Iterative Method for Solving Rectangular Plates

1972 ◽  
Vol 98 (1) ◽  
pp. 135-151
Author(s):  
B. Sen ◽  
S. Sengupta ◽  
T. K. Nath
Keyword(s):  
Iterative Method ◽  
Rectangular Plates

scholarly journals A Modified Iterative Automatic Method for Characterization at Shear Resonance: Case Study of Ba0.85Ca0.15Ti0.90Zr0.10O3 Eco-Piezoceramics

Materials ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1666
Author(s):  
Lorena Pardo ◽  
Armando Reyes-Montero ◽  
Álvaro García ◽  
Alfredo Jacas-Rodríguez ◽  
Pilar Ochoa ◽  
...  
Keyword(s):  
Iterative Method ◽  
Piezoelectric Coefficient ◽  
Complex Impedance ◽  
Shear Mode ◽  
Rectangular Plates ◽  
Material Models ◽  
Shear Plate ◽  
Standard Plate ◽  
Shear Resonance

Coupling between electrically excited electromechanical resonances of piezoelectric ceramics is undesirable for the purpose of their characterization, since the material models correspond to monomodal resonances. However, coupling takes place quite often and it is unavoidable at the shear resonance of standard in-plane poled and thickness-excited rectangular plates. The piezoelectric coefficient e15, the elastic compliance s55E and the dielectric permittivity component ε11S for a piezoelectric ceramic can be determined, including all losses, using the automatic iterative method of analysis of the complex impedance curves for the shear mode of an appropriated resonator. This is the non-standard, thickness-poled and longitudinally excited, shear plate. In this paper, the automatic iterative method is modified. The purpose is to be able to deal with the analysis of the impedance curves of the non-standard plate as the periodic phenomena of coupling and decoupling of the main shear resonance and other resonances takes place. This happens when the thickness of the plate is reduced, and its aspect ratio (width of the excitation (w)/thickness for poling (t)) is increased. In this process, the frequency of the shear resonance also increases and meets those of other plate modes periodically. We aim to obtain the best approach for the shear properties of near coupling and to reveal both their validity and the limitations of the thus-obtained information. Finally, we use a plate of a Ba0.85Ca0.15Ti0.90Zr0.10O3 eco-piezoceramic as a case study.

ON THE GALERKIN - ITERATIVE METHOD APPLIED TO THE NON-LINEAR VIBRATIONS OF RECTANGULAR PLATES

2011 ◽  
Author(s):  
Frederico M. A. Silva ◽  
Flávio Augusto X. C. Pinho ◽  
Zenón J. G. N. del Prado ◽  
Paulo B. Gonçalves
Keyword(s):  
Iterative Method ◽  
Rectangular Plates ◽  
Non Linear ◽  
Linear Vibrations

THE REALIZATION OF THE ITERATIVE METHOD OF THE LEAST SQUARES FOR THE ESTIMATION OF STATIC OBJECT PARAMETERS IN MATLAB ENVIRONMENT

2017 ◽  
pp. 28-36
Author(s):  
Galina Vasil’evna Troshina ◽  
Alexander Aleksandrovich Voevoda
Keyword(s):  
Parameter Estimation ◽  
Iterative Method ◽  
Least Squares ◽  
Input Signal ◽  
Layer Structure ◽  
Estimation Procedure ◽  
Parameter Estimation Procedure ◽  
Noise Simulation ◽  
Static Object ◽  
Object Parameters

It was suggested to use the system model working in real time for an iterative method of the parameter estimation. It gives the chance to select a suitable input signal, and also to carry out the setup of the object parameters. The object modeling for a case when the system isn't affected by the measurement noises, and also for a case when an object is under the gaussian noise was executed in the MatLab environment. The superposition of two meanders with different periods and single amplitude is used as an input signal. The model represents the three-layer structure in the MatLab environment. On the most upper layer there are units corresponding to the simulation of an input signal, directly the object, the unit of the noise simulation and the unit for the parameter estimation. The second and the third layers correspond to the simulation of the iterative method of the least squares. The diagrams of the input and the output signals in the absence of noise and in the presence of noise are shown. The results of parameter estimation of a static object are given. According to the results of modeling, the algorithm works well even in the presence of significant measurement noise. To verify the correctness of the work of an algorithm the auxiliary computations have been performed and the diagrams of the gain behavior amount which is used in the parameter estimation procedure have been constructed. The entry conditions which are necessary for the work of an iterative method of the least squares are specified. The understanding of this algorithm functioning principles is a basis for its subsequent use for the parameter estimation of the multi-channel dynamic objects.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

Numerical analysis of free vibrations of rectangular plates based on different approaches

2019 ◽  
pp. 33-41
Author(s):  
Oleksandr Grigorenko ◽  
◽  
Maksym Borysenko ◽  
Olena Boychuk ◽  
Volodymyr Novytskyi ◽  
...  
Keyword(s):  
Numerical Analysis ◽  
Free Vibrations ◽  
Rectangular Plates
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