Method For Vibration Analysis Research Articles

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.

Research on Bifurcated Origami Hydraulic Dampers for Real Road Vibration Loads

Cylindrical hydraulic dampers are commonly utilized to mitigate vibrations in machinery and structural applications. These devices generally feature a single linear stroke and are often linked to rotary joints to handle complex loading conditions. However, their installation in confined spaces, such as vehicle suspensions, poses considerable difficulties. In this research, we introduce an innovative bifurcated origami hydraulic damper with nonlinear damping capabilities. Initially, we formulated the collapsible conditional equations essential for the design of the bifurcated origami hydraulic dampers. We then examined the fluid dynamics within the damper and its flow channels, determining that the damping force is proportional to the square of the velocity. Furthermore, we developed motion equations based on the derived damping force and suggested vibration analysis methods using the Runge–Kutta approach. For the mass-spring vibration system, we created an experimental setup with the bifurcated origami hydraulic damper and performed vibration tests using noise signals recorded from a vehicle traveling on a gravel road, thus validating its damping performance and efficacy. Additional tests, which varied the orifice size at the end of the origami structure, as well as the type and temperature of the internal fluid, showed that the orifice size had a more pronounced effect on damping efficiency than the fluid type and temperature. This confirmed the vibration-damping effectiveness of the bifurcated origami hydraulic damper.

An efficient method for solving high-dimension stationary FPK equation of strongly nonlinear systems under additive and/or multiplicative white noise

Engineering structures may suffer from drastic nonlinear random vibrations in harsh environments. Random vibration has been extensively studied since 1960s, but is still an open problem for large-scale strongly nonlinear systems. In this paper, a random vibration analysis method based on the Neural Networks for large-scale strongly nonlinear systems under additive and/or multiplicative Gaussian white noise (GWN) excitations is proposed. In the proposed method, the high-dimensional steady-state Fokker–Planck-Kolmogorov (FPK) equation governing the state’s probability density function (PDF) is firstly reduced to low-dimensional FPK equation involving only the interested state variables, generally one or two dimensions. The equivalent drift coefficients (EDCs) and diffusion coefficients (EDFs) in the low-dimensional FPK equation are proven to be the conditional mean of the coefficients given the interested variables. Furthermore, it is shown that the conditional mean can be optimally estimated by regression. Subsequently, the EDCs and EDFs, as functions of the retained variables, are approximated by the semi-analytical Radial Basis Functions Neural Networks trained with samples generated by a few deterministic analyses. Finally, the Physics Informed Neural Network is employed to solve the reduced steady-state FPK equation, and the PDF of the system responses is obtained. Four typical examples under additive and/or multiplicative GWN excitations are used to examine the accuracy and efficiency of the proposed method by comparing its results with the exact solution (if available) or Monte Carlo simulations. The proposed method also exhibits greater accuracy than the globally-evolving-based generalized density evolution equation scheme, a similar method of its kind, especially for strongly nonlinear systems. Notably, even though steady-state systems are applied in this paper, there is no obstacle to extending the proposed framework to transient systems.

Experimental investigations to assess surface fatigue failure in rolling contact bearing

Rolling element bearings are the most important components in almost all rotating machines. These bearings are often subjected to repetitive load cycles at different operating conditions. Excessive loads, speeds, and improper operating conditions lead to the propagation of defects on their load-bearing surfaces, thereby causing a negative impact on the performance of rotating machines. This paper presents the results of experimental investigations to assess wear propagation in roller bearings using lubricant degradation, vibration, and statistical parameter analysis methods. A roller bearing setup was developed in the laboratory, and the test bearing (NJ 307E) was subjected to fatigue tests over a period of 900 h. The bearing was operated at a speed and radial load of 800 rpm and 1 kN, respectively. The film thickness analysis revealed a transition in lubrication regimes during 600–900 h of operation. Grease structure degradation and oxidation analyses were carried out using scanning electron microscope images and the Fourier transform infrared radiation technique. Further, the vibration signals are extracted from the bearing housing at regular intervals. Using the fast Fourier transform technique, these vibration signals were used to analyze bearing fault frequencies to highlight the faults developed on bearing contact surfaces. The statistical features of vibration signals such as root mean square, kurtosis, and crest factor were used to assess the severity of wear propagated on the bearing contact surfaces. Integrating tribological and vibration parameter analysis techniques provided a reliable assessment of surface fatigue wear propagated on the roller-bearing contact surfaces.

A node-based smoothed finite element method (NS-FEM) for free and forced vibration analysis of three-dimensional (3D) structures

A node-based smoothed finite element method (NS-FEM) for free and forced vibration analysis of three-dimensional (3D) structures

Zonal free element method for free and forced vibration analysis of two- and three-dimensional structures

This paper presents a new numerical method called the zonal free element method (ZFREM) for the free and forced vibration analysis of elastodynamic problems. In this approach, a complex computational domain is divided into some simple zones and generates a series of regularly arranged nodes in each zone, which can improve the accuracy during the analysis of complex models. The distinguishing feature of the ZFREM is that an independent isoparametric element is formed by only one freely chosen surrounding node at each configuration node. In this method, the mass term exists only in the internal nodes, which can accelerate the assembly of the final system equations. Building upon this foundation, the present study developed the Krylov reduced dimensional iterative method, which approximates the solution of the equation system by constructing a lower-dimensional subspace. This approach avoids the complex equation transformations involved in traditional algorithms for solving eigenvalue problems, thereby further enhancing computational efficiency. Moreover, to tackle damped vibration problems encountered in engineering applications, the proposed method is further extended to solve the non-linear forced vibration problems. The accuracy and effectiveness of the method are verified by numerical examples of free and forced vibration problems.

Vibration and underwater noise simulation of a river-crossing tunnel based on a 2.5D structural-acoustic finite element method

To protect the underwater ecosystem and species, the vehicle-induced vibration and underwater radiated noise of river-crossing tunnels need to be calculated efficiently and accurately. For this purpose, this study proposed a 2.5-dimensional (2.5D) structural-acoustic finite element method which combines 2.5D finite element vibration algorithm and 2.5D infinite element acoustic algorithm. The proposed method utilizes the spatial wave number transformation theory and the acoustic transfer vector (ATV) method. Based on a river-crossing tunnel, a 2.5D numerical simulation model was established in this study to analyze the vehicle-induced tunnel-soil vibration as well as the underwater radiated noise during operation. The results showed that the tunnel vibration and the associated radiated noise mainly distributed in the range of 10 to 40 Hz, with two peaks at 15.6 Hz and 31.5 Hz, respectively. The total sound pressure level (SPL) of the predicted noise at each field point reached a maximum value of 126 dB. The 2.5D algorithm proposed in this study achieves higher computational efficiency compared to traditional 3D vibration and noise analysis methods, which can provide theoretical and technical supports for the protection of underwater ecological diversity.

Method for vibration and acoustic radiation analysis of underwater stiffened plates with acoustic coatings

Based on the effective medium theory as well as the three-dimensional viscoelastic theory, a semi-analytical model of the three-dimensional underwater vibration and acoustic radiation with cavity-type stiffened plate structures covered with acoustic coatings is established to solve the issues related to underwater vibration and acoustic radiation calculation of the stiffened plate and shell structure with complex acoustic coatings. By comparing the far-field acoustic radiation characteristics of the proposed semi-analytical model and the finite element numerical model, this research verifies the validity and accuracy of the proposed model. On such a basis, this research preliminarily investigates the coupling effect exerted by stiffeners and parent plates in stiffened plates as well as the vibroacoustic characteristics of acoustic coatings, thereby providing a valuable idea for the prediction of vibroacoustic characteristics concerning underwater structures.

Experimental Research on Dynamic Characteristics of a Multi-Disc Rotor System Supported by Aerostatic Bearings

Gas bearings have the advantages of small friction loss, wide applicable speed range, no pollution, etc., and have important application prospects in micro and small high-speed rotating machinery. However, due to its compressibility and low viscosity, its dynamic stability in high-speed rotating machinery is the key to constraining its development. The experimental study of shaft system dynamics is the main means to explore the mechanism of rotor behavior. On the test platform of dynamic characteristics of multi-disc rotor system supported by aerostatic bearings, experimental research on the nonlinear dynamic characteristics of a rotor system was carried out, and nonlinear vibration test and analysis methods, such as axial orbits, bifurcation diagrams, and spectral characteristics, were adopted, and vibration phenomena, including the critical rotational speed accumulating energy and low-frequency accumulating energy, were presented and the vibration characteristics of bearing fracture faults were presented. The bearing supply pressure and rubber damping pad were introduced as a method to suppress the low-frequency vibration of the aerostatic bearing rotor system, and its vibration-reduction effect was verified by experiments. The above results can provide technical support for vibration control and fault diagnosis of rotor systems supported by aerostatic bearings.

An analytical method for free vibration analysis of multi‐directional functionally graded porous doubly‐curved shells in thermal environment with various boundary conditions

This paper uses the analytical method with arbitrary boundary conditions to model and analyze the free vibrations of multi‐directionally functionally graded porous (MFGP) doubly‐curved shallow shells resting on the Pasternak foundation in a temperature environment. It is anticipated that all mechanical parameters, except Poisson's ratio, will change in the direction of length, width, and thickness. To comprehensively describe the shell's displacement, strain, and stress fields, a modified first‐order shear deformation theory (FSDT) with an assumption of cosine distribution shear stresses has been developed. The fact that the enhanced FSDT theory does not require the use of shear correction and that the shear stress at the two free faces of the shells is zero are two of the theory's most significant advantages. Using Hamilton's principle and improved FSDT, one may get the governing equation for free vibration analysis of MFGP doubly‐curved shallow shells. The Galerkin approach is proposed to solve the governing equation of MFGP doubly‐curved shallow shells with various boundary conditions. The trustworthiness of the article is evaluated via its publication in the article model's several special cases. From this point on, a collection of findings about the natural frequency of MFGP doubly‐curved shallow shells is identified and shown in the form of tables and graphs. The results provided in this manuscript can be used as a benchmark solution for further studies as far as the vibration behavior of the MFGP doubly‐curved shallow shells is concerned.

THE INFLUENCE OF VIBRATIONS ON THE EFFICIENCY OF THE INTERNAL COMBUSTION ENGINE

This article is devoted to the study of the influence of vibrations on the efficiency and reliability of the internal combustion engine (ICE). The authors consider in detail the amount of vibration that occurs as a result of engine operation and its possible consequences for various components. The article examines modern methods of vibration analysis and their impact on various types of technical systems, including electromechanical, hydromechanical, and thermal energy equipment. Vibration reduction technologies and their implementation to increase the efficiency of technical systems are being studied. The study also includes consideration of possible technologies and innovations aimed at reducing the impact of vibration on engine performance, such as the use of shock absorbers, design optimization and the use of new materials. In particular, the article analyzes the use of the latest materials for vibration reduction, the development of control and diagnostic systems, and also studies the impact of vibrations on human health and the environment. The importance of considering vibration aspects in the process of design, operation and maintenance of technical equipment is noted. Possible implications for measurement accuracy, electronic stability, and overall control efficiency are highlighted. The authors offer practical solutions to reduce these negative impacts, including the use of innovative technologies and the development of improved electronics systems. This article is aimed at the engineering and scientific community, as well as at professionals who are interested in improving the efficiency of technical systems and understanding the effect of vibrations on their functioning. The conclusions and recommendations presented in this paper can be used for further research and development in the field of vibration engineering and technology.

Research on modified lumped parameter method in torsional vibration analysis of reciprocating compressor shaft

Abnormal vibrations often occur during the operation of reciprocating compressors under different load conditions. To efficiently and accurately calculate the torsional vibration response of the shafting under various working conditions, a modified lumped parameter method (MLPM) based on finite element mode modification is proposed. MLPM is derived from the lumped parameter method (LPM) and incorporates corrections to the stiffness matrix based on the multi-degree-of-freedom modal calculation using a finite element model. This allows MLPM to combine the high accuracy of finite element method (FEM) with the fast computing speed of LPM. To demonstrate the effectiveness of MLPM, an abnormal vibration compressor equipped with a stepless capacity control system is considered. MLPM is utilized to calculate the torsional natural frequency (TNF) and torsional torque response of the compressor’s shafting. The computed 1st-order TNF error between MLPM and FEM is only 0.20%. In the time domain, the torque response error of MLPM is less than 3.07%, while in the frequency domain, it is less than 0.57%. Moreover, MLPM exhibits a significantly increased calculation speed of more than 95% compared to FEM. By comparing MLPM results with torsional vibration test data, the 1st-order TNF error is found to be less than 0.50%, and the frequency-domain torque response error is no more than 8.91%. Furthermore, MLPM is effectively applied to solve the abnormal vibration problem of the compressor. It proposes a modification plan for the shafting, which successfully avoids torsional resonance and reduces the peak value of the torque response by 54.77%. These results demonstrate that MLPM is highly suitable for practical engineering applications due to its combination of high accuracy and fast computing speed.

Mechanism and quantitative criterion of free vibration characteristics of hydraulic systems using the water hammer reflection coefficient

Hydraulic vibration is a periodic hydraulic transient in piping systems, which can result in local damage and operating accidents involving hydraulic, mechanical, and electrical systems. However, traditional hydraulic vibration theory is limited in practical application because of its complex mathematical form and low computational efficiency. This study presents a free vibration analysis method of hydraulic systems using the water hammer reflection coefficient. A physically meaningful criterion (i.e., the product of the water hammer reflection coefficients at the upstream and downstream boundaries of the pipe, denoted as rurd), is proposed for quantifying free vibration characteristics, and it is verified via traditional hydraulic vibration theory. The modulus of rurd determines the damping factor of free vibration, and the argument of rurd determines the natural frequency. Because of the elasticity of water column, there are multiple vibration modes that correspond to multiple water hammer reflection coefficients at the pipe boundary. For a single pipe, the stability condition requires the modulus of rurd for all vibration modes to be less than 1. For a multi-pipe system, the stability condition requires every single pipe is stable. Furthermore, the applicability of this new method is demonstrated using a reservoir-pipe-valve-turbine system. The influence mechanism of some dominant factors on the free vibration characteristics of the hydraulic system is revealed. The results indicates that the free vibration stability can be improved by reducing the wave velocity or increasing the valve local loss (which changes the water hammer reflection characteristics of the hydraulic system), or by increasing the pipe friction loss to dissipate the energy of the water hammer waves as they propagate. Overall, this study presents a new perspective for understanding hydraulic vibration and offers potential significance in engineering applications.

Hybrid Method for Large Diameter Spool Vortex-Induced and Flow-Induced Vibration Analysis

Hybrid Method for Large Diameter Spool Vortex-Induced and Flow-Induced Vibration Analysis

Applying Bayesian networks in making intelligent applications for static and dynamic unbalance diagnosis

<span lang="EN-US">One of the problems often encountered in vibration analysis is unbalanced or imbalanced, namely the occurrence of a shift in the center of mass from the center of rotation to cause high vibrations. Unbalance itself is divided into two, namely static and dynamic unbalance. Identification of the right type of unbalance must be done because each type of unbalance requires different handling. Therefore, this study aims to design a system to identify the type of unbalance based on the required parameters. The system design determines the input and then builds an algorithm by combining vibration analysis methods and Bayesian networks (BN). Systems and applications are built using MATLAB. After the application is finished, testing is carried out using vibration measurement data obtained from a demo machine that has previously been conditioned for damage. The BN method has been successfully applied to the unbalance diagnosis system. When there is evidence of large amplitude in 1X the frequency spectrum and the value of the static phase range, the percentage of static unbalance from 26.8% increases to 75%. The system can predict all testing data quickly and precisely for the six experiments.</span>

Development of a universal method for vibrational analysis of the terminal alkyne C≡C stretch.

The terminal alkyne C≡C stretch has a large Raman scattering cross section in the "silent" region for biomolecules. This has led to many Raman tag and probe studies using this moiety to study biomolecular systems. A computational investigation of these systems is vital to aid in the interpretation of these results. In this work, we develop a method for computing terminal alkyne vibrational frequencies and isotropic transition polarizabilities that can easily and accurately be applied to any terminal alkyne molecule. We apply the discrete variable representation method to a localized version of the C≡C stretch normal mode. The errors of (1) vibrational localization to the terminal alkyne moiety, (2) anharmonic normal mode isolation, and (3) discretization of the Born-Oppenheimer potential energy surface are quantified and found to be generally small and cancel each other. This results in a method with low error compared to other anharmonic vibrational methods like second-order vibrational perturbation theory and to experiments. Several density functionals are tested using the method, and TPSS-D3, an inexpensive nonempirical density functional with dispersion corrections, is found to perform surprisingly well. Diffuse basis functions are found to be important for the accuracy of computed frequencies. Finally, the computation of vibrational properties like isotropic transition polarizabilities and the universality of the localized normal mode for terminal alkynes are demonstrated.

An analytical method for vibration analysis of multi-span Timoshenko beams under arbitrary boundary conditions

An analytical method for vibration analysis of multi-span Timoshenko beams under arbitrary boundary conditions

Gegenbauer-Ritz method for free vibration analysis of rotating functionally graded graphene reinforced porous composite stepped cylindrical shells with arbitrary boundary conditions

In this paper, a semi-analytic method with Gegenbauer polynomials as an admissible function is presented. Free vibration analysis of rotating functionally graded graphene reinforced porous composite (FG-GPLRPC) stepped cylindrical shells with arbitrary boundary conditions is analyzed by using the unified Gegenbauer-Ritz method. The effective material properties of rotating FG-GPLRPC stepped cylindrical shells are obtained with Halpin-Tsai micromechanical model and the open-cell body theory. The boundary conditions at both ends of the structure and the continuous coupling between the shell segments are simulated with the artificial spring technique. Then, based on the first-order shear deformation theory (FSDT), the Rayleigh-Ritz method is employed to derive the equations of rotating FG-GPLRPC stepped cylindrical shells. Finally, the influences of several factors on dimensionless frequency of the shell are also assessed. The results show that this method has excellent convergence and higher computational efficiency. Furthermore, the traveling wave frequencies of different modes show different trends with the increase of rotating speed under elastic boundary conditions. In high-order modes, the influence of porosity coefficient is smaller than that of rotating speed.

An efficient parallel computing method for random vibration analysis of a three-dimensional train-track-soil coupled model using Seed-PCG algorithm

An efficient parallel computing method for random vibration analysis of a three-dimensional train-track-soil coupled model using Seed-PCG algorithm

Frequency dependent exact trial functions in Galerkin boundary method for free vibration analysis of thin plate

Method of frequency dependent exact trial functions for thin plate vibration based on fundamental solutions of Voigt is suggested. Contrary to other methods, where one of the functions is chosen as the scale and specific boundary condition dependent, it employs only the frequency dependent functions for both space coordinates. Thus they are scale independent, so the same functions can be used for different boundary conditions and plate dimensions. General rule for the choice of exact trial functions is formulated. The boundary conditions are satisfied according to the Galerkin boundary method, which actually minimizes the energy residuals with respect to each weight function (fundamental solution).The verification of method is performed on examples of rectangular plate with various boundary conditions. Several arbitrarily chosen sets of trial functions were employed in calculation of the same tasks, and it is shown that accuracy of the method is almost independent from the choice of them. Even the small number of trial functions provides the very accurate results for natural frequencies.