An Analytical Method for Calculating the Natural Frequencies of a Motor Considering Orthotropic Material Parameters

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.

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UNCOUPLED VIBRATIONS IN FUNCTIONALLY GRADED TIMOSHENKO BEAM

Vietnam Journal of Science and Technology ◽

10.15625/0866-708x/54/6/7719 ◽

2016 ◽

Vol 54 (6) ◽

pp. 785 ◽

Cited By ~ 2

Author(s):

Nguyen Tien Khiem ◽

Nguyen Ngoc Huyen

Keyword(s):

Free Vibration ◽

Timoshenko Beam ◽

Natural Frequencies ◽

Flexural Vibration ◽

Functionally Graded ◽

Mode Shapes ◽

Power Law Distribution ◽

Material Parameters ◽

Flexural Vibrations ◽

Fgm Beam

Free vibration of FGM Timoshenko beam is investigated on the base of the power law distribution of FGM. Taking into account the actual position of neutral plane enables to obtain general condition for uncoupling of axial and flexural vibrations in FGM beam. This condition defines a class of functionally graded beams for which axial and flexural vibrations are completely uncoupled likely to the homogeneous beams. Natural frequencies and mode shapes of uncoupled flexural vibration of beams from the class are examined in dependence on material parameters and slendernes

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Identification of orthotropic material parameters for acute, necrotic, fibrotic and remodelling myocardial infarcts in the rat

10.1101/754754 ◽

2019 ◽

Author(s):

Mazin S. Sirry ◽

Laura Dubuis ◽

Neil H. Davies ◽

Jun Liao ◽

Thomas Franz

Keyword(s):

Constitutive Model ◽

Orthotropic Material ◽

Constitutive Models ◽

Biaxial Stress ◽

Percentage Error ◽

Fe Model ◽

Stress Strain ◽

Material Parameters ◽

Strain Data ◽

Tensile Experiment

AbstractFinite element (FE) models have been effectively utilized in studying biomechanical aspects of myocardial infarction (MI). Although the rat is a widely used animal model for MI, there is a lack of material parameters based on anisotropic constitutive models for rat myocardial infarcts in literature. This study aimed at employing inverse methods to identify the parameters of an orthotropic constitutive model for myocardial infarcts in the acute, necrotic, fibrotic and remodelling phases utilizing the biaxial mechanical data developed in a previous study. FE model was developed mimicking the setup of the biaxial tensile experiment. The orthotropic case of the generalized Fung constitutive model was utilized to model the material properties of the infarct. The parameters of Fung model were optimized so that the FE solution best fitted the biaxial experimental stress-strain data. A genetic algorithm was used to minimize the objective function. Fung orthotropic material parameters for different infarct stages were identified. The FE model predictions best approximated the experimental data of the 28 days infarct stage with 3.0% mean absolute percentage error. The worst approximation was for the 7 days stage with 3.6% error. This study demonstrated that the experimental biaxial stress-strain data of healing rat infarcts could be successfully approximated using inverse FE methods and genetic algorithms. The material parameters identified in this study will provide an essential platform for FE investigations of biomechanical aspects of MI and the development of therapies.

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

Journal of Mechanical Engineering Science ◽

10.1243/jmes_jour_1968_010_044_02 ◽

1968 ◽

Vol 10 (3) ◽

pp. 294-298 ◽

Cited By ~ 3

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.

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Free Vibration Analysis of Rings via Wave Approach

Shock and Vibration ◽

10.1155/2018/6181204 ◽

2018 ◽

Vol 2018 ◽

pp. 1-14

Author(s):

Wang Zhipeng ◽

Liu Wei ◽

Yuan Yunbo ◽

Shuai Zhijun ◽

Guo Yibin ◽

...

Keyword(s):

Free Vibration ◽

Vibration Analysis ◽

Natural Frequencies ◽

Classical Method ◽

Free Vibration Analysis ◽

Material Parameters ◽

Wave Approach ◽

Out Of Plane ◽

Vibration Transmissibility ◽

Ring Structures

Free vibration of rings is presented via wave approach theoretically. Firstly, based on the solutions of out-of-plane vibration, propagation, reflection, and coordination matrices are derived for the case of a fixed boundary at inner surface and a free boundary at outer surface. Then, assembling these matrices, characteristic equation of natural frequency is obtained. Wave approach is employed to study the free vibration of these ring structures. Natural frequencies calculated by wave approach are compared with those obtained by classical method and Finite Element Method (FEM). Afterwards natural frequencies of four type boundaries are calculated. Transverse vibration transmissibility of rings propagating from outer to inner and from inner to outer is investigated. Finally, the effects of structural and material parameters on free vibration are discussed in detail.

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A New Analytical Method for Spherical Thin Shells’ Axisymmetric Vibrations

Mathematical Problems in Engineering ◽

10.1155/2020/1074236 ◽

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.

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

Shock and Vibration ◽

10.1155/2017/9125045 ◽

2017 ◽

Vol 2017 ◽

pp. 1-10 ◽

Cited By ~ 1

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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Guided ultrasonic waves for determining effective orthotropic material parameters of continuous-fiber reinforced thermoplastic plates

Ultrasonics ◽

10.1016/j.ultras.2017.10.005 ◽

2018 ◽

Vol 84 ◽

pp. 53-62 ◽

Cited By ~ 8

Author(s):

Manuel Webersen ◽

Sarah Johannesmann ◽

Julia Düchting ◽

Leander Claes ◽

Bernd Henning

Keyword(s):

Orthotropic Material ◽

Ultrasonic Waves ◽

Fiber Reinforced ◽

Continuous Fiber ◽

Material Parameters ◽

Guided Ultrasonic Waves

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TORSION OF FUNCTIONALLY GRADED OPEN-SECTION MEMBERS

International Journal of Applied Mechanics ◽

10.1142/s1758825112500202 ◽

2012 ◽

Vol 04 (02) ◽

pp. 1250020 ◽

Cited By ~ 7

Author(s):

M. R. HEMATIYAN ◽

E. ESTAKHRIAN

Keyword(s):

Shear Modulus ◽

Cross Section ◽

Analytical Method ◽

Functionally Graded ◽

Torsion Problem ◽

Uniform Thickness ◽

Analytical Formulation ◽

Material Parameters ◽

Open Section ◽

Open Cross Section

There exist some approximate analytical methods for torsion analysis of homogeneous open cross-section members; however, no analytical formulation has been presented for solving a torsion problem of inhomogeneous open cross-section members yet. In this paper, an approximate analytical method for the torsion analysis of thin- to moderately thick-walled functionally graded open-section members with uniform thickness is presented. The shear modulus of rigidity is assumed to have a variation across the thickness. The cross-section is decomposed into some straight, curved and end segments. The torsion problem is then solved in each segment considering some appropriate approximations. By presenting three examples, accuracy of the presented method with respect to thickness, corner radius, and material parameters are investigated. The results show that the proposed method is useful for torsion analysis of thin- to moderately thick-walled functionally graded open-section members.

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Effects of Tension–Compression Asymmetry on Bending of Steels

Applied Sciences ◽

10.3390/app10093339 ◽

2020 ◽

Vol 10 (9) ◽

pp. 3339 ◽

Cited By ~ 1

Author(s):

Hamed Mehrabi ◽

Richard (Chunhui) Yang ◽

Baolin Wang

Keyword(s):

Analytical Method ◽

Metal Forming ◽

Yield Function ◽

Asymmetry Coefficient ◽

Pure Bending ◽

Material Parameters ◽

Mechanical Responses ◽

Tension Compression Asymmetry ◽

Full Loading ◽

Good Agreement

Stainless steels (SUS) and dual-phase (DP) steels have tension-compression asymmetry (TCA) in mechanical responses to full loading cycles. This phenomenon can significantly influence sheet metal forming of such metals, however, it is difficult to describe this behaviour analytically. In this research, a novel analytical method for asymmetric elastic-plastic pure bending using the Cazacu–Barlat 2004 asymmetric yield function is proposed. It only uses material parameters in tension along with an asymmetry coefficient related to the yield function. Bending operations of SUS304 and DP980 are investigated as two case studies. In the pure bending for both SUS304 and DP980, moment–curvature diagrams are analytically obtained. Furthermore, linear and nonlinear springback behaviours of SUS304 are analytically investigated. Moreover, using the analytical model as a user-defined material, a numerical model is developed for both steels under pure bending. In the V-bending case of SUS304 with and without TCA effects, the springback behaviours of the material are investigated numerically. In addition, considering friction effects, the analytical method is further modified for predicting springback behaviours in the V-bending of 16 types of SUS304 with various strengths are determined. All the analytical and numerical results have good agreement with those experimental results from literature for validation.

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