Vibration Problems Research Articles

On one solution of the problem of vibrations of mechanical systems with moving boundaries

An analytical method of solving the wave equation describing the oscillations of systems with moving boundaries is considered. By changing the variables that stop the boundaries and leave the equation invariant, the original boundary value problem is reduced to a system of functional-difference equations, which can be solved using direct and inverse methods. An inverse method is described that makes it possible to approximate quite diverse laws of boundary motion by laws obtained from solving the inverse problem. New particular solutions are obtained for a fairly wide range of laws of boundary motion. A direct asymptotic method for the approximate solution of a functional equation is considered. An estimate of the errors of the approximatemethod was made depending on the speed of the boundary movement.

A smart structural optimization method of magnetorheological damper for ultra-precision machine tool

To address the problem of multi-source vibration in ultra-precision machine tools, a vibration reduction stand was designed by replacing passive damping components with magnetorheological dampers (MRDs). In this work, the structural parameters of MRDs were optimized using an improved pelican optimization algorithm (IPOA) to realize the maximum capability in reducing vibration. Firstly, the working principle of MRDs was explained, and the mathematical models of MRDs were established. Then, an IPOA based on singer chaotic mapping, nonlinear inertia weight factor, and Cauchy mutation strategy was proposed to enhance the global search capability and convergence efficiency of the algorithm. Subsequently, the IPOA was applied to optimize key structural parameters of MRDs, including output damping force, controllable damping range, response time, and power consumption. Finally, COMSOL Multiphysics software was used to verify the effectiveness of the proposed algorithm by comparing the magnetic induction intensity distribution of MRDs before and after optimization, as well as the variation of the four performance indexes under the different applied currents. After being optimized using the proposed IPOA, the MRDs can deliver a larger maximum damping force and a wider damping controllable range, with less power consumption and quick response, which could meet the requirement for vibration suppression of ultra-precision machine tools.

Comparative Analysis of Transmission Housings to Evaluate Whining Noise Performance

A quite cabin is always a preferred choice of the customer. Powertrain acts as a source for many noise and vibration problems in a passenger car. Transmission plays a major role in modulating the power from engine to the drive train and is exposed to a high vibration and noise environments. Hence design of transmission for low vibration & noise is need of the hour. This paper attempts to perform a comparative study of 6 housings of different design of a two-wheel drive passenger car to evaluate the vibration performance and Noise radiation characteristics by using FEM (Finite Element Method) & BEM (Boundary Element Method) & finite element analysis techniques. The authors also try to put forward a layout comparison study for the housings and conclude what design is best suited for better NVH whine performance in view of vibrations & sound radiation. These indicative results from this paper can be referred by the design & analysis engineers during early product development of the transmission.
 Keywords: Transmission, Housings, Whining Noise, Bionic Design, NVH Analysis, Durability Analysis, Study of Housings, Housings NVH Analysis

Vibrational Analysis of Axially Loaded Rayleigh Beams on Variable Winkler Foundations with Implications for Structural Design

In this study, we explore the complex vibration problem of a Rayleigh beam under axial loads, positioned over a variable Winkler foundation with elastic properties changing along its length. The investigation delves into how factors like rotational inertia, axial forces, and foundation properties affect the beam’s dimensionless eigenvalues and eigenmodes. Employing the Differential Transform Method (DTM), we tackle the governing equations across various foundation conditions, including constant, linear, and parabolic variations. The results align well with the previous research, affirming their precision between scenarios considering or neglecting the elastic foundation’s effects. Notably, we emphasize the influence of linear spring stiffness on vibration characteristics, overshadowing rotary spring stiffness. Thus, the important novelty of the study lies in its comprehensive investigation into the vibration dynamics of a Rayleigh beam under axial loads on a variable Winkler foundation with elastic properties varying along its length. The findings illuminate a previously unexplored dynamic: the intricate interplay between linear and rotary spring stiffness, showcasing the dominant impact of linear stiffness on vibration characteristics. Of significant note is the profound effect of axial forces on fundamental eigenvalues, underscoring their critical role in structural behavior. These developments possess substantial practical implications, providing invaluable guidance for the accurate modeling of beams supported by elastic foundation, thereby enhancing structural design and performance.

Network-based System of Mechanical Vibration Fault Diagnosis

Nowadays researchers are investing in electrical machines fault diagnosis area. The users and manufacturers are strong for containing diagnostic features for reliability and scalability improvement. The regular monitoring enables machine faults early detection and hence helpful for automation by providing process control. The fault detection performance and machine-learning algorithms classification are highly dependent on features involved. The aim of this paper is to solve the network mechanical vibration problem and for that a research on mechanical vibration fault diagnosis is proposed. The first is to use the vibration signal receiving device to record the vibration signal of the target device. In the process of receiving the signal, the measurement point is related to the accuracy of the received signal, so it is necessary to prepare the measurement point. Secondly, the principle of fault detection based on vibration detection is introduced. The main purpose of this method is to identify the fault characteristics, simulate the fault with MATLAB, and obtain the error time-frequency diagram behavior. The feature vector dimension obtained by the idling confirmation example is the same as that of the rotor, which is 14, including 8 relative wavelet packet intensity entropy feature indexes and higher values, minimum value, peak-to-peak value, mean value, mean square error and variance. Finally, the deficiencies of the detected vibration faults are identified and similar improvements are proposed. Improvements only reduce signal vibration, disrupting feature isolation and identifying patterns.The observed percentage accuracy for classification of faults through proposed approach is 98.2%.

Review on Vibration Monitoring and Its Application during Shield Tunnel Construction Period

With the rapid development of metro construction, shield machines inevitably have to traverse a variety of complex geological conditions, leading to the frequent occurrence of geological disasters, equipment failures, building vibration and other problems. Vibration, as an important feature of the shield tunneling process, has received more and more attention in recent years. This paper summarizes the relevant research progress of vibration monitoring during shield construction from 2015 to 2023. It analyzes the shield vibration generation mechanism, monitoring methods and application areas. Firstly, the shield vibration type is divided into mechanical vibration triggered by internal excitation and forced vibration triggered by external excitation, and the principles of vibration generated by shield main bearing, gearbox and disc cutter are discussed. Then, the commonly used vibration monitoring methods are outlined according to the installation location of the sensors (inside and outside of the shield). Finally, the applications of vibration signals in the diagnosis of shield faults, the identification of geologic conditions, and the evaluation of the current status of the interference with the buildings are summarized. This paper discusses the development trend of vibration monitoring during shield tunneling based on the current research situation and the current technology level, which provides valuable insights to enhance the safety and intelligence of shield construction.

Research on Vibration Suppression Methods for Industrial Robot Time-Lag Filtering

This paper analyzes traditional vibration suppression methods in order to solve the vibration problem caused by the stiffness of flexible industrial robots. The principle of closed-loop control dynamic feedforward vibration suppression is described as the main method for solving robot vibration suppression. This paper proposes a method for time-lag filtering based on T-trajectory interpolation, which combines the T-planning curve and the time-lag filtering method. The method’s basic principle is to dynamically adjust the trajectory output through the algorithm, which effectively suppresses the amplitude of the harmonic components of a specific frequency band to improve the vibration response of industrial robot systems. This experiment compared traditional vibration suppression methods with the time-lag filtering method based on T-trajectory interpolation. A straight-line method was proposed to measure the degree of vibration. The results demonstrate that the time-lag filtering method based on T-trajectory interpolation is highly effective in reducing the vibration of industrial robots. This makes it an excellent option for scenarios that demand real-time response and high-precision control, ultimately enhancing the efficiency and stability of robots in performing their tasks.

Research on the model of staggered tooth phase to reduce vibration of single-stage gear transmission system: Theoretical analysis and experiments.

Aiming at the problems of high vibration and high noise in gear transmission systems, a model of gear with staggered tooth phase structure(GSTPS) for reducing vibration is proposed. Without changing the overall structure of the gear transmission system, the purpose of reducing mesh stiffness fluctuations is achieved by staggering adjacent gears at a certain angle along the axis, thereby the vibration of the gear transmission system could be reduced. The characterization method of time-varying mesh stiffness of the GSTPS is studied. Then, the impact of different staggered tooth phases(STP) on reducing vibration of the transmission system are researched, and the basis for selecting the optimal STP are obtained. The experimental platform for reducing vibration with STP is established. And some experimental studies were conducted to validate the theoretical model.

Longtime dynamics of solutions for higher-order (m1,m2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(m_{1},m_{2})$\\end{document}-coupled Kirchhoff models with higher-order rotational inertia and nonlocal damping

The Kirchhoff model is derived from the vibration problem of stretchable strings. This paper focuses on the longtime dynamics of a higher-order (m1,m2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(m_{1},m_{2})$\\end{document}-coupled Kirchhoff system with higher-order rotational inertia and nonlocal damping. We first obtain the state of the model’s solutions in different spaces through prior estimation. After that, we immediately prove the existence and uniqueness of their solutions in different spaces through the Faedo-Galerkin method. Subsequently, we prove their family of global attractors using the compactness theorem. Finally, we reflect on the subsequent research of the model and point out relevant directions for further research on the model. In this way, we systematically study the longtime dynamics of the higher-order (m1,m2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(m_{1},m_{2})$\\end{document}-coupled Kirchhoff model with higher-order rotational inertia, thus enriching the relevant findings of higher-order coupled Kirchhoff models and laying a theoretical foundation for future practical applications.

Numerical Analysis of Unsteady Vibrations of a Plate Resting on an Elastic Isotropic Half-Space

The paper is devoted to the numerical solution of the problem of vibrations of an infinite elastic plate resting on an elastic isotropic half-space using the analytical method based on the ray method with its numerical realization via the Maplesoft package. Unsteady oscillations are caused by the action of instantaneous loads on the plate, resulting in the appearance of two plane wave surfaces of strong discontinuity in the elastic half-space, behind the fronts of which, up to the contact boundary, the solution is constructed using ray series. The unknown functions entering the coefficients of the ray series and the equation of plate motion are determined from the boundary conditions of the contact interaction between the plate and the half-space. Previously, the approximate solution of this problem was obtained analytically without using mathematical packages, and the dynamic deflection of the plate involving only the first three terms of the ray series was written down. In this work, a two-layer medium with different properties was investigated using an algorithm developed to solve contact dynamic problems related to the occurrence and propagation of strong and weak discontinuity surfaces.

Symplectic superposition method for the free-vibrating problem of sigmoid functionally graded material rectangular thin plates clamped at four edges

The symplectic superposition method (SSM) is implemented to investigate the free vibration problem of sigmoid functionally graded material (FGM) rectangular thin plates clamped at four edges. Firstly, the vibration equation of the sigmoid FGM rectangular thin plate is transformed into Hamiltonian canonical equations. Then based on the analysis of boundary conditions of the plate, the vibration problem of the sigmoid FGM rectangular thin plate clamped at four edges is decomposed as two sub-problems simply supported on two opposite edges. And then based on the symplectic elasticity method (SEM), the series expansion solutions for the two sub-vibrating problems are obtained. Afterward, by superposing the series expansion solutions for the two sub-vibrating problems, a symplectic superposition solution of the freely vibrating sigmoid FGM rectangular thin plates clamped at four edges is obtained. Finally, we apply the obtained symplectic superposition solution to research the frequencies and vibration mode functions of some specific sigmoid FGM rectangular thin plates, and the impact of the aspect ratio a/b and material gradient index k on the vibration frequencies of the sigmoid FGM rectangular thin plates is studied.

Dynamic vibration modeling of the ball screw feed system considering travel deviation

The vibration problem of the ball screw feed system in working conditions limits its application in precision machinery. However, few studies have developed models to investigate the vibration mechanism of the ball screw feed system in running status. In this paper, a dynamic model considering travel deviation and ball motion is proposed to explain the vibration mechanism of the ball screw feed system. This model is numerically solved and experimentally verified. Simulation results showed that, the travel deviation mainly affects the vibration amplitude rather than the frequency when the rotation speed is constant. Higher travel deviation introduces higher vibration amplitude, and the vibration of the feed system is more sensitive to the travel deviation of low frequency.

Potential method in the coupled theory of thermoelastic triple-porosity nanomaterials

In this paper, the coupled linear theory of thermoelasticity for nanomaterials with triple porosity is considered in which the combination of Darcy’s law and the volume fraction concept for three levels of pores (macro-, meso- and micropores) is provided. The 3D basic boundary value problems (BVPs) of steady vibrations of this theory are formulated and these BVPs are investigated using the potential method (boundary integral equation method) and the theory of singular integral equations. Namely, the formula of integral representation of regular vectors is obtained. The surface (single-layer and double-layer) and volume potentials are introduced and their basic properties are given. Some useful singular integral operators are defined for which Noether’s theorems are valid. The symbolic determinants and indexes of these operators are calculated. The BVPs of steady vibrations are reduced to the equivalent singular integral equations. Finally, with the help of the potential method, we prove the existence theorems for classical solutions of the aforementioned BVPs.

Nonlinear resonant responses and chaotic dynamics of three-dimensional braided composite cylindrical shell

The advanced three-dimensional braided composite structure has excellent integrity, which can effectively avoid the problems of interlayer stress jump and interface debonding that may occur in traditional composite laminated structures. However, most of the existing references on the three-dimensional braided composite structure are fragmented, and there is little research on their vibrations. Taking the cylindrical shell of a rocket as the object and considering the complex flight environment, a general framework for the vibration problems of the three-dimensional braided composite shell is proposed for the first time. The equivalent mechanical parameters of the three-dimensional braided composite material are calculated based on the volume averaging method. Then, the nonlinear dynamic model of the three-dimensional braided composite cylindrical shell is established, and the natural vibration characteristics are analyzed. Under the case of 1:1 internal resonance, the pseudo-arc length continuation method is used to solve the nonlinear resonant responses of this nonlinear system. Finally, we apply the fourth-order Runge-Kutta algorithm to study the chaotic dynamics of the three-dimensional braided composite cylindrical shell model. This framework presented in this paper can be extended to the study of nonlinear vibrations and chaotic dynamics of other three-dimensional braided composite structures.

Experimental and numerical investigations on non-synchronous vibration and frequency lock-in of transonic compressor rotor blades

Non-synchronous vibration (NSV) problems in axial compressors are challenging and frequently result in high vibration stress or structural failure within the frequency lock-in region. A deeper understanding of the lock-in phenomenon in NSV is necessary to improve blade reliability and safety. In this study, an experiment was conducted on a multistage transonic axial compressor to obtain frequency lock-in characteristics. The enforced motion of the flexible blade simulation method was used to study the frequency lock-in mechanism between blade vibration and tip unstable flow. The results showed that the aerodynamic frequency characteristic changed from a broadband spectrum to a distinct frequency peak as the NSV onset. The nonlinear vibration pattern could maintain the limited cycle oscillation for 26 s. The vibration stress of the frequency locked-in case was approximately 19 times that of the frequency unlocked one. The pressure fluctuations generated by the large-scale radial separation vortex structures were stronger than those of the tip leakage flow, and the third-order harmonic frequency of the circumferential instability flow was close to the first-order bending model natural frequency. The periodic shedding and reattachment process of flow separation provided the initial non-synchronous aerodynamic excitation source. The frequency lock-in phenomenon occurred at a maximum vibration amplitude of 2 % and 3 % tip chord length. The tip unstable flow characteristics were consistent and entirely dominated by blade vibration.

Applying a New Trigonometric Radial Basis Function Approximation in Solving Nonlinear Vibration Problems

Applying a New Trigonometric Radial Basis Function Approximation in Solving Nonlinear Vibration Problems

Accurate free and forced vibration behavior prediction of functionally graded sandwich beams with variable cross-section: A finite element assessment

The current investigation proposes an enhanced finite element beam model to assess the dynamic behavior of functionally graded sandwich beams with variable cross-sections. By integrating the shear effect, this beam model integrates both C0 and C1 continuities to generate elementary matrices using an efficient three-unknown shear deformation beam theory. The model focuses on advanced sandwich beams with functionally graded material face-sheets and metallic cores, exploring various geometric arrangements. The originality of this study addresses variable cross-sections in sandwich beams, evaluating the influence of material composition and geometric configurations on free and forced vibration responses, including different boundary conditions. The methodology uses the eigenvalue method for examining free vibration and applies Newmark’s algorithm for solving forced vibration problems. The current model expands the scope of analysis compared to previous models that primarily focus on uniform cross-sections and conventional material distributions. The developed model incorporates non-uniform geometrics, material gradient parameters, and advanced finite element analysis to enhance precision and efficacy through detailed parametric investigations and comparisons with existing literature. This contribution significantly improves the mechanical modeling of composite sandwich structures, particularly those incorporating functionally graded materials and complex geometrical aspects.

Parametric control of quasi-zero stiffness mechanisms for vibration isolation at near-zero frequencies

Infra-frequency vibration, including near-zero frequencies, has become a critical limiting factor for developers of next-generation ultra-high precision measurement systems. Mechanisms involving quasi-zero stiffness show potential to solve this new vibration problem. An approach for designing a novel type of the mechanisms for this class is presented. An algorithm is developed and tested for numerical solution of nonlinear elasticity problem in designing the mechanism structural and parametric elements based on FEM models. The elements are spatially prestressed multi-layer designs of polymer composites for modeling elastic postbuckling in large and the effect of a “floating” binder. An algorithm and models following the Nelder-Mead method are used for optimizing the designs. Examples of Euler-beam-shaped composite elements under postbuckling demonstrate a qualitative leap in mechanisms design and efficiency, specifically, in terms of compactness, lightness, and strength. A dramatically expanded control range for the linear section of operating travel with quasi-zero stiffness is obtained. A damping threshold is evaluated, and an optimal type diagram of the mechanism is designed and enumerated as necessary conditions for vibration isolation at near-zero frequencies. The validity and effectiveness of the approach are demonstrated with the results of theoretical design and testing of the prototype for vibration isolation of the ultra-high precision optical system. The learning capability of the mechanisms is estimated by an adapted version of the Levenberg-Marquardt algorithm with stepwise refinement in the test mode using Rosenbrock’s function.

Numerical Study of the Strength Radial Turbomachines Based on the Use of Stainless Steel 316L

By studying various properties of materials came to the conclusion that stainless steel 316L has good properties. This material is suitable for making radial wheel turbines compared to other materials. The object of the study is a radial wheel with 10 blades manufactured by “Schiele” (Germany), which specializes in the production of units for the chemical industry and ventilation equipment. The finite element method was chosen as the basic research method for solving problems of natural and forced vibrations, static stress and studying the degree of reactivity blades radial wheels of turbomachines. It can be argued that the numerical analysis of the strength characteristics of heavily loaded turbine elements with the help of electronic computers provides a greater depth of research, the breadth of the issues covered, significantly reduces the amount of expensive experimental research, reduces the time for designing new turbines in terms of efficiency, reliability, technology and resource saving of highly loaded units. In this paper, calculations were made of the characteristics of natural frequencies, equivalent stresses, deformation and the degree of reactivity blades when using material stainless steel 316L. It is noted that this material provides the criterion of stress concentration in the wheel as low as possible and the natural frequencies of the wheel are reduced, but it does not lead to a change in the oscillation modes of this wheel. So 316L stainless steel is recommended for evaluating options in the manufacture of this radial wheel of turbomachines in the field of power, chemical and transport engineering.

Service Performance Optimization and Experimental Study of a New W-W Type Non-circular Planetary Gear Train

To address the vibration problem in traditional W-W-type non-circular planetary gear trains during operation, this study proposes two new combinations of W-W-type non-circular planetary gear trains. The study focuses on analysing the transmission error and improving service performance. By utilizing the conjugate theory and the coordinate transformation theory, an accurate mathematical model for non-circular gears is derived. The transmission error models for the two combination forms of the non-circular planetary gear train are established using the incremental meshing line method. The analysis also examines the influence of eccentricity on the transmission error. Kinematic analysis of the multi-body dynamics model confirms that the new W-W type non-circular planetary gear train, formed by combining non-circular gears and cylindrical gears, exhibits superior transmission performance. Furthermore, a test analysis is conducted on the roller pumping unit test platform and the indicator diagrams of the pumping unit under various working conditions are obtained. The study concludes that the optimal matching mode for the sucker rod counterweight and motor frequency of the reversing device of the pumping unit is 20 kN and 20 Hz, and the dynamic balance of the pumping unit load can be achieved by adjusting the motor frequency.