Vibration Research Articles

Analytical solution for forced vibration of multilayer structures composed of plates with different geometric dimensions

Multilayer system composed of parallel plate components with different geometric dimensions is frequently used to describe engineering objects, such as electronic assembly. In this work, an analytical method was proposed for forced vibration of this type of multilayer system. The proposed method overcomes the limitation that the traditional wave method is only applicable to all plate components must have the same in-plane dimensions. The proposed analytical method has an efficiency advantages in parameter analysis than element-based methods such as finite element method (FEM). The connection joints between two adjacent plate components, such as ball grid array (BGA) solder interconnect, are represented by elastic springs. The vibration of each component are described in terms of general and physical analytical waves, respectively, and the dynamic coupling between them are established by an equivalent dynamic flexibility matrix. The forced responses of the multilayer system are analytically calculated by solving the system equation in wave space. In the numerical examples, the effectiveness of the proposed method is validated by comparing the present results with the FEM results. The influence of number of the defective solder joints on vibration response is also investigated.

Frequency response sensitivity to crack for piezoelectric FGM beam subjected to moving load

Since functionally graded material (FGM) is increasingly used in high-tech engineering, free and forced vibrations of FGM structures become an important issue. This report addresses the analysis of frequency response sensitivity to crack for piezoelectric FGM beams subjected to moving load. First, a frequency domain model of a cracked FGM beam with a piezoelectric layer is conducted to derive an explicit expression of the electrical charge produced in the piezoelectric layer under the moving load. It was shown in the previous works of the authors that the electrical charge is a reliable representation of the beam frequency response to moving load and can be efficiently employed as a measured diagnostic signal for structural health monitoring. Then, a damage indicator acknowledged as a spectral damage index (SDI) calculated from the electrical frequency response is introduced and used for sensitivity analysis of the response to crack. Under the sensitivity analysis the effect also of FGM and moving load parameters on the sensitivity is examined and illustrated by numerical results.

Longitudinal forced harmonic vibrations of vertical rods with concentrated mass.

Longitudinal forced harmonic vibrations of vertical rods with concentrated mass.

Response Properties of Electrorheological Composite Hydrophilic Elastomers Based on Different Morphologies of Magnesium-Doped Strontium Titanate.

As smart materials, electrorheological elastomers (EREs) formed by pre-treating active electrorheological particles are attracting more and more attention. In this work, four Mg-doped strontium titanate (Mg-STO) particles with spherical, dendritic, flake-like, and pinecone-like morphologies were obtained via hydrothermal and low-temperature co-precipitation. XRD, SEM, Raman, and FT-IR were used to characterize these products. The results showed that Mg-STOs are about 1.5-2.0 μm in size, and their phase structures are dominated by cubic crystals. These Mg-STOs were dispersed in a hydrogel composite elastic medium. Then, Mg-STO/glycerol/gelatin electrorheological composite hydrophilic elastomers were obtained with or without an electric field. The electric field response properties of Mg-doped strontium titanate composite elastomers were investigated. We concluded that dendritic Mg-STO composite elastomers are high-performance EREs, and the maximum value of their energy storage was 8.70 MPa. The significant electrorheological performance of these products is helpful for their applications in vibration control, force transducers, smart structures, dampers, and other fields.

The effective finite element method for free and forced vibration analysis of 2D-FGSW plates lying an elastic foundation

The purpose of this study is to analyze the influence of geometric parameters and material properties on the free and forced vibration of bi-directional functionally graded sandwich (2D-FGSW) plates lying on an elastic foundation (EF) using an effective finite element method (FEM) based on the trigonometric shear deformation theory (TrSDT). The mechanical properties of 2D-FGSW are variable in both the x- and z-directions. The EF includes the springer stiffness k 1 and the shear layer stiffness k 2. Moreover, the impacts of structural damping and periodic loading on the behavior of 2D-FGSW plates are considered. Element matrices are created using a four-node quadrilateral plate element (Q4) with eight degrees of freedom per node. The effectiveness and accuracy of the current formulation are confirmed by contrasting the acquired results with those of earlier works. Then, many studies are carried out to illustrate how input parameters might affect the vibration characteristics of 2D-FGSW plates lying on EF. In addition, the eigenfrequencies of different types of 2D-FGSW plates with a center hole are investigated.

Ligand Characterization and DNA Intercalation of Ru(II) Polypyridyl Complexes: A Local Vibrational Mode Study.

We investigated in this work ruthenium-ligand bonding across the RuN framework in 12 Ru(II) polypyridyl complexes in the gas phase and solution for both singlet and triplet states, in addition to their affinity for DNA binding through π-π stacking interactions with DNA nucleobases. As a tool to assess the intrinsic strength of the ruthenium-ligand bonds, we determined local vibrational force constants via our local vibrational mode analysis software. We introduced a novel local force constant that directly accounts for the intrinsic strength of the π-π stacking interaction between DNA and the intercalated Ru(II) complex. According to our findings, [Ru(phen)2(dppz)]2+ and [Ru(phen)2(11-CN-dppz)]2+ provide an intriguing trade-off between photoinduced complex excitation and the strength of the subsequent π-π stacking interaction with DNA. [Ru(phen)2(dppz)]2+ displays a small singlet-triplet splitting and a strong π-π stacking interaction in its singlet state, suggesting a favorable photoexcitation but potentially weaker interaction with DNA in the excited state. Conversely, [Ru(phen)2(11-CN-dppz)]2+ exhibits a larger singlet-triplet splitting and a stronger π-π stacking interaction with DNA in its triplet state, indicating a less favorable photoinduced transition but a stronger interaction with DNA postexcitation. We hope our study will inspire future experimental and computational work aimed at the design of novel Ru-polypyridyl drug candidates and that our new quantitative measure of π-π stacking interactions in DNA will find a general application in the field.

Study on particle size and density segregation law in the separating process of poor quality coal with high gangue content under the action of composite force field

ABSTRACT Thin-seam mining frequently captures a significant proportion of gangue and interbedded coal in surface coal mines. Consequently, raw coal has a broad range of particle size distributions and a high percentage of components with intermediate densities, which are complex and challenging to separate. This study aims to determine the method of product division and the segregation law of particle size and density of raw coal during the separation process using a vibration and airflow composite force field. A difference in the particle size segregation of the coal particles was evident. Particle-size segregation primarily occurs in the separation area. Large-particle-size coal has a wide distribution range, spreading over the entire bed and fully utilizing the bed to achieve separation. The material becomes increasingly displaced into the separation area as its particle size decreases, thereby weakening the separation effect. Large coal particles can undergo density segregation in the vertical direction, with low-density material placed in the upper layer. This ensures that low-density material is incorporated into the refined coal product. Regardless of density, the coal tended to tilt more toward the bottom layer as the particle size decreased. This results in a poor density stratification effect with refined coal products mixed with gangue and an increase in the mismatch content. The extent of fine coal discharge was determined to be two-fifths of the entire length of the discharge side. This ensures that the majority of refined coal is recovered and that there is no excessive gangue mixing with the refined coal output. Achieving a 55.54% yield, refined coal lowers its ash content by 16%, increases its calorific value by 1400 kcal/kg, and effectively separates coal with a high gangue concentration.

Free and forced vibration analysis of uniform and stepped conical shell based on Jacobi-Ritz time domain semi-analytical method

Free and forced vibration analysis of uniform and stepped conical shell based on Jacobi-Ritz time domain semi-analytical method

Modal, Structural, and Comfort Analyses for Improving Customized Bicycles for Recreational Ridings of People with Disabilities

Leisure activities are known to be especially important for the health of people with disabilities. In Belém, PA, an Amazonian city in Brazil, a nonprofitable organization has promoted leisure ridings in bicycles for those people in Utinga State Park, a large green area for physical and leisure activities. The handcrafted bikes have a sidecar attached for users with disabilities which are ridden by trained volunteers. Since such bikes have been empirically manufactured, they require some minor improvements in safety, comfort, and handling, and verification of structural strength. Therefore, ergonomic, modal, and forced vibration analyses assessed the user’s comfort and safety and a structural analysis with the use of strain gauges evaluated the bicycle’s structural strength. Initially, a numerical modal analysis was performed using the finite element method, and the modal model obtained was validated by an experimental modal analysis employing shaker excitation. ISO-2631-based evaluations of forced vibration and human body comfort were conducted regarding whole-body vibration in vehicles and mechanical equipment. Vibration measurements at the position of the rider and sidecar occupant were obtained during rides on the bicycle and, according to the results, in general, when subjected to loads, the bicycle showed low stress levels far from the yield stress of the material, promoting an excellent safety factor in relation to its structural integrity. The modal, comfort, and forced vibration analyses revealed a mode of vibration in the sidecar that caused discomfort to the back of the users. Ergonomics analysis pointed out changes in the handlebars, the bicycle seat, the coupling between the sidecar and the bike, and the dimensions of the sidecar will provide greater comfort and safety. This paper presents and discusses the proposed modifications to both bicycle and sidecar.

Study on the keyhole oscillation mechanism of laser welding based on electro-mechano-acoustical analogy theory

The acoustic emission phenomena generated by the laser welding process are closely related to the keyhole's forced oscillation and the dynamic pressure balance at the keyhole bottom. In this study, we constructed the mechanical equation of keyhole bottom pressure balance and used the “electro-mechano-acoustical” analogy theory to convert it into an acoustic equation, the acoustic resonant frequency as well as the magnification amplification factor of the keyhole oscillation in different penetration states were derived. A monitoring platform combining acoustic sensor and high-speed photography was established to obtain acoustic emission signals and lateral keyhole images. The acoustic and image features extracted from the monitoring data validated the derived formulas. Additionally, the acoustic phenomena of different frequency-energy components were explained according to the derived formulas in turn. The results demonstrated that the derived theory is compatible with experimental comparisons, showcasing its great interpretability and applicability. The introduced analogy theory effectively establishes a bridge between keyhole forced pressure and acoustic emission vibration, aiding in the understanding of keyhole oscillation characteristics. A novel model of keyhole oscillation was proposed and verified using process monitoring data in this study, which provides a new approach for the investigation of keyhole dynamic.

Mechanical characteristics of new mesh-type elastic plate under different temperatures and vehicle dynamics loads

The dynamic characteristics of the elastic plate are affected by changes in ambient temperature. In this study, tensile tests of rubber materials at different temperatures were conducted, revealing that rubber materials exhibit significant nonlinearity and sensitivity at low temperatures. Finite element models of Groove Elastic Plate (GEP) and New Mesh-Type Elastic Plate (NMTEP) were established, incorporating the corresponding rubber material parameters to simulate temperature effects. The stress, deformation, stiffness, and damping characteristics of the two types of elastic plates were analyzed under varying temperature conditions. Finite element calculations show that NMTEP maintains better structural stability, lower static/dynamic stiffness, and a higher damping ratio at low temperatures. Additionally, dynamic calculations indicate that temperature variations significantly impact the track system's dynamic performance. The vibration and wheel-rail forces for NMTEP are significantly lower than those for GEP under all temperature conditions, suggesting that NMTEP is more conducive to vehicle safety and stability at low temperatures.

Dynamic simulation of a simply supported beam subjected by multiple constant moving forces

Abstract Dynamic simulation models, which are conducted with Simulink, are introduced to study behaviors of a simply supported beam under constant moving forces based on the vibration mechanics model established by Bernoulli-Euler beam theory. By utilizing the orthogonality of vibration, a set of decoupled forced vibration equations can be obtained, which can be constructed as a subsystem of the Simulink model. The generalized loads in each decoupled vibration equation are also separately formed into submodules to facilitate the extension of the action of a single moving load to multiple moving loads. Every partial and general simulation model in Matlab/Simulink are made and the simulation results indicate that dynamic responses are related to the distance between moving loads and beam span.

Simulation Study on Mechanical Vibration Characteristics of GIS Bus Misalignment

Abstract Gas-insulated switchgear (GIS) has been widely used in power grid systems. The busbar is a crucial element within a GIS system, responsible for facilitating electrical connections between different GIS components. Any defects during manufacturing or improper installation procedures can lead to busbar misalignment, resulting in abnormal vibrations within the GIS. This study focuses on analyzing the mechanical vibration characteristics of GIS bus misalignment using a simulation model based on the finite element method for a 252kV GIS. When the busbar is misaligned and the conductor experiences an unbalanced force, it undergoes Coulomb forces at double the voltage frequency. Under normal or misaligned conditions, the conductor exhibits forced vibrations at the power frequency of 100Hz. However, when misalignment occurs, there is a coupling effect between electrodynamics and vibrations, causing the shell to display integer frequency vibration components.

Decentralised [formula omitted] robust control of MTMDs for mitigating vibration of a slender MDOF floor configuration

In this research, a novel robust decentralised H (H∞ and H2) design combined with a pattern search method (PSM), incorporating considerations of multiple modal dynamics, was developed to address the vibration issue in slender structures. To verify the effectiveness of the concept, a full-scale laboratory reconfigurable multiple degrees of freedom (MDOF) test-bed floor panel structure was selected, equipping with a passive multiple-tuned mass damper (MTMD) as a coupling system. The optimal parameters of the MTMDs were tailored using the decentralised H design and the PSM, considering the dynamic engagement of multiple modes. Furthermore, a crucifix-type configuration of 2DOF MTMDs was proposed to mitigate the vibration of the floor panel structure. Full-scale forced vibration testing (FVT) was conducted to validate the dynamic performance of the 2DOF MTMDs. The test results provide satisfactory verification and high-quality curve-fitting testing data for parameter study and dynamic simulation. By examining the field data from the 2DOF MTMDs and performing various numerical simulations and analyses, the control performance robustness of the MTMDs was comprehensively evaluated, considering practical engineering variations such as the number and stiffness of MTMDs, as well as the stiffness and mass of the floor panel structure. As a result, the proposed H control strategies for the MTMDs demonstrated robust control capabilities by effectively dissipating significant amounts of externally applied energy.

Research on the mechanism of acoustic radiation characteristics of granular assemblies

To study the acoustic radiation characteristics of forced vibration of granular assemblies, the acoustic radiation model of a single particle and the acoustic radiation model of granular assemblies are established. Combined with experimental verification, the variation law of radiated sound power in the process of forced vibration of granular assemblies is studied. The effects of vibration characteristics, material characteristics, mass characteristics, and distance characteristics on the acoustic radiation of forced vibration of granular assemblies are explored. The radiation range of radiated ultrasound in the process of forced vibration of granular assemblies is analyzed. The research results show that under the condition of forced vibration, the radiated sound power of the granular assemblies is obvious. The internal vibration of the granular assemblies will cause the granular particles to radiate the sound power of multiple frequencies outward. The granular particles will produce obvious ultrasonic sound power in the violent vibration state. The frequency of the sound wave will generally have a significant attenuation effect at 10 cm. Considering the relevant experimental research and engineering application of granular materials, the ultrasonic radiation characteristics should be analyzed to avoid the influence of ultrasonic radiation caused by its severe vibration.

Statistics of kinetic and thermal energy dissipation rates in two-dimensional thermal vibrational convection

We investigate the statistical properties of kinetic ϵu and thermal ϵθ energy dissipation rates in two-dimensional (2D) thermal vibrational convection (TVC). Direct numerical simulations were conducted in a unit aspect ratio box across a dimensionless angular frequency range of 103≤ω≤107 for amplitudes 0.001≤a≤0.1, with a fixed Prandtl number of 4.38. Our findings indicate ϵu is primarily associated with the characteristics of the vibration force, while ϵθ is more related to the large-scale columnar structures. Both energy dissipation rates exhibit a power-law relationship with the oscillational Reynolds number Reos. ϵu exhibits a scaling relation as ⟨ϵu⟩V,t∼a−1Reos0.93±0.01, while ϵθ exhibits two distinct scaling behaviors, i.e., ⟨ϵθ⟩V,t∼a−1Reos1.97±0.04 for Reos<Reos,cr and ⟨ϵθ⟩V,t∼a−1Reos1.31±0.02 for Reos>Reos,cr, where the fitted critical oscillational Reynolds number is approximately Reos,cr≈80. The different scaling of ⟨ϵθ⟩V,t is determined by the competition between the thermal boundary layer and the oscillating boundary layer. Moreover, the probability density functions (PDFs) of both dissipation rates deviate significantly from the lognormal distribution and exhibit a bimodal shape. By partitioning the contributions from the boundary layer and bulk regions, it is shown that the bulk contributes to the small and moderate dissipation rates, whereas the high dissipation rates are predominantly contributed by the boundary layer. As Reos increases, the heavy tail of the PDFs becomes more pronounced, revealing an enhanced level of small-scale intermittency. This small-scale intermittency is mainly caused by the influence of BL due to vibration. Our study provides insight into the small-scale characteristics of 2D TVC, highlighting the non-trivial scaling laws and intermittent behavior of energy dissipation rates with respect to vibration intensity.

Damping characteristics of High-Temperature superconducting pinning maglev levitation system

High-temperature superconducting (HTS) pinning maglev has achieved rapid development in recent decades. The levitation system of the HTS pinning maglev is mainly composed of Dewar with built-in HTS bulks and permanent magnet guideway (PMG). For a maglev transportation system, damping is important for vibration attenuation, and the inherent damping characteristics of the HTS pinning maglev system have not been evaluated clearly. In this paper, the damping characteristics of the HTS pinning maglev system are analyzed through experiments and simulations. Experiments are conducted to measure the dynamic responses of the system under free and forced vibrations. The logarithmic envelope method is used to evaluate the system damping under free vibration. The cross-correlation function is utilized to obtain the phase difference between the system vibration signal and excitation signal, and then calculate the system damping under forced vibration conditions. In addition, a two-dimensional finite element model including HTS bulks, PMG, and Dewar conductive shells is established to evaluate the damping force generated by each component during system vibrations. The additional eddy current damping of the conductive Dewar shell is considered and analyzed. Finally, from the perspective of system damping and thermal stability of HTS bulks, suggestions for selecting Dewar shell materials are proposed.

Cost-Effective Data Acquisition Systems for Advanced Structural Health Monitoring.

With the growing demand for infrastructure and transportation facilities, the need for advanced structural health monitoring (SHM) systems is critical. This study introduces two innovative, cost-effective, standalone, and open-source data acquisition devices designed to enhance SHM through the latest sensing technologies. The first device, termed CEDAS_acc, integrates the ADXL355 MEMS accelerometer with a RaspberryPi mini-computer, ideal for measuring strong ground motions and assessing structural modal properties during forced vibration tests and structural monitoring of mid-rise buildings. The second device, CEDAS_geo, incorporates the SM24 geophone sensor with a Raspberry Pi, designed for weak ground motion measurements, making it suitable for seismograph networks, seismological research, and early warning systems. Both devices function as acceleration/velocity Data Acquisition Systems (DAS) and standalone data loggers, featuring hardware components such as a single-board mini-computer, sensors, Analog-to-Digital Converters (ADCs), and micro-SD cards housed in protective casings. The CEDAS_acc includes a triaxial MEMS accelerometer with three ADCs, while the CEDAS_geo uses horizontal and vertical geophone elements with an ADC board. To validate these devices, rigorous tests were conducted. Offset Test, conducted by placing the sensor on a leveled flat surface in six orientations, demonstrating the accelerometer's ability to provide accurate measurements using gravity as a reference; Frequency Response Test, performed at the Gebze Technical University Earthquake and Structure Laboratory (GTU-ESL), comparing the devices' responses to the GURALP-5TDE reference sensor, with CEDAS_acc evaluated on a shaking table and CEDAS_geo's performance assessed using ambient vibration records; and Noise Test, executed in a low-noise rural area to determine the intrinsic noise of CEDAS_geo, showing its capability to capture vibrations lower than ambient noise levels. Further field tests were conducted on a 10-story reinforced concrete building in Gaziantep, Turkey, instrumented with 8 CEDAS_acc and 1 CEDAS_geo devices. The building's response to a magnitude 3.2 earthquake and ambient vibrations was analyzed, comparing results to the GURALP-5TDE reference sensors and demonstrating the devices' accuracy in capturing peak accelerations and modal frequencies with minimal deviations. The study also introduced the Record Analyzer (RECANA) web application for managing data analysis on CEDAS devices, supporting various data formats, and providing tools for filtering, calibrating, and exporting data. This comprehensive study presents valuable, practical solutions for SHM, enhancing accessibility, reliability, and efficiency in structural and seismic monitoring applications and offering robust alternatives to traditional, costlier systems.

Combined repetitive control system for active damping of forced vibrations

Combined repetitive control system for active damping of forced vibrations

A proposed model to investigate the dynamic response of stay cables with viscous damper

Viscous dampers commonly mitigate structural vibrations, and various models exist to capture their nonlinear behavior. This article proposes a Hysteretic Maxwell model obtained by evolving the standard Maxwell model to effectively integrate the hysteresis effect. The model entails only a limited number of parameters. The optimized model parameters are identified by fitting model predictions with reported experimental measurements. A numerical case study is conducted, focusing on the longest stay cable of the Rades-La Goulette cable-stayed bridge. Simulation results emphasize the significant improvement of the proposed model over its predecessor, showcasing reductions in both free and forced first-mode vibrations.