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.

scholarly journals Identification of dynamical characteristics for distributed parameters systems from measured vibration data

1995 ◽  
Vol 17 (1) ◽  
pp. 35-44
Author(s):  
Nguyen Tien Khiem ◽  
Dao Nhu Mai ◽  
Nguyen Van Dac ◽  
Nguyen Viet Khoa
Keyword(s):  
Natural Frequencies ◽  
Damping Ratio ◽  
Elastic Beam ◽  
Mode Shapes ◽  
Vibration Data ◽  
Dynamical Characteristics ◽  
Distributed Parameters

This article is devoted to determinate the dynamical characteristics (Natural Frequencies, Mode Shapes, Damping Ratio) of elastic beam from measured responce auto-spectrum. Developed here method is based on the assumptions of smallness of the damping and sparse distribution of natural frequencies. Accuracy and practical meaning of the method are confirmed by the agreement of the theory with experiments.

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.

scholarly journals Isospectrals of non-uniform Rayleigh beams with respect to their uniform counterparts

2018 ◽  
Vol 5 (2) ◽  
pp. 171717 ◽  
Author(s):  
Srivatsa Bhat K ◽  
Ranjan Ganguli
Keyword(s):  
Boundary Condition ◽  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Beam Equation ◽  
The Finite Element Method ◽  
Rayleigh Beam ◽  
Uniform Beam ◽  
Governing Differential Equation ◽  
The Given

In this paper, we look for non-uniform Rayleigh beams isospectral to a given uniform Rayleigh beam. Isospectral systems are those that have the same spectral properties, i.e. the same free vibration natural frequencies for a given boundary condition. A transformation is proposed that converts the fourth-order governing differential equation of non-uniform Rayleigh beam into a uniform Rayleigh beam. If the coefficients of the transformed equation match with those of the uniform beam equation, then the non-uniform beam is isospectral to the given uniform beam. The boundary-condition configuration should be preserved under this transformation. We present the constraints under which the boundary configurations will remain unchanged. Frequency equivalence of the non-uniform beams and the uniform beam is confirmed by the finite-element method. For the considered cases, examples of beams having a rectangular cross section are presented to show the application of our analysis.

Finite Element Analysis for the Crankshaft of the Piston Compressor

2010 ◽  
Vol 102-104 ◽  
pp. 17-21
Author(s):  
Bin Zhao
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Piston Compressor ◽  
Element Model ◽  
Ansys Software ◽  
Element Analysis ◽  
Rotating Speed ◽  
Dynamical Characteristics ◽  
The Finite Element Model

In order to study the static and dynamical characteristics of the crankshaft, ANSYS software was used to carry out the corresponding calculations. The entity model of the crankshaft was established by UG software firstly, and then was imported into ANSYS software for meshing, and then the finite element model of the crankshaft was constructed. The crankshaft satisfied the requirement of stiffness and strength through static analysis. The top six natural frequencies and corresponding shapes were acquired through modal analysis, and the every order critical rotating speed of the crankshaft was calculated. The fatigue life of the crank was calculated by fatigue module of ANSYS software finally. These results offered the theoretical guidance for designing, manufacturing and repairing the crankshaft.

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 Boundary condition modelling and identification for cantilever-like structures using natural frequencies

2019 ◽  
Vol 32 (6) ◽  
pp. 1451-1464 ◽  
Author(s):  
Wei LIU ◽  
Zhichun YANG ◽  
Le WANG ◽  
Ning GUO
Keyword(s):  
Boundary Condition ◽  
Natural Frequencies

A Probabilistic Analysis for Static and Dynamic Frequency of Blade With Uncertain Boundary Conditions

2005 ◽  
Author(s):  
Z. Q. Wang ◽  
L. Q. An ◽  
Z. Z. Peng
Keyword(s):  
Boundary Condition ◽  
Probabilistic Analysis ◽  
Natural Frequencies ◽  
Perturbation Technique ◽  
Ritz Method ◽  
Joint Stiffness ◽  
Matrix Perturbation ◽  
Sensitivity Matrix ◽  
The Matrix ◽  
Uncertain Boundary

A probabilistic analysis method is developed for frequencies analysis of turbine blade with uncertain boundary condition at the root of blade. The Ritz method is used to derive the eigenvalues equation of the rotating blade with uncertain root boundary condition. The matrix perturbation technique is employed for the probabilistic analysis to obtain the deterministic part of natural frequencies and vibration modes, the sensitivity matrix, the covariance matrix and the coefficient of variance (COV) for the natural frequencies. The effects of variations in the expectation and the variance of joint stiffness on the expectation and the variance of the natural frequencies are investigated.

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.

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