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  1. 26 Vibrations in Physical Systems
  2. 10 Scientific Letters of Rzeszow University of Technology. Mechanics
  3. 10 Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika
  4. 9 Journal of Applied Mathematics and Computational Mechanics
  5. 9 Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
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  1. 14 Szmidla J.
  2. 13 Kukla S.
  3. 10 Tomski L.
  4. 9 Uzny S.
  5. 8 Posiadała B.
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  1. 2 2023
  2. 3 2022
  3. 4 2021
  4. 3 2020
  5. 3 2019
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1
Content available 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.
2
Content available remote 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.
3
Content available A discrete model for geometrically nonlinear free and forced vibrations of stepped and continuously segmented Euler-Bernoulli AFG beams (SAFGB) carrying point masses
Moukhliss Anass, Rahmouni Abdellatif, Bouksour Othman, Benamar Rhali
Diagnostyka
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2022
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Vol. 23, No. 4
art. no. 2022401
EN
A discrete model is applied to handle the geometrically nonlinear free and forced vibrations of beams consisting of several different segments whose mechanical characteristics vary in the length direction and contain multiple point masses located at different positions. The beam is presented by an N degree of freedom system (N-Dof). An approach based on Hamilton's principle and spectral analysis is applied, leading to a nonlinear algebraic system. A change of basis from the displacement basis to the modal basis has been performed. The mechanical behavior of the N-Dof system is described in terms of the mass tensor mij, the linear stiffness tensor kij, and the nonlinear stiffness tensor bijkl. The nonlinear vibration frequencies as functions of the amplitude of the associated vibrations in the free and forced cases are predicted using the single mode approach. Once the formulation is established, several applications are considered in this study. Different parameters control the frequency-amplitude dependence curve: the laws that describe the variation of the mechanical properties along the beam length, the number of added masses, the magnitude of excitation force, and so on. Comparisons are made to show the reliability and applicability of this model to non-uniform and non-homogeneous beams in free and forced cases.
4
Content available remote Nonlinear free vibration and transient responses of porous functionally graded magneto-electro-elastic plates
Sh Esayas L., Kattimani Subhaschandra, Vinyas M.
Archives of Civil and Mechanical Engineering
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2022
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Vol. 22, no. 1
art. no. e38, 2022
EN
The geometrically nonlinear free vibration and transient response of porous functionally graded magneto-electro-elastic (PFG-MEE) plates are studied based on the first-order shear deformation (FSDT) theory, von Karman's nonlinear strain–displacement relations along with modified power law. With Hamilton's theory, the coupled equations of motion are obtained and analyzed by adapting finite element methods (FEM). Moreover, using Newmark's, Picard's, and Newton–Raphson methods, a porous FG-MEE plate's nonlinear and transient response is analyzed using MATLAB software. After validating the present study, the influence of porosity distribution, porosity index, boundary conditions, aspect ratios, and thickness to length ratios on the nonlinear frequency ratio and nonlinear transient response of porous FG-MEE plate is investigated. It is revealed that geometric parameters, porosity index, boundary conditions, and form of porosity distribution significantly influence the nonlinear frequency ratio and nonlinear transient deflections of porous FG-MEE plates.
5
Content available remote 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.
6
Content available remote 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.
7
Content available 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.
8
Content available 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%.
9
Content available 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%.
10
Content available Influence of temperature on dynamic properties of plates with viscoelastic dampers
Lenartowicz Agnieszka, Przychodzki Maciej
Vibrations in Physical Systems
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2020
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Vol. 31, nr 3
art. no. 2020310
EN
The free damped vibrations of thin (Kirchhoff-Love) plates equipped with viscoelastic dampers are considered in the paper. It is assumed that the dampers are described according to the generalized rheological model. Influence of temperature on the parameters of dampers is taken into account using the frequency-temperature correspondence principle. Isotropic and rectangular plates are analysed in numerical tests included in this study. The natural frequencies and non-dimensional damping ratios are determined for these plates by solving the non-linear eigenproblem using the continuation method. The Finite Element Method is used to determine the stiffness matrix and the mass matrix occurring in the considered eigenproblem. The results of exemplary numerical calculations are presented and discussed at the end of this paper.
11
Content available Liquid vibrations in cylindrical tanks with and without baffles under lateral and longitudinal excitations
Strelnikova E., Kriutchenko D., Gnitko V., Tonkonozhenko A.
International Journal of Applied Mechanics and Engineering
|
2020
|
Vol. 25, no. 3
117--132
EN
The paper is devoted to issues of estimating free surface elevations in rigid cylindrical fluid-filled tanks dunder external loadings. The possibility of baffles installation is provided. The liquid vibrations caused by lateral and longitudinal harmonic loadings are under consideration. Free, forced and parametrical vibrations are examined. Modes of the free liquid vibrations are considered as basic functions for the analysis of forced and parametric vibrations. The modes of the free liquid vibrations in baffled and un-baffled cylindrical tanks are received by using single-domain and multi-domain boundary element methods. Effects of baffle installation are studied. The problems of forced vibrations are reduced to solving the systems of second order ordinary differential equations. For parametric vibrations the system of Mathieu equations is obtained. The numerical simulation of free surface elevations at different loadings and baffle configurations is accomplished. Beat phenomena effects are considered under lateral harmonic excitations. The phenomenon of parametric resonance is examined under longitudinal harmonic excitations.
12
Content available 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
|
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.
13
Content available Nonlinear vibrations of the partially tensioned system taking into account the asymmetry of the stiffness of supports
Uzny Sebastian, Osadnik Michał
Vibrations in Physical Systems
|
2019
|
Vol. 30, nr 2
art. no. 2019217
EN
The nonlinear vibrations of the partially tensioned slender column are presented in this paper. The considered system is subjected to Euler’s load, which direction of action is consistent with the non-deformed axis of the column. The magnitude of the external load is variable and its application point is located at different heights between the upper and lower supports. In addition, the longitudinal displacement and rotation of both of the system ends are limited by the discrete elements in the form of translational and rotational springs. This nonlinear system is based on the screw drive used in the vertical lift platform for disabled people or cargo lift equipped with an engine room located in the lower part of the frame. The boundary problem of free vibrations of the mentioned system has been formulated on the basis of Bernoulli - Euler theory and due to nonlinear expressions the solution of the problem was conducted with small parameter method. The results of numerical simulations are concern on linear and nonlinear component of vibrations in relation to the location of external load application and influence of asymmetric value of supports stiffness on the free vibration frequency.
14
Content available Free vibrations of the column taking into account compressive and thermal load
Uzny Sebastian, Kutrowski Łukasz, Skrzypczak Tomasz
Vibrations in Physical Systems
|
2019
|
Vol. 30, nr 2
art. no. 2019211
EN
Free vibrations of slender systems are the subject of many scientific and research works. In this work, the boundary problem of free vibrations of a compressed column, which is additionally heat loaded, is considered. The issue of heat flow in the column is solved using the Finite Element Method. Averaged distribution of material properties is obtained in individual segments of the column in subsequent heating times. The mathematical model of free vibrations takes into account the thermal expansion of the material and the effect of changing the Young's modulus resulting from the effect of heat load. The boundary problem of the free vibrations of the considered system is limited to the linear range (the linear component of natural frequency is considered). The influence of the heat source exposure time on the course of characteristic curves (on the plane: load – natural frequency) is determined. The results are presented for various column diameters.
15
Content available Transverse vibration analysis of nonlocal beams with various slenderness ratios, undergoing thermal stress
Babaei Alireza, Rahmani Arash, Ahmadi Isa
Archive of Mechanical Engineering
|
2019
|
Vol. LXVI, nr 1
5--24
EN
In this paper, thermally-excited, lateral free vibration analysis of a small-sized Euler-Bernoulli beam is studied based on the nonlocal theory. Nonlocal effect is exerted into analysis utilizing differential constitutive model of Eringen. This model is suitable for design of sensors and actuators in dimensions of micron and submicron. Sudden temperature rise conducted through the thickness direction of the beam causes thermal stresses and makes thermo-mechanical properties to vary. This temperature field is supposed to be constant in the lateral direction. Temperatures of the top and bottom surfaces of the system are considered to be equal to each other. Governing equation of motion is derived using Hamilton’s principle. Numerical analysis of the system is performed by Galerkin’s approach. For verification of the present results, comparison between the obtained results and those of benchmark is reported. Numerical results demonstrate that dynamic behavior of small-sized system is been effected by temperature shift, nonlocal parameter, and slenderness ratio. As a result, taking the mentioned parameters into account leads to better and more reliable design in miniaturized-based industries.
16
Content available remote On the modeling of periodic sandwich structures with the use of the broken line hypothesis
Marczak J.
Mechanics and Mechanical Engineering
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2018
|
Vol. 22, nr 3
761--773
EN
In this paper a dynamic analysis of sandwich plate with a certain periodic microstructure is considered. The initial system of governing equations is derived basing on the classic broken line hypothesis. As a result of transformations one can obtain a system of three differential equations of motion with periodic, highly oscillating and non-continuous coefficients. In order to derive a system of equations with constant coefficients tolerance averaging technique is applied. Eventually, in the calculation example a free vibration analysis of certain periodic plate strip is performed with the use of both the derived model and a FEM model. It can be observed that the consistency of obtained results is highly dependent on the calculation assumptions.
17
Content available Study on harmonic analysis of functionally graded plates using FEM
Sharma A. K., Sharma P., Chauhan P. S., Bhadoria S. S.
International Journal of Applied Mechanics and Engineering
|
2018
|
Vol. 23, no. 4
941--961
EN
This paper presents the harmonic and vibration analysis of functionally graded plates using the finite element method. Initially, the plates are assumed isotropic and the material properties of it are assumed to vary continuously through their thickness direction according to a power-law distribution of the volume fractions of the plate constituents. The four noded shell element is used to analyse the functionally graded plates. Four functionally graded plates-Al/Al2O3, Al/ZrO2, Ti–6Al–4V/Aluminium oxide, and SUS304/Si3N4 are considered in the study, and their results are obtained so that the right choice can be made in applications in high temperature environment and in reducing the vibration amplitudes in applications such as aircrafts, rockets, missiles, etc. Numerical results for the natural frequency and harmonic response amplitude are presented. Results are compared and validated with available results in the literature. Effects of boundary conditions, material and damping on natural frequency and harmonic response of the functionally graded plates are also investigated.
18
Content available The analysis of non-linear free vibration of FGM nano-beams based on the conformable fractional non-local model
Rahimi Z., Sumelka W., Shafiei S.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2018
|
Vol. 66, nr 5
737--745
EN
Continuum models generalized by fractional calculus are used in different mechanical problems. In this paper, by using the conformable fractional derivative (CFD) definition, a general form of Eringen non-local theory as a fractional non-local model (FNM) is formulated. It is then used to study the non-linear free vibration of a functional graded material (FGM) nano-beam in the presence of von-Kármán non-linearity. A numerical solution is obtained via Galerkin and multiple scale methods and effects of the integer and non-integer (fractional) order of stress gradient (in the non-local stress-strain relation) on the ratio of the non-local non-linear natural frequency to classical non-linear natural frequency of simply-supported (S-S) and clamped-free (C-F) FGM nano-beams are presented.
19
Content available A Fundamental Study on the Free Vibration of Geometrical Nonlinear Cantlever Beam using an Exact Solution and Experimental Investigation
Jamal-Omidi M., Shayanmehr M., Sazesh S.
Archive of Mechanical Engineering
|
2018
|
Vol. LXV, nr 1
65--82
EN
Two fundamental challenges in investigation of nonlinear behavior of cantilever beam are the reliability of developed theory in facing with the reality and selecting the proper assumptions for solving the theory-provided equation. In this study, one of the most applicable theory and assumption for analyzing the nonlinear behavior of the cantilever beam is examined analytically and experimentally. The theory is concerned with the slender inextensible cantilever beam with large deformation nonlinearity, and the assumption is using the first-mode discretization in dealing with the partial differential equation provided by the theory. In the analytical study, firstly the equation of motion is derived based on the theory of large deformable inextensible beam. Then, the partial differential equation of motion is discretized using the Galerkin method via the assumption of the first mode. An exact solution to the obtained nonlinear ordinary differential equation is developed, because the available semi analytical and approximated methods, due to their limitations, are not always sufficiently reliable. Finally, an experiment set-up is developed to measure the nonlinear frequency of oscillations of an aluminum beam within a domain of initial displacement. The results show that the proposed analytical method has excellent convergence with experimental data.
20
Content available remote Application of the homotopy analysis method for determining the free vibrations of beam
Gromysz K., Słota D.
Architecture Civil Engineering Environment
|
2018
|
Vol. 11, no. 1
61--71
EN
In this paper we present the application of the homotopy analysis method for determining the free vibrations of the simply supported beam. The linear and nonlinear cases are considered. The homotopy analysis gives the possibility to search for the solution of a wide range of problems described by means of the operator equations. The numerical examples are presented to confirm the exactness and fast convergence of the introduced method. The presented computational examples confirm the precision and the fast convergence of investigated method. In the linear case we knew the exact solutions, so we could compare with them the solutions obtained with the aid of homotopy analysis method. Differences between the obtained solutions were slight. However, the advantage of the examined method is that we receive here the approximate solution in the form of continuous function which can be used then in a further analysis or to perform various simulations.
PL
W artykule przedstawiono homotopijną metodę analizy równań opisujących drgania swobodne układu o jednym stopniu swobody opisane równaniami liniowymi oraz nieliniowymi. Homotopijna metoda analizy daje możliwość poszukiwania rozwiązania szerokiego zakresu problemów opisanych za pomocą równań operatorowych. W artykule przedstawiono przykłady liczbowe w celu potwierdzenia dokładności i szybkiej zbieżności metody. W przypadku liniowym znane było dokładne rozwiązanie, dzięki czemu można było porównać je z rozwiązaniami uzyskanymi za pomocą analizy homotopijnej. Różnice między otrzymanymi roztworami były niewielkie. Zaletą badanej metody jest jednak to, że otrzymano przybliżone rozwiązania w postaci ciągłych funkcji, które można wykorzystać w dalszych analizach, w tym do interpretacji wyników badań doświadczalnych.
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