An Analytical Method for Calculating the Natural Frequencies of the Cab Carrier Systems Vibrations of Transport and Technological Machines

2022 ◽  
pp. 473-481
Author(s):  
P. V. Sirotin ◽  
I. Yu. Lebedinsky ◽  
M. V. Perushkin
Keyword(s):  
Analytical Method ◽  
Natural Frequencies ◽  
Carrier Systems

Natural Frequency of Laminated Composite Plates Using a Sinusoidal Theory

2014 ◽  
Vol 709 ◽  
pp. 148-152
Author(s):  
Guo Qing Zhou ◽  
Ji Wang ◽  
Song Xiang
Keyword(s):  
Differential Equations ◽  
Analytical Method ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
Simply Supported ◽  
Sinusoidal Shear Deformation Theory

Sinusoidal shear deformation theory is presented to analyze the natural frequencies of simply supported laminated composite plates. The governing differential equations based on sinusoidal theory are solved by a Navier-type analytical method. The present results are compared with the available published results which verify the accuracy of sinusoidal theory.

Vibration of Box-Type Structures with Flexible Joints between Constituent Plates

1968 ◽  
Vol 10 (3) ◽  
pp. 294-298 ◽  
Author(s):  
S. M. Dickinson
Keyword(s):  
Analytical Method ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Flexible Joints ◽  
Joint Flexibility ◽  
Rigid Joints

In a recent paper by Dickinson and Warburton (1), an analytical method of determining natural frequencies and mode shapes of box-type structures having rigid joints between constituent plates was given. Practical box-type structures may well include joints having some flexibility, and it is the purpose of this Note to indicate how the earlier analysis can be modified to apply to such structures and to show the effect of joint flexibility on the natural frequencies of a particular structure.

scholarly journals A New Analytical Method for Spherical Thin Shells’ Axisymmetric Vibrations

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Mariame Nassit ◽  
Abderrahmane El Harif ◽  
Hassan Berbia ◽  
Mourad Taha Janan
Keyword(s):  
Analytical Method ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Current Method ◽  
Free Edge ◽  
Free Vibrations ◽  
Thin Shells ◽  
Element Calculation ◽  
Spherical Shells ◽  
Clamped Edge

In order to improve the spherical thin shells’ vibrations analysis, we introduce a new analytical method. In this method, we take into consideration the terms of the inertial couples in the stress couples’ differential equations of motion. These inertial couples are omitted in the theories provided by Naghdi–Kalnins and Kunieda. The results show that the current method can solve the axisymmetric vibrations’ equations of elastic thin spherical shells. In this paper, we focus on verifying the current method, particularly for free vibrations with free edge and clamped edge boundary conditions. To check the validity and accuracy of the current analytical method, the natural frequencies determined by this method are compared with those available in the literature and those obtained by a finite element calculation.

scholarly journals Modal Analysis of a Simply Supported Steel Beam with Cracks under Temperature Load

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Yijiang Ma ◽  
Guoping Chen ◽  
Fan Yang
Keyword(s):  
Modal Analysis ◽  
Transfer Matrix ◽  
Analytical Method ◽  
Natural Frequencies ◽  
Steel Beam ◽  
Simply Supported ◽  
Local Flexibility ◽  
Temperature Load ◽  
Different Temperatures ◽  
Torsion Springs

Based on the transfer matrix method, an analytical method is proposed to conduct the modal analysis of the simply supported steel beam with multiple transverse open cracks under different temperatures. The open cracks are replaced with torsion springs without mass, and local flexibility caused by each crack can be derived; the temperature module is introduced by the mechanical properties variation of the structural material, and the temperature load is caused by the temperature variation, which can be transformed to the axial force on the cross-section. The transfer matrix of the whole beam with the temperature and geometric parameters of cracks can be obtained. According to boundary conditions of the simply supported beam, natural frequencies of the beam can be calculated, which are compared with the finite element results. Results indicate that the analytical method proposed has a high accuracy; the natural frequencies of the simply supported steel beam are mostly affected by the temperature load, which cannot be ignored.

scholarly journals Three-Dimensional Vibration Analysis of a Functionally Graded Sandwich Rectangular Plate Resting on an Elastic Foundation Using a Semi-Analytical Method

Materials ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 3401 ◽  
Author(s):  
Cui ◽  
Zhou ◽  
Ye ◽  
Gaidai ◽  
Li ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Elastic Foundation ◽  
Power Law ◽  
Analytical Method ◽  
Sandwich Plate ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Sandwich Plates

The three-dimensional vibration of a functionally graded sandwich rectangular plate on an elastic foundation with normal boundary conditions was analyzed using a semi-analytical method based on three-dimensional elasticity theory. The material properties of the sandwich plate varied with thickness according to the power law distribution. Two types of functionally graded material (FGM) sandwich plates were investigated in this paper: one with a homogeneous core and FGM facesheets, and another with homogeneous panels and an FGM core. Various displacements of the plates were created using an improved Fourier series consisting of a standard Fourier cosine series along with a certain number of closed-form auxiliary functions satisfying the essential boundary conditions. The vibration behavior of the FGM sandwich plate, including the natural frequencies and mode shapes, was obtained using the Ritz method. The effectiveness and accuracy of the suggested technique were fully verified by comparing the natural frequencies of sandwich plates with results from investigations of other functionally graded sandwich rectangular plates in the literature. A parametric study, including elastic parameters, foundation parameters, power law exponents, and layer thickness ratios, was performed, and some new results are presented.

Analytical method for the prediction of natural frequencies of switched reluctance motor based on electromechanical analogy method

2018 ◽  
Vol 37 (1) ◽  
pp. 224-241 ◽  
Author(s):  
Chao Tan ◽  
Honghua Wang ◽  
Ling Chen
Keyword(s):  
Analytical Method ◽  
Natural Frequencies ◽  
Equivalent Stiffness ◽  
Additional Mass ◽  
Stator Core ◽  
Content Type ◽  
Switched Reluctance ◽  
Analogy Method ◽  
Reluctance Motor ◽  
3D Fea

Purpose An improved analytical method for calculating the natural frequencies of a switched reluctance motor (SRM) stator is proposed in this paper. The method is different from traditional analytical methods, which only consider the influence of mass of the stator poles and windings on the natural frequencies of the SRM stator. This paper aims to consider the influence of stiffness and mass of the stator poles and windings simultaneously and reasonably. Design/methodology/approach An innovated analytical method based on the electromechanical analogy method is presented. In the proposed analytical formulae for calculating the natural frequencies, the influence of the windings on natural frequencies is considered by using the springs to simulate the flexible connection between the stator core and windings, and the stator poles are treated as both additional mass and additional equivalent stiffness. Both three-dimensional (3D) finite-element analysis (FEA) and experimental modal analysis results validate the improved method. Findings The influence of the mass and stiffness of stator winding is considered by using the springs to simulate the flexible connection between the stator core and windings, and the stator poles are treated as both additional mass and additional equivalent stiffness. The traditional analytical method only considers the influence of mass. Therefore, the calculation results are comparatively lower than 3D FEA results and may lead to a large error. The 3D FEA and experimental modal analysis confirm that the proposed method has good precision for low-order natural frequency calculation of SRMs. Originality/value An improved analytical method for calculating the natural frequencies of an SRM stator is proposed. Unlike the traditional analytical method, the proposed method can consider the influence of stiffness and mass of the stator poles and windings. This method is valuable for designers to predict the natural frequencies accurately.

scholarly journals Somes problems in the identification of elastic beam by the dynamical characteristics

1995 ◽  
Vol 17 (3) ◽  
pp. 20-26
Author(s):  
Nguyen Tien Khiem
Keyword(s):  
Boundary Condition ◽  
Mechanical System ◽  
Unique Solution ◽  
Analytical Method ◽  
Natural Frequencies ◽  
Elastic Beam ◽  
Dynamical Characteristics

Two problems in the identification of Mechanical system are presented and solved by the analytical method. Firstly, the length of an elastic beam is found from measured natural frequencies. Secondly, the boundary condition of the beam was also obtained with given frequencies. In both the cases, unique solution can be found only with condition, that is given in this paper.

A Study on the Natural Frequencies of Coupled In-Line Towers

1991 ◽  
Vol 113 (1) ◽  
pp. 81-85
Author(s):  
N. Qingde ◽  
C. Jiaqi ◽  
Z. Mingxian ◽  
H. Zenyan
Keyword(s):  
Experimental Data ◽  
Dynamic Analysis ◽  
Analytical Method ◽  
Natural Frequencies ◽  
Wind Loads ◽  
Seismic Loads ◽  
Wind Induced Vibration ◽  
Theoretical Results ◽  
Good Agreement

The natural frequencies of the coupled in-line towers are the most important parameters for dynamic analysis when the designer takes steps to assure that damages due to wind loads, seismic loads, or wind-induced vibration would not occur. In this paper the authors present an analytical method for determining these parameters. The theoretical results are compared with the experimental data obtained from the industrial towers in the field, and are in good agreement.

Vibration of the Rotor Shell in a Trochoidal-Type Machine Without Apex Seals

1998 ◽  
Author(s):  
Shuangqing Li ◽  
John B. Shung ◽  
Randall F. Barron
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cylindrical Shell ◽  
Dynamic Response ◽  
Analytical Method ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Type Machine ◽  
Element Method

Abstract The natural frequencies and dynamic response of a trochoidal cylindrical shell in a trochoidal-type machine are studied. Both analytical method and finite element method (FEM) solutions are obtained. The mode shapes obtained by the two approaches match quite well. The model established can be applied to control the running clearance between rotor and chamber in this type of machine, which is critical to the performance of the machine.

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