshenko beam theory is developed for the first time. By applying the method of separation of variables, the complex mode shapes and eigenvalues are obtained. To the best knowledge of the authors, there is no study carried out on the complex eigenvalue problem for vibration analysis of the Timoshenko fluid-conveying pipes. Given this oversight, in this study the effects of fluid velocity on the imaginary and real parts of the mode shapes and natural frequencies of a clamped-clamped fluid-conveying pipe are investigated. The results show that for very low fluid velocities, the first and the second mode shapes are similar to that of an equivalent beam. For high fluid velocities, the first mode shape experiences some deviation so that it looks like the second mode shape of a pipe having very low fluid velocity. The results show that fluid flow in the pipeline effectively reduces its bending moment as well as the energy of vibration. In addition, the nodal points corresponding to the second mode are replaced with quasi-node points.

Detection of Total Hip Replacement Loosening Based on Structure-Borne Sound: Influence of the Position of the Sensor on the Hip Stem.

Accurate detection of implant loosening is crucial for early intervention in total hip replacements, but current imaging methods lack sensitivity and specificity. Vibration methods, already successful in dentistry, represent a promising approach. In order to detect loosening of the total hip replacement, excitation and measurement should be performed intracorporeally to minimize the influence of soft tissue on damping of the signals. However, only implants with a single sensor intracorporeally integrated into the implant for detecting vibrations have been presented in the literature. Considering different mode shapes, the sensor's position on the implant is assumed to influence the signals. In the work at hand, the influence of the position of the sensor on the recording of the vibrations on the implant was investigated. For this purpose, a simplified test setup was created with a titanium rod implanted in a cylinder of artificial cancellous bone. Mechanical stimulation via an exciter attached to the rod was recorded by three accelerometers at varying positions along the titanium rod. Three states of peri-implant loosening within the bone stock were simulated by extracting the bone material around the titanium rod, and different markers were analyzed to distinguish between these states of loosening. In addition, a modal analysis was performed using the finite element method to analyze the mode shapes. Distinct differences in the signals recorded by the acceleration sensors within defects highlight the influence of sensor position on mode detection and natural frequencies. Thus, using multiple sensors could be advantageous in accurately detecting all modes and determining the implant loosening state more precisely.

Toward Indirect Real-Time Prediction of Bridge Vibration Responses Under Traffic Flow Through a Population of Connected Sensing Vehicles

Condition monitoring of bridge structures as the lifelines of smart cities is high of importance. While indirect vehicle scanning techniques have shown promising results and have less cost compared to mounting fixed sensors on the bridge, they have limitations in predicting response under traffic flow since the crossing time of one vehicle is very short. This paper presents a novel crowsensing-based framework for predicting bridge acceleration responses and identifying the modal characteristics. This method utilizes smartphone data from a diverse population of sensing vehicles as they traverse the bridge to predict bridge acceleration response at various virtual sensing locations. Subsequently, the predicted acceleration is used to identify the mode shapes and natural frequencies of the bridge. The principal innovation in this practical and cost-effective monitoring solution is the utilization of a randomly selected set of sensing vehicles at each timestamp. These selections may differ from one timestamp to the next, reflecting the real-world conditions where certain vehicles may intermittently lose or disconnect their internet connectivity. By consistently updating the set of sensing agents while other vehicles cross the bridge, the proposed framework overcomes the data length limitations of conventional vehicle-based methods by leveraging multiple vehicles and continuous data collection. Comprehensive numerical studies are conducted to evaluate the performance of the method. In the numerical investigations, a three-span bridge is subjected to the continuous passing of a large number of half-car vehicle models with random speeds and initial locations. Vehicle-bridge interaction is considered in the analysis. Utilizing a single randomly selected sensing agent at each timestamp, the results demonstrate the effectiveness of the framework in predicting bridge acceleration response with a relative error of less than 5%. Additionally, the method achieves an accuracy level of 95% in identifying the bridge's initial three mode shapes.

Development of Modified Rhombus Amplifier of Positioning Stage Compliant Mechanisms

Abstract This paper presents a modified design of rhombus-type amplifier used in positioning stage compliant mechanism. The new rhombus design is introduced to enhance the performance of rhombus and the results are promising. The new approach of rhombus amplifier is based on mixing the concept of rhombus type with the idea of hinges (reduced section portions) existed in bridge type. The performance of the proposed design is investigated by the pseudo rigid body model and validated by the finite element analysis. The new rhombus design improves displacement amplification ratio by (22.3%) with slightly change in master mode natural frequency (1.3%). The pseudo rigid body model for new rhombus design is consistent with the ANSYS results, and hence can be used in modelling and analysis of the new rhombus design.

Investigation of structural parameters influencing vibration characteristics of heavy-duty truck diesel tanks.

The working conditions of heavy-duty trucks are very complicated as the diesel shaking and resonance problems, which causes weld tears, separators to fall off, and other failures occur. Through experiments and finite element simulation, the natural frequency and vibration mode of a given 400 L diesel tank were calculated to study the influences of structural parameters such as the fill ratio (0.1-0.9), the number of baffle plates (0, 1, 2), the spacing of the plates (240 mm, 400 mm, 560 mm) and the aperture (38 mm, 78 mm, 118 mm) on the modal parameters with the wet mode method. The results of the hammering mode test and the simulation modal analysis agree well with the maximum error is 4.8%; the natural frequency of the diesel tank will increase with fill ratio decrease; the increase of the baffle plate number (0, 1, 2) can effectively increase the first-order natural frequency of the diesel tank, but the change of the natural frequency is not obvious on the higher order; the higher plates spacing has a smaller natural frequency; increasing the aperture will highly increase the natural frequency, 188 mm has better vibration safety.

Isogeometric free vibration of functionally graded porous magneto-electro-elastic plate reinforced with graphene platelets resting on an elastic foundation

This article investigates the free vibration behavior of functionally graded porous reinforced with graphene platelets magneto-electro-elastic (FGP-GPL-MEE) plates. The FGP-GPL-MEE plate is supported by the Winkler-Pasternak foundation and subjected to the initial external electric voltage and magnetic loads. The governing equations for FGP-GPL-MEE plates are derived from the combination of Hamilton's principle and the refined plate theory (RPT) with four variables. The FGP-GPL-MEE plate is formed by combining three porosity distributions of functionally graded materials and three patterns of graphene platelets dispersion distributed along the plate thickness. Using the modified Halpin-Tsai model, effective material properties of the FGP-GPL-MEE plate are estimated. Isogeometric approach (IGA) is used to discretize the plate geometry and extract mode shapes and natural frequencies. The effects of various parameters such as porosity distributions, porosity coefficient, GPLs distributions and magnetic and electric potentials on the natural frequencies of the FGP-GPL-MEE plate are performed. The results indicate that the GPLs reinforcement can be significantly enhanced the natural frequencies of the FGP-GPL-MEE plate. Moreover, the free vibration behavior is significantly influenced by porosity, as well as magnetic and electric fields. The results of this study provide valuable insights into the vibrational characteristics of FGP-GPL-MEE plates.

Dynamic Modeling and Experimental Modal Analysis for the Central Rod-Fastened Rotor With Hirth Couplings Based on Fractal Contact Theory

Abstract The central rod-fastened rotor of gas turbine exhibits pronounced noncontinuous characteristics due to the large number of contact interfaces between the compressor and turbine disks. It is necessary to establish an accurate dynamic modeling method for the central rod-fastened rotor that fully considers the contact surface effect. In this work, the contact behavior of the rough surface is characterized by the fractal theory. The normal and tangential contact stiffness models are developed, and the influence of fractal parameters is discussed. Besides, the finite element model for the central rod-fastened rotor is established by developing an improved contact element considering the equivalent stiffness segment of Hirth couplings. Finally, the proposed model is verified by conducting the modal testing and measuring the first four modes of natural frequencies and modal shapes of the central rod-fastened rotor. The results show that the numerical results are in good agreement with the experimental ones, and the fractal contact model can effectively predict the connection stiffness of Hirth couplings, which in turn improves the simulation accuracy for the modal characteristics of the central rod-fastened rotor and provides a dynamic modeling approach with high efficiency and less computational complexity.

Transient behavior of a plate partially immersed in the fluid subjected to impact loadings: Theoretical analysis and experimental measurements

This study aimed to investigate the transient behavior of a rectangular plate partially in contact with fluid subjected to a dynamic external force. To this purpose, a theoretical model was developed to analyze vibration characteristics and transient wave propagation. Based on superposition method, the dry mode shapes and natural frequencies of the plate under vacuum could be obtained. The dry mode shapes were treated as the fundamental function to construct the wet mode that describes the vibration behavior of the fluid-plate coupled system. The velocity potential and fluid pressure within a finite tank due to the plate deflection were derived using an equation governing the incompressible fluid. Based on the relationship between dry mode shape and wet mode shape, the fluid-plate coupled system's wet mode shape and resonant frequency could be determined from the frequency response function. Applying the normal mode method, the transient displacement of plate and fluid pressure can be obtained by solving a system of non-homogeneous differential equations. The theoretical predictions were verified by finite element method (FEM) and experimental measurements. Experiments were conducted using piezoelectric film sensors (polyvinylidene fluoride, PVDF) to measure the force history induced by a steel ball impact to quantitatively analyze the transient response. The comparison results proved that the theoretical predictions and experiments were in good agreement, including the transient responses of the displacement and in-plane strain of a plate partially submerged in the fluid. The results indicate that changes in water depth can induce resonance frequency shifts and wet mode shape distortions, which also illustrate that the vibrational properties of wet modes affect transient behavior. The proposed transient solution demonstrates an analytical approach that connects the physical significance of the dynamic behavior of the fluid-plate coupled system in time and frequency domains; it provides a connection between the transient behaviors and vibration characteristics.

Thermal-structural and prestressed modal analyses for a solar sail with nonlinear shape memory alloy spring

The objective of this research is to forecast the impact of alternating non-uniform temperature distributions on the deformation and internal stress within the thin film of a solar photon sail, as well as to assess how stress variations affect the sail’s characteristics. To maintain the internal stress amplitude within the film during extreme temperature fluctuations, the solar sail employs an innovative pre-tensioning technique utilizing shape memory alloy (SMA) springs. A thermal-structural model is formulated specifically for a hexagonal solar sail. Subsequently, thermal-structural analyses are conducted to quantify deformations and stresses within the sail during its operation on the Earth-Moon L1 halo orbit. Incorporating the prestress factor, the out-of-plane deflection of the film under solar pressure is computed. Furthermore, prestressed modal analyses are performed to determine mode shapes and natural frequencies, taking into account both the prestress and the solar pressure acting on the film. Finally, numerical results are used to compare the performance of the solar sail in hot and cold environments.

Investigation on vibration characteristics of rock based on circular plate and cylinder model: dimension, geometric shape and boundary condition

Abstract The declaration on the “natural frequency of rock” exists in many engineering areas, and it has caused many misunderstandings. Different from the mass-spring model usually used, the circular plate model and cylinder model are respectively established to clarify the relationship between the vibration characteristics (including natural frequency and vibration mode) and their influencing factors of rock by modal analysis. The effect of dimension, geometric shape, and boundary condition on the vibration characteristics of rock with plate structure is investigated, in which the semi-analytical solutions agree well with the simulation results. By using the cylinder model based upon the Lamé-Navier Eq., the effect of such influencing factors on the vibration characteristics of the block rock sample is further studied and verified by numerical simulation and experimental results. The results suggest that the natural frequency of “rock” (including the experimental rock sample) is strongly dependent on the dimension, geometric shape, and boundary condition. The resonance frequency observed in the excitation experiment is not only closely associated with the natural frequency of a specific order, but also dependent on the dominance of the particular vibration mode. These findings contribute to a better understanding of the rock-breaking mechanism under dynamic loads with a certain excitation frequency.

Vibration control and stroke evaluation of bi-directional bistable nonlinear energy sinks applied in monopile offshore wind turbines during emergency shutdown

Monopile offshore wind turbines (OWTs) in complex wind and wave environments can generate more excessive vibrations in the fore-aft (FA) and side-to-side (SS) directions when emergency shutdowns occur, and therefore damping techniques to alleviate such vibrations are essential. Due to the potential frequency detuning (reduced damping effectiveness) of traditional tuned mass dampers (TMDs) and stroke issues (such as large strokes of TMDs and limited maximum strokes of unidirectional nonlinear energy sinks (NESs)) in existing absorbers, this paper proposes a bi-directional bistable nonlinear energy sink (BBNES) to mitigate the vibration of the OWT in the FA and SS directions during the emergency shutdown. First, the proposed device and its operation mechanism are elaborated, and an optimization method for the device is introduced. Then, the dynamic analysis model of the BBNES is developed for vibration control of the OWT and incorporated into a fully coupled numerical simulation tool with high fidelity, FAST v8. Subsequently, the responses of the OWT without and with the proposed BBNES and the bi-directional tuned mass damper (BTMD) are exhaustively investigated under diverse conditions (including mass ratios, wind-wave loadings, emergency shutdown times, wind-wave misalignments, and 1st mode natural frequencies of the OWT) to reveal their performances and compare them. The research results show that under most conditions, the BBNES and BTMD have a similar damping performance in the FA direction, whereas the BBNES has a slightly lower damping performance in the SS direction than the BTMD. In addition, except for the wind velocity of 8 m/s at the hub and the wind-wave misalignment of 90°, the FA stroke of the BBNES with a small mass ratio (i.e., 0.01∼0.035) is significantly smaller than that of the BTMD with the same mass ratio by more than 1.1 m, and even up to about 4 m. The SS stroke of the BBNES is slightly greater than that of the BTMD, and in most cases, the difference between both is less than 0.52 m. Therefore, the BBNES is superior to the BTMD in this regard. When the 1st mode natural frequency of the OWT decreases, the BTMD can lose its tuning efficacy and makes the tower more susceptible to resonance caused by 1p and wave loadings, while the BBNES is not affected by the 1st mode natural frequency variation of the OWT, demonstrating its stronger robustness.