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1

Frequency-based crack effect study on beams under free vibration using finite element analysis

Sahu Ompriya, Das Priyadarshi, Muni Manoj Kumar, Pradhan Nibedita, Basa Bidyadhar, Sahu Shishir Kumar

Engineering Transactions

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2024

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Vol. 72, iss. 1

95--114

EN

A numerical computation-based analysis of the free vibration analysis of uniform beams with rectangular cross-sections is presented in this work using finite element analysis. The approach involves dividing the beam into segments at the crack section, which is then modelled for simulation for eigenfrequencies on the ABAQUS platform. The numerical simulation results are in excellent agreement with the findings of previous research, confirming the efficacy and applicability of the developed beam model. A sequential comprehensive approach towards analysis of the effects of the position and depth of the cracks on the natural frequencies are addressed in numerical results. The research findings confirm that the simulation model is suitable for the vibration analysis of beams or beam-like elements with different cross-sections.

2

Analysis of out-of-plane free vibration of single damaged curved beam based on precise algorithm of structural mechanics

Li Xiaofei, Pan Zhouyang, Guo Hainan

Journal of Theoretical and Applied Mechanics

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2023

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Vol. 61 nr 2

407--414

EN

Based on a dynamic discrete model of an out-of-plane curved beam with a constant cur- vature, eigen-properties of the spatial curved beam structure in undamaged and damaged configurations are considered in this paper. In the literature, based on the equivalent sec- tion reduction method, a distributed damage modeling method is proposed. Accoding to Euler-Bernoulli beam theory, the stiffness matrix of shear, bending and torsion coupling is derived. Combined with the lumped mass matrix and the characteristic equation of the multi degree of freedom system, natural frequencies of the undamaged and damaged structures are calculated.

3

Free vibration of a two-stage hydraulic cylinder

Uzny Sebastian, Adamek Franciszek, Kutrowski Łukasz

Journal of Applied Mathematics and Computational Mechanics

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2023

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Vol. 22, nr 1

70--81

EN

This paper presents the problem of natural vibration of a two-stage hydraulic cylinder subjected to Euler compression load. The considered hydraulic cylinder is freely supported at both of its ends. The linear vibration problem of the telescopic hydraulic cylinder is based on the kinetic stability criterion using Hamilton’s principle and the Bernoulli-Euler theory. The stiffness of the guide and sealing elements between successive stages of the hydraulic cylinder were considered in this paper. These stiffnesses were modelled using translational and rotational springs. The effects of cylinder wall thickness, piston rod diameter, and thickness of guiding and sealing elements on the natural vibration of the system were analysed. Results are presented in the form of characteristic curves on the plane load – natural frequency with different parameters characterizing the considered hydraulic cylinder.

4

Effects of non-classical boundary conditions on the free vibration response of a cantilever Euler-Bernoulli beams

Afras Abderrachid, El Ghoulbzouri Abdelouafi

Diagnostyka

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2023

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Vol. 24, No. 1

art. no. 2023107

EN

In this article, the problem of the free vibration behavior of a cantilever Euler-Bernoulli beam with various non-classical boundary conditions, such as rotational, translational spring, and attached mass is investigated. For describing the differential equation of the system. An analytical procedure is proposed firstly, and a numerical method based on the differential transform method DTM is developed in order to validate the obtained results. A parametric study for various degenerate cases is presented with the aim to analyze the influence of rotational stiffness, vertical stiffness, and mass ratio on the free vibration response of the beam, particularly on its modal characteristics. The results show that the non-classical boundary conditions significantly affect the natural frequency and mode shapes of the studied beam system in comparison to the case of a classical boundary conditions such as Simply supported, clamped-clamped, etc. The comparison between the obtained results based on the proposed analytical solution and numerical scheme, and those available in the literature shows an excellent agreement.

5

Free flexural vibration of a sandwich beam on an elastic foundation with variable properties

Magnucki K., Wstawska I., Kedzia P.

Archives of Mechanics

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2023

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Vol. 75, nr 6

619--646

EN

Free flexural vibration of a simply supported sandwich beam on an elastic foundation is the main purpose of the presented investigation. An analytical model of multi-layered beam on elastic foundation has been prepared. The authors submitted an original beam-foundation interaction model which based on variable parameters of the foundation and their influence on the beam response. This explanation leads to the possibility of continuous characterization of the beam-foundation interplay. A nonlinear mathematical function for symmetrical properties of the foundation has been adopted. The frequency equation as a function of geometric and mechanical properties of the beam and the parameters of the elastic foundation was derived using the Galerkin method. The analytical investigation has been divided into two parts: the analysis of elastic foundation with constant and variable properties. The unconventional shape function and the function of deflection have been introduced and employed. Moreover, the finite element analysis has been performed. Sample analytical and numerical calculations have been performed, demonstrating a good concurrence between both models. The difference between analytical and numerical values of the fundamental natural frequency did not exceed 0:5%.

6

Bending and free vibration analysis of porous functionally graded sandwich plate with various porosity distributions using an extended layerwise theory

Belarbi Mohamed-Ouejdi, Daikh Ahmed Amine, Garg Aman, Hirane Hicham, Houari Mohammed Sid Ahmed, Civalek Ömer, Chalak H. D.

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 1

art. no. e15, 2023

EN

In this paper, for the first time, the bending and free vibration analysis of porous functionally graded sandwich plates with various porosity distributions is investigated using an efficient layerwise model. The present model, proposed recently by the authors, supposes a first-order displacement field for the two face sheets and a higher-order displacement field for the core, thereby ensuring the displacement continuity at the layer's interface. Unlike the conventional layerwise models, the number of degrees of freedom is fixed and does not increase when increasing the number of layers. This is a very important feature compared to the conventional layerwise models and facilitates significantly the engineering analysis. Three different types of porosity distribution including even, logarithmic-uneven, and linear-uneven porosities are considered. The material properties of the FGM sandwich porous plate are graded continuously through the thickness direction according to a power-law function. The numerical analysis is carried out by using an efficient C0 continuous eight-node quadrilateral isoparametric element developed for this purpose. The governing equations are derived according to Hamilton’s principle and solved by employing the finite element method. The robustness and accuracy of the proposed formulation are ascertained by comparing its results with those available by other researchers in the existing literature. Further, a comprehensive parametric study is examined in detail to show the effects of material distribution, aspect ratios, porosity coefficient, side-to-thickness ratio, porosity distribution, core-to-face thickness ratio, boundary conditions, volume fraction index, modes shapes on the bending and free vibration behaviors of symmetric and non-symmetric FGM porous sandwich plate. The numerical results show that these parameters play significant roles in the bending and free vibration behaviors of the FGM sandwich porous plates. Many new results are also reported, which will serve as a benchmark for future analysis of FGM sandwich plates with porosity.

7

Free vibration of composite cylindrical shells with orthogonal stiffeners

Wu Yongfu, Zhao Chen, Liang Haofeng, Yao Sishi, Xue Jianghong, Xu Peng

Journal of Theoretical and Applied Mechanics

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2022

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Vol. 60 nr 2

239--252

EN

This paper proposes theoretical and numerical approaches to scrutinize the free vibration of orthogonal stiffened cylindrical shells. According to K´arman-Donnell shell theory, the total energy of the stiffened cylindrical shells is derived. Based on the principle of minimum potential energy, the eigenfunction related to the frequency is established and solved by developing a Matlab program. Analytical solutions of the natural frequency for free vibraion of the stiffened cylindrical shells are calculated and are verified against the finite element results from ABAQUS software. On account of the observations from the parametric study, an optimization scheme of the stiffeners is proposed.

8

Free vibration and buckling analysis of composite laminated shells using the refined zigzag theory

Zhang Haibo, Gao Yihang, He Dan, Yang Wanli

Journal of Theoretical and Applied Mechanics

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2022

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Vol. 60 nr 3

435--448

EN

In this study, a new composite laminated shell model is proposed for free vibration and stability analysis based on the refined zigzag theory (RZT). In contrast to the published shell models based on the first-order shear deformation theory (FSDT), piecewise-linear zigzag functions are utilized to provide a more realistic representation of deformation states of a transverse shear-flexible shell. In the present formulation, the governing equations and boundary conditions of composite laminated shells are established by d’Alembert’s principle to obtain natural frequencies and critical buckling loadings. In order to evaluate the effectiveness and performance of the present new model for composite laminated shells, examples of free vibration and buckling analysis are carried out for cylindrical and spherical shells involving different lamination schemes and design parameters. The results are compared with the three dimensional (3D) exact, first-order and some high-order solutions in the literature. Numerical results show that the present model not only has high accuracy but also has superior computational efficiency in comparison with high-order models, such that it may show a great potential in engineering applications.

9

A modified Fourier-Ritz method for free vibration of rectangular plates with elastic constrains

Wu Tao, Chen Zhao Bo, Qu Jian Jun

Journal of Theoretical and Applied Mechanics

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2022

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Vol. 60 nr 1

77--89

EN

In this paper, a modified Fourier-Ritz method is used to study free vibration of a rectangular plate with a set of simply supported opposite sides and another set of arbitrary elastic constraints. The influence of different elastic constraint stiffness values on the modal response of the rectangular plate is also analyzed. In order to avoid that the displacement function of the rectangular plate calculated by the traditional method and its derivative may be discontinuous or non-derivable at the boundary, the displacement function is expressed in the form of the sum of standard cosine series and a periodic polynomial function. Compared with the sine series expansion, the convergence of the result is enhanced. Several sets of numerical examples with different boundary conditions are given in the article, the data shows that the results calculated by this method have good accuracy and fast convergence. In addition, this paper also analyzes the boundary conditions and discusses the influence of different spring stiffness values on the setting of boundary conditions. The results can be applied to the setting of general boundary conditions and the study of vibration control of rectangular plates.

10

Wave propagation and free vibration of FG graphene platelets sandwich curved beam with auxetic core resting on viscoelastic foundation via DQM

Al Mukahal F. H. H., Sobhy Mohammed

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 1

art. no. e12, 2022

EN

A novel shear and normal deformations theory is presented in this article to illustrate the wave propagation and free vibration of three-layer sandwich curved beams subjected to elevated temperature and moisture environments and resting on viscoelastic foundation. The upper and lower layers are made of metal matrix reinforced with functionally graded (FG) graphene platelets (GPLs). While, the core layer is made of auxetic honeycomb structures. For the layers to be more bonded, the matrix of the face layers and the auxetic layer are both made of aluminum material. The volume fraction of GPLs is varied through the thickness of the face layers according to a layer-wise rule. The modified Halpin–Tsai model is used to describe the effective material properties of the face layers. Four types of GPLs distribution are considered in the present analysis. The differential quadrature method (DQM) is employed to discretize the equations of motion and then converted to a system of algebraic equations. This system can be solved to obtain the natural frequencies of the sandwich curved beams. Whereas, the wave dispersion relations are determined by solving the motion equations analytically. Convergence and comparison examples are presented to adjust and validate the present solution. In addition, comprehensive parametric studies are performed to investigate the effects of the weight fraction of GPLs, temperature, moisture concentrations, core thickness, boundary conditions, and viscoelastic foundation stiffness on the natural frequency, wave frequency and phase velocity of the honeycomb sandwich curved beams.

11

Electro-magneto-mechanical formulation of a sandwich shell subjected to electro-magneto-mechanical considering thickness stretching

Arefi Mohammad, Mannani Shayan, Collini L.

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 4

art. no. e196, 2022

EN

Thickness stretching included formulation of a multi-layered doubly curved shell in small scale is studied in the present work. Out-of-plane normal strain is accounted in our formulation based on a higher-order theory. Based on this theory, the total transverse deflection is divided into three portions named as bending, shear and stretching parts. Transient formulation of the nanoshell is derived using Hamilton’s principle and nonlocal formulation. The natural frequencies of the nanoshell are obtained in terms of main input parameters, such as initial electric and magnetic potentials, nonlocal parameters, aspect ratio, radii ratio and foundation parameters.

12

A parametric analysis of free vibration and bending behavior of sandwich beam containing an open-cell metal foam core

Garg A., Chalak H. D., Belarbi M. O., Zenkour A. M.

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 1

art. no. e56, 2022

EN

Free vibration and bending behavior of sandwich beams containing open-cell metal foam core are studied in the present work using zigzag theory. Hamilton’s principle and the principle of minimum potential energy are applied for determining the governing equations for free vibration and bending behavior, respectively. Three types of distribution of pores are used during the present study. The influence of the distribution of pores, end condition, thickness of the core, foam coefficients on beam behavior is studied in detail. The face sheets are assumed to be made up of the same material like foam. It was noticed that the nature of the distribution of pores and the end conditions widely determine the behavior of the beam.

13

ANSYS code applied to investigate the dynamics of composite sandwich beams

Chudzik Agnieszka

Mechanics and Mechanical Engineering

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2021

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Vol. 25, nr 1

62--71

EN

A numerical analysis of the effect of temperature on the dynamics of the sandwich beam model with a viscoelastic core is presented. The beam under analysis was described with a standard rheological model. This solution allows one to study the effect of temperature on material strength properties. Calculations were performed with the Finite ElementMethod in the ANSYS software. The analysis of the results of the numerical calculations showed a significant influence of temperature on the strength properties of the model under test. The analysis confirmed damping properties of viscoelastic materials.

14

Axisymmetric free vibration of layered cylindrical shell filled with fluid

Izyan M. D. Nurul, Sabri Nur Ain Ayunni, Hafizah A. K. Nor, Sankar D. S., Viswanathan K. K.

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 4

63--76

EN

The aim of the study is to analyse the axisymmetric free vibration of layered cylindrical shells filled with a quiescent fluid. The fluid is assumed to be incompressible and inviscid. The equations of axisymmetric vibrations of layered cylindrical shell filled with fluid, on the longitudinal and transverse displacement components are obtained using Love’s first approximation theory. The solutions of displacement functions are assumed in a separable form to obtain a system of coupled differential equations in terms of displacement functions. The displacement functions are approximated by Bickley-type splines. A generalized eigenvalue problem is obtained and solved numerically for a frequency parameter and an associated eigenvector of spline coefficients. Two layered shells with three different types of materials under clamped-clamped boundary conditions are considered. Parametric studies are made on the variation of the frequency parameter with respect to length-to-radius ratio and length-to-thickness ratio.

15

Free vibration analysis of multi-span orthotropic bridge deck with rubber bearings

Farah Imed, Rezaiguia Abdelouahab, Mouassa Ahcene, Debra Laefer, Guenfoud Salah

Diagnostyka

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2021

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Vol. 22, No. 1

11--21

EN

In this paper, a semi-analytical approach is proposed for free vibration analysis of a multi-span, orthotropic bridge deck with rubber bearings. This allows more realistic modeling of vibration transmission from a bridge’s deck to its supports. The approach is based on modal superposition incorporating intermodal coupling. The bridge deck was modeled as a continuous, multi-span, orthotropic rectangular plate with equivalent rigidities. The rubber bearings were inserted between the girders and rigid supports to absorb traffic induced vibrations. The rubber bearing was modeled by linear elastic, vertical supports as very flexible in rotation and highly rigid in the vertical direction. The method’s efficacy was validated against two numerical examples. The absolute error was less than 10%.

16

Analytical and numerical free vibration analysis of porous functionally graded materials (FGPMs) sandwich plate using Rayleigh-Ritz method

Njim E.K., Bakhy S.H., Al-Waily M.

Archives of Materials Science and Engineering

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2021

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Vol. 110, nr 1

27--41

EN

Purpose: This study introduces a new approximated analytical solution of the free vibration analysis to evaluate the natural frequencies of functionally graded rectangular sandwich plates with porosities. Design/methodology/approach: The kinematic relations are developed based on the classical plate theory (CPT), and the governing differential equation is derived by employing the Rayleigh-Ritz approximate method. The FGM plate is assumed made of an isotropic material that has an even distribution of porosities. The materials properties varying smoothly in the thickness direction only according to the power-law scheme. Findings: The influences of changing the gradient index, porosity distribution, boundary conditions, and geometrical properties on the free vibration characteristics of functionally graded sandwich plates are analysed. Research limitations/implications: A detailed numerical investigation is carried out using the finite element method with the help of ANSYS 2020 R2 software to validate the results of the proposed analytical solution. Originality/value: The results with different boundary conditions show the influence of porosity distribution on the free vibration characteristics of FG sandwich plates. The results indicated a good agreement between the approximated method such as the Rayleigh-Ritz and the finite element method with an error percentage of no more than 5%.

17

Wpływ rozmiaru otworów drzwiowych i okiennych oraz ich lokalizacji na zmianę częstotliwości drgań własnych i sztywności ściany wykonanej w technologii szkieletu drewnianego

Borowska Klara, Szczepański Marcin

Materiały Budowlane

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2020

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nr 11

31--32

18

Timoshenko beam model for vibration analysis of composite steel-polymer concrete box beams

Niesterowicz Beata, Dunaj Paweł, Berczyński Stefan

Journal of Theoretical and Applied Mechanics

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2020

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Vol. 58 nr 3

799--810

EN

The free vibration model of a steel-polymer concrete beam based on Timoshenko beam theory is presented in this paper. The results obtained on the basis of the model analysis, describing the values of the natural frequencies of the beam vibrations, were compared with the results obtained by the solution of the model formulated on the basis of the classical Euler-Bernoulli beam theory, the finite element model and the results of experimental studies. The developed model is characterized by high compliance with experimental data: the relative error in the case of natural vibration frequencies does not exceed 0.4%, on average 0.2%.

19

Hybrid sandwich panels: a review

Sandeep S. H., Srinivasa C. V.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 3

64--85

EN

A high specific stiffness, high specific strength, and tailoring the properties for specific application hale attracted the attention of the researchers to work in the field of laminated composites and Sandwich structures. Rapid use of these laminated composites and Sandwich structures necessitated the development of new theories that suitable for the bending, buckling and vibration analysis. Many articles were published on free vibration of beams, plates, shells laminated composites and sandwich structures. In this article, a review on free vibration analysis of shear deformable isotropic beams, plates, shells, laminated composites and sandwich structures based on various theories and the exact solution is presented. In addition to this, the literature on finite element modeling of beams, plates, shells laminated composites and sandwich structures based on classical and refined theories is also reviewed. The present article is an attempt to review the available literature, made in the past few decades on free flexural vibration response of Fiber Metal laminated Composites and Sandwich panels using different analytical models, numerical techniques, and experimental methods.

20

Influence of Cast Iron Modification on Free Vibration Frequency of Casting

Konopka Z., Łągiewka M., Zyska A.

Archives of Foundry Engineering

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2020

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Vol. 20, iss. 1

23--26

EN

The paper presents the results of investigations concerning the influence of gray cast iron modification on free vibration frequency of the disc casting. Three different chemical composition melts of gray cast iron were prepared in induction furnace. During gravity casting 0.05% and 0.3% mass of the Inolate modifier was added on stream of metal for changing graphite flakes in castings. Sound signal vibration of cast iron sample was registered by means on microphone for free vibration frequency measurements. Decreasing of free vibration frequency of modified cast iron in comparison with non modified castings was observed. Higher contents of modifier causes more decreasing of free vibration frequency. Cast iron with smaller contents of carbon and silicon have higher free vibration frequency in comparison with eutectic composition cast iron. Hardness of examined cast iron is lower when the more modifier is added during modification process. Free frequency is smaller with smaller Brinell hardness of disc casting. It was concluded that control of free vibration frequency of disc castings by means of chemical composition and modification process can improved comfort and safety of working parts.