## About

95

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Introduction

Free linear and nonlinear vibration and dynamical stability FGM plates and shallow shells.
Application Mesh less and variational methods to these structures..

Additional affiliations

January 1995 - November 2015

## Publications

Publications (95)

To investigate nonlinear bending of the functionally graded (FGM) plates with complex shape and resting on elastic foundation a variational-structural method (RFM) is proposed. Mathematical statement of nonlinear boundary value problems of plate bending is carried out in the framework of the classical geometrically nonlinear plate theory. To solve...

Free vibrations of shallow shells of an arbitrary shape are investigated. It is assumed that shell is fabricated of functionally graded materials. Mathematical model has been constructed on base of shear deformation shell theory of the higher-order (HSDT). Voigt’s model is applied to define effective material properties of the structure. To study a...

Free vibrations of the orthotropic micro/nanoplate with nonclassical shape are investigated. The considered model is based on the nonlocal elasticity theory. The developed method uses the Ritz method as well as R-function theory for the construction of the system of coordinate functions. The linear frequencies are obtained for a rectangular plate w...

Free vibrations of shallow sandwich shells resting on elastic foundations are investigated. It is assumed that the shell consists of three layers of defined thickness. The core is made of ceramics or metal, while the upper and lower layers are made of functionally graded material (FGM). The volume fractions of metal and ceramics are described by th...

Geometrically nonlinear vibrations of shallow shells resting on elastic foundations are investigated. It is assumed that the shell is fabricated of functionally graded materials. Shear deformation shell theory of the first (FSDT) and higher order (HSDT) that include an interaction with elastic foundations is considered. Voigt’s model is applied to...

In the chapter the variational Ritz's method combined with the R-functions theory is used in order to study free vibrations and parametric stability of functionally graded (FG) sandwich plates. Developed approach has been realized in framework of a refined theory of the FG sandwich plates of the first order (the Timoshenko type). The proposed metho...

The article is dedicated to the outstanding scientist of the twentieth century, Academician of the National Academy of Sciences of Ukraine Volodymyr Logvynovych Rvachev, who would have turned 95 in 2021. At one time VL Rvachev was the first rector of HIRE, in 1970 he became head of the Department of Theoretical and Mathematical Physics of KhPI (now...

This paper considers the application of the R-functions method to a new class of problems: the study of vibrations of sandwich FGM shallow shells with variable thickness of layers and complex shape. The core is fabricated of FGM, and the face sheets are made of metal. Mathematical formulation of the problem has been done in the framework of the ref...

We propose a method for the evaluation of the critical loads for laminated plates with holes. Plates and holes made in these plates may have different geometric shapes and conditions of their fastening. It is assumed that the plate is compressed by static forces in its middle plane. The mathematical statement of the problem is formulated within the...

The vibration and buckling analysis of symmetrically laminated plates with complex form subjected to in–plane uniform and non–uniform loading is performed using variational Ritz’s method and the R-functions theory. First order shear deformations theory of Timoshenko’s type are adopted. Each ply is assumed to be an orthotropic homogeneous one withou...

The buckling and vibration of laminated plates with various types of non-uniform compressive edge loads is analyzed. This problem requires that first the elasticity problem be considered to obtain the distribution of in-plane stresses, and after that, the buckling problem is solved. The method of solution is based on the R-functions theory and the...

We propose a numerical-analytic method aimed at the investigation of free vibrations and stability of functionally graded sandwich-type plates and based on the refined Timoshenko-type theory of the first order. We considered various schemes of arrangement of the layers: (1) the filler is a functionally graded material and the top and bottom layers...

The free vibration of plates and shallow shells with/without cutouts made of functionally graded materials (FGM) is investigated using variational FG shallow shells with temperature dependent mechanical characteristics of the constituent materials. First‐order shear deformation theory of shallow shells is employed. It is supposed that material prop...

Free vibrations of microplates with non‐classical shape are considered in the paper. Governing equations are based on the modified couple stress theory and Kirchhoff–Love plate theory. It is assumed that the plate is isotropic or orthotropic and satisfy various boundary conditions. An analysis is performed by the variational‐structural method which...

The purpose of the paper is to study stability and free vibrations of laminated plates and shallow shells composed of functionally graded materials. The approach proposed incorporates the Ritz method and the R-functions theory. It is assumed that the shell consists of three layers and is loaded in the middle plane. The both cases of uniform as well...

The R-functions theory and Ritz approach are applied for analysis of free vibrations of laminated functionally graded shallow shells with different types of curvatures and complex planforms. Shallow shells are considered as sandwich shells of different types: a) face sheets of the shallow shells are made of a functionally graded material (FGM) and...

Linear and geometrically nonlinear vibrations of the three-layered functionally graded shallow shells with a complex form of the base are studied. It is assumed that outer and inner layers are made of functionally graded materials (FGM) or an isotropic material (metal or ceramic). The first-order shear deformation theory of shallow shells (FSDT) is...

In present work, an effective method to research geometrically nonlinear free vibrations of elements of thin-walled constructions that can be modeled as laminated shallow shells with complex planform is applied. The proposed method is numerical–analytical. It is based on joint use of the R-functions theory, variational methods, Bubnov–Galerkin proc...

Geometrically nonlinear vibrations of functionally graded shallow shells of complex planform are studied. The paper deals with a power-law distribution of the volume fraction of ceramics and metal through the thickness. The analysis is performed with the use of the R-functions theory and variational Ritz method. Moreover, the Bubnov-Galerkin and th...

The article is devoted to the 90th anniversary of the birth of the outstanding Ukrainian scientist in the field of mathematics, mechanics
and cybernetics, Academician of NAS of Ukraine Vladimir L. Rvachev. The article describes the life and creative path of
V. Rvachev. The main scientific results of V. Rvachev, that allowed a significant breakthrou...

In present work an effective method to research geometrically nonlinear free vibrations of elements of thin-walled constructions that can be modeled as laminated shallow shells with complex planform is applied. The proposed method is based on joint use of R–functions theory, variational methods and Bubnov–Galerkin procedure. It allows reducing an i...

The method for studying the geometrically nonlinear vibrations of functionally graded shallow shells with a complex planform is proposed. Сomposite shallow shells made from a mixture of ceramic and metal are considered. In order to take into account varying of the volume fraction of ceramic the power law is accepted. Formulation of the problem is c...

A novel numerical/analytical approach to study geometrically nonlinear vibrations of shells with variable
thickness of layers is proposed. It enables investigation of shallow shells with complex forms and different
boundary conditions. The proposed method combines application of the R-functions theory, variational
Ritz’s method, as well as hybrid B...

We propose a numerical-analytic method for the investigation of parametric vibrations of the plates under the action of static and periodic loads applied in the middle plane. The method is used for the equations of motion of plates obtained within the framework of the classical theory. The developed approach is based on the application of the theor...

Geometrically nonlinear vibrations of laminated shallow shells with layers of variable thickness are studied. Nonlinear equations of motion for shells based on the first order shear deformation and classical shells theories are considered. In order to solve this problem authors propose new numerical-analytical method. According to this approach the...

Dynamic instability and nonlinear parametric vibrations of laminated plates with complex shape are studied. Numerically analytical method based on a combination of R-functions theory and a variational method is proposed. Developed approach is illustrated on an example of a laminated plate with inhomogeneous subcritical state. Instability domains an...

The problem of nonlinear vibrations and stability analysis for the symmetric laminated plates with complex shape, loaded by static or periodic load in-plane is considered. In general case research of stability and parametric vibrations is connected with many mathematical difficulties. For this reason we propose approach based on application of R-fu...

The present formulation of the analysed problem is based on Donell's nonlinear shallow shell theory, which adopts Kirchhoff's hypothesis. Transverse shear deformations and rotary inertia of a shell are neglected. According to this theory, the non-linear strain-displacement relations at the shell midsurface has been proposed. The validity and reliab...

In this work we are aimed on the development of a novel method suitable for analysis of geometrically nonlinear vibrations of the shallow shells with complex plan form and layers of the variable thickness. This method is based on combined application of the R-functions theory, variation Ritz's method, as well a hybrid Bubnov-Galerkin and Runge-Kutt...

Method for study of nonlinear parametric vibrations of the laminated plates of the symmetrically structure with respect to thickness is proposed. Mathematical statement is fulfilled in framework of the classical theory based on hypothesis by Kirchhoff-Love [2]. The developed method essentially uses the R-functions theory. That is why it may be appl...

Early R-functions theory [1] combined with variational methods have been applied to linear [2] and nonlinear vibration problems [3,4] of the shallow shells theory of the constant thickness. In the present study, we first apply R-functions theory in order to investigate the geometrically nonlinear vibrations of orthotropic shallow shells of complex...

The effective numerically analytical method of parametric vibrations research for orthotropic plate with complex shape is proposed. The novel approach is based on hybrid applications of variation-type methods with R-functions theory. Using proposed method and developed software the regular and chaotic regimes of an orthotropic plates with an arbitr...

The bending behavior of the laminated shallow shells under static loading has been studied using the R-functions theory together with the spline-approximation. Formulation is based on the first order shear deformation theory. Due to usage of the R-functions theory the laminated shallow shells with complex shape and different types of the boundary c...

We propose a method for investigating parametric vibrations of orthotropic plates with complex shape for different types of
boundary conditions, which is based on variational methods in combination with the R -function theory. The proposed approach is used for the solution of specific problems. In the process of numerical realization
of an algorith...

The paper proposes a method to solve geometrically nonlinear bending problems for thin orthotropic shallow shells and plates
interacting with a Winkler–Pasternak foundation under transverse loading. This method is based on Ritz’s variational method
and the R-function method. The developed algorithm and software are used to solve a number of test pr...

The paper proposes a method to study the parametric vibrations of orthotropic plates with complex shape. The method is based
on the R-function theory and variational methods. Dynamic-instability domains and amplitude–frequency responses for plates
with complex geometry and different types of boundary conditions are plotted
Keywordsparametric vibra...

The original method of studying parametric vibrations of orthotropic plate with complex shape is proposed. Suggested approach is based on combined application of variational methods and the R-functions theory. Using the proposed method and developed software the regular and chaotic regimes of T-shaped plate are analyzed. INTRODUCTION Since the elem...

The parametric vibrations of orthotopic plates with complex forms for different types of boundary conditions are studied. The proposed novel hybrid approach is based on combination of the so called Rfunctions method and the variation method. In particular, advantages of a multimode approximation used for plate behavior analysis are addressed, among...

We propose a method to study free nonlinear vibrations of multilayer shallow shells with a complicated form of the plan. The
mathematical statement of the problem is realized in the frame of a refined firstorder theory of the Tymoshenko type. A distinctive
specific feature of the work is the application of the theory of R -functions and variational...

The paper proposes a method to study the natural vibrations of orthotropic shells with varying thickness. The method employs
the R-function and Ritz methods. The use of R-functions allows examining shells with complex planform and different boundary
conditions. The method is validated by comparing the results it produces with those obtained by othe...

The most modern constructions used in building, aerospace and other fields are modulated by plate and shell structures. Vibration research of plates loaded by compressive pulsating force has received particular interest, since in such system dynamic instability may occur, due to certain combinations of parameters of load and eigenfrequency. Given p...

The parametric vibrations of plates with cutouts subjected to in-plane periodic and compressive loads, are studied. The proposed approach is based on R-functions method and the classical variational approach. The influence of cutouts parameters, as well as static factors of load on stability regions and nonlinear vibrations are investigated.

Geometrically nonlinear vibrations of shallow circular cylindrical panels with complex shape of the boundary are considered. The R-functions theory and variational methods are used to study the problem. The R-functions method (RFM) allows constructing in analytical form the sequence of basis functions satisfying the given boundary conditions in cas...

We have developed an effective approach to the solution of problems on geometrically nonlinear vibrations of orthotropic multilayer
plates of irregular shapes in a classical statement based on the use of the R-function theory, Ritz variational method and
Bubnov-Galerkin method. Using the proposed method, problems of vibrations of both multilayer re...

A method is proposed for studying the free vibrations of flexible shallow shells with a complex planform. The method is based
on variational and R-function methods. The R-function method allows constructing a system of basis functions in an analytic
form. This makes it possible to reduce the Donnell-Mushtari-Vlasov equations to Duffing equations. T...

The paper outlines a method for studying the vibrations of plates of complex geometry subjected to in-plane loading. The method
is based on the R-function and variational methods. It is used to plot frequency response of plates with complex geometry
and different boundary conditions

This paper deals with effects of large amplitude on the free and
forced flexural vibrations of elastic orthotropic plates of
arbitrary shape. R-function method (RFM) is applied to obtain
the basis functions need for expansion of sought solution into
Fourier series. The initial nonlinear system of differential
equations with partial derivatives is r...

An efficient method is developed to solve the free-vibration problems for arbitrarily shaped orthotropic multilayer plates
in a refined formulation. The method is based on the R-function and Ritz methods. Sequences of coordinate functions satisfying
kinematic boundary conditions are constructed in an analytic form. The method is used to solve the v...

A technique for analyzing the natural vibrations of variable-thickness plates under in-plane loading has been developed. The technique is based on variational and R-function methods. It is used to study the dependence of the natural frequencies of the plates on their shape and boundary and loading conditions

In this paper free large-amplitude flexural vibrations of thin plates with various planforms and boundary conditions are studied by the R-function method. This method is based on the joint application of the R-function theory and variational methods. The main feature of the R-function theory is the possibility to present all geometric information g...

A linear, static bending analysis of truss-core sandwich plates for arbitrary shape and boundary conditions is presented. The three-dimensional truss-core sandwich plate is idealized as an equivalent two-dimensional structurally orthotropic thick plate continuum. This analysis is based on the small deflection, first-order shear deformation theory o...

An effective method for the free vibration of arbitrary plan-form shallow shells is proposed. The algorithm is based on the R-function theory and variational Ritz method. The effectiveness of the method offered is illustrated by examples of shallow shells of a complex plan form at different boundary conditions. Three types of curvatures are conside...

Free flexural vibrations of homogeneous, thin, orthotropic plates of an arbitrary shape with mixed boundary conditions are studied using the R-function method. The proposed method is based on the use of the R-function theory and variational methods. In contrast to the widely used methods of the network type (finite differences, finite element, and...

We propose an algorithm for the solution of the problem of free vibrations of multilayer shallow shells and plates based on the variational methods and the theory of R-functions. By using this algorithm, we solve the problems posed for shallow shells (spherical and cylindrical) and plates of complex shape in plan. We present the results of investig...

An algorithm is offered for solving problems of natural vibrations of multilayer shells and plates based on variational methods and the theory of R-functions. With the help of this algorithm we solved problem for mildly sloping shells (spherical and cylinder) and plates with a complex shape in plan. We established a dependence of natural vibration...

A new approach is proposed to study the dynamic behavior of shells with an arbitrary planform weakened by surface cuts (cracks.) The approach is based on the method of R-functions. The computer simulation is carried out using the POLE-SHELL problem-oriented system, which implements the method of R-functions and variational methods. Numerical result...

A new approach is proposed to study the dynamic behavior of shells with arbitrary in plan form, weakened by surface slits (cracks). The approach is based on the RF-method (method of R-function). The computer simulation is assumed to be carried out using the problem-oriented system POLE-SHELL, RF-method, and variational methods. Numerical results ar...

A method has been developed to solve non-linear fourth order differential equations which model the elasto-plastic bending of arbitrary-shape-plane plates with complex boundary conditions. The plates are made of a material with strengthening according to linear and non-linear laws. Linearization of the physical relationships is carried out using th...

The development of the theory of R-functions has stimulated the emergence of efficient numerical-analytical methods for a wide class of problems associated with physico-mechanical fields. R-functions are the basis for computer-aided level source language, which is sufficiently close to an ordinary mathematical language. Despite the powerful capabil...

We study the application of the method of R-functions to the solution of problems of bending of elastic three-layer plates of arbitrary shape. We obtain new solution structures for plates that are freely supported over the whole boundary. We solve test problems and compare the experimental and theoretical results. All numerical results were obtaine...

The problem of the stability of a multiply-connected plate is solved by means of a classical approach in which the problem is broken down into two parts: the problem of the stress-strain state before loss of stability; and the problem of stability. The theory of R-functions and the Ritz variational method are used to solve these two problems. Thus,...

Solution of problems on stability of thin plates of complex shape is considered. A consistent solution of the elasticity theory problem and the finding of the critical load itself are implemented by the method of R-functions. Numerical results are presented for multiply connected and singly connected plates with mixed conditions of fastening.

It is shown possible to apply the method of R-functions for solving problems of forced vibrations of complex-shape plates under different conditions of fastening and kinds of loading. Results of determining natural frequencies of a freely supported square plate with an elliptical hole, graphs of deflections in various sections under the effect of u...

## Projects

Projects (3)

DSTA is a conference organized by the Department of Automation, Biomechanics and Mechatronics of the Lodz University of Technology under the auspices of the Committee of Mechanics of the Polish Academy of Sciences every two years since 1992. It continuously enjoys great success, as evidenced by the constantly increasing number of participants. The previous edition (DSTA 2015) was attended by over 200 scientists representing 28 countries.
The scope of the conference includes mostly: bifurcations and chaos, control in dynamical systems, asymptotic methods in nonlinear dynamics, stability of dynamical systems; vibrations of discrete and continuous systems, original numerical methods of vibration analysis, human-machine interaction, dynamics in life sciences, bioengineering, medicine, and many others.
During DSTA 2017, the keynote lectures will be given by leading specialists:
- ANDRZEJ BARTOSZEWICZ (Lodz University of Technology, Poland),
- ALEXEY V. BORISOV (Izhevsk Institute of Computer Science, Russia),
- MATTHEW P. CARTMELL (University of Strathclyde, UK),
- LIVIJA CVETIĆANIN (University of Novi Sad, Serbia),
- WALTER LACARBONARA (Sapienza University of Rome, Italy),
- SADAGOPAN NARAYANAN (IIITDM, India),
- MIGUEL A.F. SANJUÁN (Universidad Rey Juan Carlos, Spain).
The Scientific Committee is represented by outstanding specialists from all over the world - see https://dys-ta.com/scientific_committee or the "Collaborators" section.
A wide range of topics covered during the conference allows for exchange of new ideas and results of recent research in the field of scientific and technological advances in modern dynamical systems.
Peer-review accepted papers will be published in the DSTA 2017 Proceedings and in Springer multi-volume Edited Books under Proceedings in Mathematics & Statistics. Furthermore, the most valuable of them will be selected and recommended for publication, in the extended form, in Special Issues of highly acclaimed journals, such as:
- Applied Mathematical Modelling: Simulation and Computation for Engineering and Environmental Systems, IF = 2.291,
- International Journal of Nonlinear Sciences and Numerical Simulation, IF = 0.687,
- International Journal of Structural Stability and Dynamics, IF = 1.059,
- Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, IF = 0.889,
- Latin American Journal of Solids and Structures, IF = 0.849,
- Nonlinear Dynamics: An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems, IF = 3.000,
- ZAMM — Journal of Applied Mathematics and Mechanics, IF = 1.293.
The deadline for abstract submission is May 21. More information can be found at http://www.dys-ta.com
We are looking forward to receiving your submission and welcoming you in Lodz!

The goal is to develop a reliable method/approach for geometrically nonlinear free vibration of shallow shells investigation. The method is planned to be applied for analysis of boundary conditions and other factors influence on nonlinear vibrations of shells with a central cutout.

Geometrically nonlinear vibrations problems of FG shallow shells