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1
Content available 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
|
2022
|
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.
2
Content available Reduced differential transform method for thermoelastic problem in hyperbolic heat conduction domain
Chaudhari K. K., Sutar C. S.
International Journal of Applied Mechanics and Engineering
|
2021
|
Vol. 26, no. 1
76--87
EN
In the present study, we have applied the reduced differential transform method to solve the thermoelastic problem which reduces the computational efforts. In the study, the temperature distribution in a two-dimensional rectangular plate follows the hyperbolic law of heat conduction. We have obtained the generalized solution for thermoelastic field and temperature field by considering non-homogeneous boundary conditions in the x and y direction. Using this method one can obtain a solution in series form. The special case is considered to show the effectiveness of the present method. And also, the results are shown numerically and graphically. The study shows that this method provides an analytical approximate solution in very easy steps and requires little computational work.
3
Content available Dynamic response analysis of a thin-walled rectangular plate subjected to thermoacoustic loadings
Dang Zhigao, Mao Zhaoyong
Archives of Thermodynamics
|
2020
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Vol. 41, no 1
151--174
EN
For thin-walled structures invariably exposed to thermal and noise environment, their dynamic response is an extreme concern in the design of the component of advanced hypersonic aircraft. To address the problem, three theoretical models are established with three typical graded thermal distributions considered. By introducing the thermal moment, membrane forces and acoustic loadings into the vibration equation of plate, the governing equation is derived and it is solved combined with boundary conditions of the plate, the modal function and velocity compatibility equations at the fluid-structure coupling surface. The accuracy of the theoretical predictions is checked against finite element results with good agreement achieved. The results show that not the physical parameters with variation of temperature but the thermal moments and membrane forces, cause the buckling phenomenon. It is noted that buckling phenomenon occurs not only in uniform temperature field but also in graded temperature distribution filed. The mechanism analysis about modal snap-through and losing phenomenon indicates that thermoacoustic loadings will affect the stiffness matrix and mass matrix of structure. With the increase of temperature, the lower modes of the plate are lost, the higher modes appear in advance, and the losing phenomenon occurs in accordance with the order.
4
Content available Vibration frequencies of a rectangular plate with linear variation in thickness and circular variation in Poisson’s ratio
Sharma Amit
Journal of Theoretical and Applied Mechanics
|
2019
|
Vol. 57 nr 3
605--615
EN
The frequency for the first two modes of vibration of a nonhomogeneous tapered rectangular plate is calculated under a bi linear (i.e., linear along both the axes) temperature field. For consideration of the nonhomogeneous material, the author assumed circular variation in Poisson’s ratio. Tapering in the plate is assumed to be linear in one direction. The results are calculated for different values of plate parameters and presented with the help of graphs. Comparison of the results is also given, to support the results of the present study.
5
Content available Modelling method of dynamic characteristics of marine thin-walled structure
Doan Do Van, Szeleziński Adam, Murawski Lech, Muc Adam
Journal of KONES
|
2019
|
Vol. 26, No. 4
39--46
EN
Thin-walled structures are very popular in industries, especially in the field of shipbuilding. There are many types of equipment and structures of ships, which are made up of thin-walled structures such as hull, deck and superstructure. Therefore, the analysis and understanding of the static and dynamic characteristics of a thin-walled structure are very important. In this article, we focus on vibration analysis of a typical thin-walled structurerectangular plate, a basic structure of the hull. Vibration analysis of a rectangular thin plate is conducted by two methods: numerical modelling method of the finite element on Patran-Nastran software platform and experimental method implemented in the laboratory of Gdynia Maritime University. Thin rectangular plate is fixed one end by four clamping plates and is modelled with finite elements and different meshing densities. The numerical model of thin rectangular plate is divided into four cases. Case 1, thin rectangular plate, and clamping plates are modelled with two-dimensional elements. Case 2, the rectangular thin plate is modelled with two-dimensional elements; the clamping plates are modelled with three-dimensional elements. Case 3, both the rectangular thin plate and clamping plates are modelled with three-dimensional elements. Case 4, the rectangular thin plate, and clamping plates are modelled with three-dimensional elements with larger mesh density to increase the accuracy of the calculation results. After that, the results of vibration analysis according to the numerical modelling method on Patran-Nastran software platform for these cases were compared with the measurement results. From there, assess the accuracy of analysis results of selected numerical model methods and the ability to widely apply this numerical model method to other marine structures
6
Content available Buckling and post-buckling behaviour of shallow – nearly flat cylindrical panels under axial compression
Magnucka-Blandzi E., Magnucki K.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2016
|
Vol. 64, nr 3
655--658
EN
The paper is devoted to buckling problem of axially compressed shallow cylindrical panels. Governing differential equations of the nonlinear theory of shallow cylindrical shells are analytically solved. Critical stresses and equilibrium paths of the panels with small curvatures are analytically studied. The formula of the critical stresses for almost flat, cylindrical panels is derived. The “shallowness” of the panel is given by the parameter α and formulae are derived for a range of this parameter. The range of values of sectorial angle for these panels is also defined.
7
Content available remote Parametric Study on Thick Plate Vibration Using FSDT
Kalita K., Haldar S.
Mechanics and Mechanical Engineering
|
2015
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Vol. 19, nr 2
81--90
EN
The prime objective of the research is to investigate the influence of various structural parameters like aspect ratio, boundary condition, size of cut-out etc. on the free vibration frequencies of a thick rectangular plate. Plates being one the most common structural elements has always enticed the interest of many researchers towards this problem. In here a general first order shear deformation theory (FSDT) is used to analyse the free vibration behaviour of rectangular isotropic plates. A finite element program has been developed using 9 node isoparametric element. A number of numerical examples are presented here. Two different sets of mass lumping scheme are considered to carry the analysis using and without using rotary inertia. The definite advantage of this work over other similar works done by using FEM pakages is its exceptional accuracy. At most the error calculated for convergence study with published literature is 1%.
8
Content available Pre-designing of a mechatronic system using an analytical approach with Dymola
Hamza G., Choley J.-Y., Hammadi M., Riviere A., Barkallah M., Louati J., Haddar M.
Journal of Theoretical and Applied Mechanics
|
2015
|
Vol. 53 nr 3
697--710
EN
This paper presents a pre-dimensioning method applied to a mechatronic system and regarding the vibrational aspect, through a simple modeling process in Dymola environment. We study the vibration transmission between dynamic exciters (motors) and receivers (electronic cards) which are located on a simply supported rectangular plate, using an analytical approach. This new method will allow us to perform representative and robust modeling and simulation. The solution for this issue would be a pre-sizing and pre-positioning procedure. It aims to determine a set of possible technical solutions and principal characteristics before the definitive choice of components and precise sizing of the system. The presented method predicts also behaviour of the mechatronic system. In order to validate the model with respect to the finite element method, selected simulation results are presented.
9
Wyznaczanie częstotliwości drgań własnych płyt prostokątnych z nieciągłymi warunkami brzegowymi z wykorzystaniem sztucznych sieci neuronowych
Kaczmarek M., Szymańska A.
Inżynieria i Budownictwo
|
2015
|
R. 71, nr 12
661--663
PL
Przedstawiono alternatywne narzędzie do wyznaczenia częstotliwości drgań własnych płyt z nieciągłymi warunkami brzegowymi – sztuczne sieci neuronowe (SSN). W celu uzyskania bazy danych wykorzystanej do uczenia i testowania SSN przeprowadzono obliczenia z wykorzystaniem programu MES. Zaprezentowano także analizy skuteczności stosowania SSN.
EN
Article shows an alternative tool to determine the natural frequencies of rectangular plates with discontinuous boundary conditions – Artificial Neural Networks (ANN). FEM calculations were carried out in order to obtain a database used for learning and testing ANN. Article presents also analysis of the efficacy of the ANN.
10
Content available Numerical study of the heat transfer phenomenon of a rectangular plate including void, notch using finite difference technique
Deb Nath S. K., Peyada N. K.
International Journal of Applied Mechanics and Engineering
|
2015
|
Vol. 20, no. 4
733--756
EN
In the present study, we have developed a code using Matlab software for solving a rectangular aluminum plate having void, notch, at different boundary conditions discretizing a two dimensional (2D) heat conduction equation by the finite difference technique. We have solved a 2D mixed boundary heat conduction problem analytically using Fourier integrals (Deb Nath et al., 2006; 2007; 2007; Deb Nath and Ahmed, 2008; Deb Nath, 2008; Deb Nath and Afsar, 2009; Deb Nath and Ahmed, 2009; 2009; Deb Nath et al., 2010; Deb Nath, 2013) and the same problem is also solved using the present code developed by the finite difference technique (Ahmed et al., 2005; Deb Nath, 2002; Deb Nath et al., 2008; Ahmed and Deb Nath, 2009; Deb Nath et al., 2011; Mohiuddin et al., 2012). To verify the soundness of the present heat conduction code results using the finite difference method, the distribution of temperature at some sections of a 2D heated plate obtained by the analytical method is compared with those of the plate obtained by the present finite difference method. Interpolation technique is used as an example when the boundary of the plate does not pass through the discretized grid points of the plate. Sometimes hot and cold fluids are passed through rectangular channels in industries and many types of technical equipment. The distribution of temperature of plates including notches, slots with different temperature boundary conditions are studied. Transient heat transfer in several pure metallic plates is also studied to find out the required time to reach equilibrium temperature. So, this study will help find design parameters of such structures.
11
Content available Inelastic stability analysis of uniaxially compressed flat rectangular isotropic CCSS plate
Ibearugbulem O. M., Eziefula U. G., Onwuka D. O.
International Journal of Applied Mechanics and Engineering
|
2015
|
Vol. 20, no. 3
637--645
EN
This study investigates the inelastic stability of a thin flat rectangular isotropic plate subjected to uniform uniaxial compressive loads using Taylor-Maclaurin series formulated deflection function. The plate has clamped and simply supported edges in both characteristic directions (CCSS boundary conditions). The governing equation is derived using a deformation plasticity theory and a work principle. Values of the plate buckling coefficient are calculated for aspect ratios from 0.1 to 2.0 at intervals of 0.1. The results compared favourably with the elastic stability values and the percentage differences ranged from -0.353% to -7.427%. Therefore, the theoretical approach proposed in this study is recommended for the inelastic stability analysis of thin flat rectangular isotropic plates under uniform in-plane compression.
12
Content available Exponential temperature effect on frequencies of a rectangular plate of non-linear varying thickness: a quintic spline technique
Gupta A. K., Mamta J.
Journal of Theoretical and Applied Mechanics
|
2014
|
Vol. 52 nr 1
15--24
EN
The differential equation governing the transverse motion of an elastic rectangular plate of non-linear thickness variation with thermal gradient has been analyzed on the basis of classi- cal plate theory. Following Levy’s approach, i.e. the two parallel edges are simply supported, the fourth-order differential equation governing the motion of such plates of non-linear vary- ing thickness in one direction with exponentially temperature distribution has been solved by using the quintic splines interpolation technique for two different combinations of clamped and simply supported boundary conditions at the other two edges. An algorithm for com- puting the solution of this differential equation is presented for the case of equal intervals. The effect of thermal gradient together with taper constants on the natural frequencies of vibration is illustrated for the first three modes of vibration.
13
Content available remote Critical state of simply supported elastic rectagular plate under non-uniformly distributed compressive load
Wittenbeck L., Kurpisz D., Magnucki K.
Archive of Mechanical Engineering
|
2008
|
Vol. LV, nr 4
301-311
EN
The paper is devoted to a simply supported rectangular plate subjected to two types of compressive edge loads. The first load is applied uniformly along a part of two opposite edges, the second one has a non-uniform distribution (defined by a half wave of the sin to the k function). The critical load value of the plate is located between the values for uniformly distributed and concentrated load. Critical value of thickness of the plate is determined. The problem is solved by the orthogonalization method, and the results are compared with those of numerical analysis done by means of the finite element method.
PL
Przedmiotem badań jest stan krytyczny nierównomiernie ściskanej prostokątnej płyty podpartej przegubowo-przesuwnie na czterech brzegach. Rozwiązania dla płyt równomiernie ściskanych i obciążonych siłą skupioną są dobrze znane. Badany stan krytyczny występuje pomiędzy stanem krytycznym dla równomiernie obciążonej płyty, a stanem krytycznym dla płyty obciążonej siłą skupioną. Krytyczne wymiary płyty są ustalone w wyniku badań. Problem rozwiązano przy pomocy metody ortogonalizacji, wyniki porównano z obliczeniami z programu ABAQUS.
14
Content available remote Vibration energy distribution in rectangular plates with RIBS
Cieślik J., Bochniak W.
Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika
|
2005
|
z. 65 [222]
69-76
EN
There are presented obtained from literature review formulations which involve the loads and strains for evaluation of structural intensity for beams, shells and plates. The method of intensity evaluation was based on complex modal analysis with use of finite element method. There are presented results of structural intensity vectors distribution on the surface of simply supported, ribbed rectangular plate. Such solved problem was intended to show the usability of structure surface intensity method in diagnostics of construction joints.
15
Content available remote Stability of parametric vibrations of functionally graded plate
Tylikowski A.
Vibrations in Physical Systems
|
2004
|
Vol. 21
391--394
EN
A study of parametric vibrations of functionally graded plates subjected to in-plane time-dependent forces is presented. The rectangular plate described by geometrically non-linear partial differential equations is studied Moderately large deflection equations taking into account a coupling of in-plane and transverse motions are used. The parametric vibrations or dynamic stability of functionally graded plate are analysed using the direct Liapunov method. Due to a small thickness coupling, and rotary inertia terms are neglected. The asymptotic stability and almost-sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunov's direct method. Material properties are graded in the thickness direction of the plate according to volume fraction power law distribution. Studies of parametric vibrations of functionally graded shells made up of steel – zirkonia, nickel – SiN and aluminum - TiC are presented. An oscillating temperature causes generation of in-plane time-dependent forces destabilizing the plane state of the plate equilibrium.
16
Content available remote On a Certain Model of Prestressed Medium Thickness Uniperiodic Plate
Baron E.
Vibrations in Physical Systems
|
2004
|
Vol. 21
101--104
17
Content available remote Free Vibrations of a Rectangular Plate Elastically Connected with Beams
Kukla S.
Vibrations in Physical Systems
|
2004
|
Vol. 21
235--238
18
Content available remote Vibrations of rectangular plate with two bearing sets
Kabała A.
Vibrations in Physical Systems
|
2002
|
Vol. 20
174--175
19
Ścisła metoda rozwiązania problemu brzegowego lepko-sprężyste j płyty prostokątnej o różnych warunkach brzegowych
Cabański J.
Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
|
2000
|
z. 14
11-15
PL
W pracy przedstawiono ścisła metodę rozwiązania problemu brzegowego lepko-sprężystej płyty prostokątnej o różnych warunkach brzegowych. Po rozdzieleniu zmiennych przestrzennych i czasu otrzymano dwa zwyczajne równania różniczkowe, tj. ruchu i postaci drgań płyty. Rozdzielenie zmiennych przestrzennych x i y oraz rozwiązanie subproblemu brzegowego dało subwartości i subfunkcje własne. Udowodniona własność ortogonalności subfunkcji własnych umożliwiła rozwiązać główny problem brzegowy, tj. wyznaczyć dwa nieskończone ciągi: częstości i postaci drgań własnych.
EN
In this paper an exact method of solution of the boundary-value problem of a viscoelastic rectangular plate is presented. After separation of spatial and time variables we obtain two ordinary differential equations, i.e. motion and modes of vibrations. Separation of spatial variables x and y as well as solution of boundary-value subproblem yiled eigensubvalues and eigensubfunctions. Proved property of orthogonality of eigensubfunctions enables to solve the main boundary-value problem, i.e. determine two infinite sequencies: eigenfrequencies and eigenmodes.
20
Content available remote Investigation of the dynamical behavior of rectangular plates of the variable thickness by means of the numerical and experimental methods
Grigorenko A., Tregubenko T.V.
Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika
|
1999
|
z. 52 [174]
397-400
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