scholarly journals Wavelet-Based Analysis of the Regular and Chaotic Dynamics of Rectangular Flexible Plates Subjected to Shear-Harmonic Loading

2012 ◽  
Vol 19 (5) ◽  
pp. 979-994 ◽  
Author(s):  
J. Awrejcewicz ◽  
I.V. Papkova ◽  
E.U. Krylova ◽  
V.A. Krysko
Keyword(s):  
Chaotic Dynamics ◽  
Time Instant ◽  
Vibration Characteristics ◽  
Harmonic Load ◽  
Rectangular Plates ◽  
Harmonic Loading ◽  
Linear Dynamics ◽  
Flexible Plates ◽  
Load Action ◽  
Real Picture

We investigate non-linear dynamics of flexible rectangular plates subjected to external shear harmonic load action. We show that an application of the classical and widely used Fourier analysis does not allow to obtain real picture of the frequency vibration characteristics in each time instant. On the other hand, we show that application of the wavelets approach allows to follow frequency time evolutions. Our numerical results indicate that vibrations in different plate points occur with the same frequencies set although their power is different. Hence, the vibration characteristics can be represented by one arbitrary taken plate point. Furthermore, using wavelets scenarios of transitions from regular to chaotic dynamics are illustrated and discussed including two novel scenarios not reported so far in the existing literature.

scholarly journals Regular and Chaotic Dynamics of Flexible Plates

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
J. Awrejcewicz ◽  
E. Yu. Krylova ◽  
I.V. Papkova ◽  
V. A. Krysko
Keyword(s):  
Nonlinear Dynamics ◽  
Hopf Bifurcation ◽  
Chaotic Dynamics ◽  
Rectangular Plates ◽  
Control Parameters ◽  
Periodic Load ◽  
Chaotic Vibrations ◽  
Flexible Plates ◽  
Independent Variable ◽  
Time Periodic

Nonlinear dynamics of flexible rectangular plates subjected to the action of longitudinal and time periodic load distributed on the plate perimeter is investigated. Applying both the classical Fourier and wavelet analysis we illustrate three different Feigenbaum type scenarios of transition from a regular to chaotic dynamics. We show that the system vibrations change with respect not only to the change of control parameters, but also to all fixed parameters (system dynamics changes when the independent variable, time, increases). In addition, we show that chaotic dynamics may appear also after the second Hopf bifurcation. Curves of equal deflections (isoclines) lose their previous symmetry while transiting into chaotic vibrations.

scholarly journals 518 Vibration Characteristics of Un-symmetrically Laminated Rectangular Plates

2011 ◽  
Vol 2011.50 (0) ◽  
pp. 185-186
Author(s):  
Seung-Cheol Lee ◽  
Kumpei Yugami ◽  
Shinya Honda ◽  
Yoshihiro Narita
Keyword(s):  
Vibration Characteristics ◽  
Rectangular Plates

scholarly journals Modeling and Simulation of Transverse Free Vibration Analysis of a Rectangular Plate with Cutouts Using Energy Principles

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Shuangxia Shi ◽  
Bin Xiao ◽  
Guoyong Jin ◽  
Chao Gao
Keyword(s):  
Rectangular Plate ◽  
Free Vibration Analysis ◽  
Entire Solution ◽  
Vibration Characteristics ◽  
Modeling Method ◽  
Solution Technique ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Cosine Series ◽  
Energy Principles

A modeling method is proposed for the vibration characteristics of rectangular plates with cutouts having variable size. Different from the existing modeling method by considering the cutout as an extremely thin part of the plate, the energy principles in conjunction with Rayleigh-Ritz solution technique are employed for the modeling of the structure. Under this theoretical framework, the effect of the cutout is taken into account by subtracting the energies of the cutout domains from the total energies of the whole plate with arbitrary boundary conditions. The displacement of the rectangular plate with nonuniform physic parameters is expressed as the combination of a two-dimensional trigonometric cosine series and supplementary terms introduced to ensure the uniform convergence of the solution over the entire solution domain including the cutouts boundary. The effectiveness and reliability of the eigenmodes of the rectangular plate with cutouts are checked against the results obtained by the finite element method (FEM). The cutout number, position, and size are varied to illustrate the effect of the cutouts on the vibration characteristics of the rectangular plate with cutouts.

scholarly journals VIBRATION OF 2D-FGSW TIMOSHENKO BEAMS UNDER A MOVING HARMONIC LOAD

2020 ◽  
Vol 58 (6) ◽  
pp. 760
Author(s):  
Kien Dinh Nguyen
Keyword(s):  
Moving Load ◽  
Excitation Frequency ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Element Formulation ◽  
Harmonic Load ◽  
Timoshenko Beams ◽  
Power Functions ◽  
Material Inhomogeneity ◽  
Moving Harmonic Load

Vibration of two-directional functionally graded sandwich (2D-FGSW) Timoshenko beams under a moving harmonic load is investigated. The beams consist of three layers, a homogeneous core and two functionally graded skin layers with the material properties continuously varying in both the thickness and length directions by power functions. A finite element formulation is derived and employed to compute the vibration characteristics of the beams. The obtained numerical result reveals that the material inhomogeneity and the layer thickness ratio play an important role on the natural frequencies and dynamic response of the beams. A parametric study is carried out to highlight the effects of the power-law indexes, the moving load speed and excitation frequency on the vibration characteristics of the beams.  The influence of the beam aspect ratio on the vibration of the beams is also examined and discussed. 

An exact solution for free vibration of thin functionally graded rectangular plates

2010 ◽  
Vol 225 (3) ◽  
pp. 526-536 ◽  
Author(s):  
A Hasani Baferani ◽  
A R Saidi ◽  
E Jomehzadeh
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Different Boundary Conditions

The aim of this article is to find an exact analytical solution for free vibration characteristics of thin functionally graded rectangular plates with different boundary conditions. The governing equations of motion are obtained based on the classical plate theory. Using an analytical method, three partial differential equations of motion are reformulated into two new decoupled equations. Based on the Navier solution, a closed-form solution is presented for natural frequencies of functionally graded simply supported rectangular plates. Then, considering Levy-type solution, natural frequencies of functionally graded plates are presented for various boundary conditions. Three mode shapes of a functionally graded rectangular plate are also presented for different boundary conditions. In addition, the effects of aspect ratio, thickness—length ratio, power law index, and boundary conditions on the vibration characteristics of functionally graded rectangular plates are discussed in details. Finally, it has been shown that the effects of in-plane displacements on natural frequencies of functionally graded plates under different boundary conditions have been studied.

Multi-Pulse Heteroclinic Orbits and Chaotic Dynamics of Laminated Composite Piezoelectric Rectangular Plate

2009 ◽  
Author(s):  
Ming-Hui Yao ◽  
Wei Zhang ◽  
Dong-Xing Cao
Keyword(s):  
Normal Form ◽  
Chaotic Dynamics ◽  
Multiple Scales ◽  
Laminated Composite ◽  
Heteroclinic Orbits ◽  
Global Dynamics ◽  
Rectangular Plates ◽  
Internal Resonances ◽  
Chaotic Motions ◽  
Simply Supported

The multi-pulse orbits and chaotic dynamics of the simply supported laminated composite piezoelectric rectangular plates under combined parametric excitation and transverse loads are studied in detail. It is assumed that different layers are perfectly bonded to each other with piezoelectric actuator patches embedded. The nonlinear equations of motions for the laminated composite piezoelectric rectangular plates are derived from von Karman-type equation and third-order shear deformation laminate theory of Reddy. The four-dimensional averaged equation under the case of primary parametric resonance and 1:2 internal resonances is obtained by directly using the method of multiple scales and Galerkin approach to the partial differential governing equation of motion for the laminated composite piezoelectric rectangular plates. The system is transformed to the averaged equation. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on normal form obtained, the extended Melnikov method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics for the laminated composite piezoelectric rectangular plates. The analysis of global dynamics indicates that there exist the multi-pulse jumping orbits in the perturbed phase space of the averaged equation. From the averaged equations obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of the laminated composite piezoelectric rectangular plates are found by using numerical simulation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense for the simply supported laminated composite piezoelectric rectangular plates.

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