Three-dimensional natural vibration analysis and energy considerations for a piezoelectric rectangular plate

2005 ◽  
Vol 283 (3-5) ◽  
pp. 1093-1113 ◽  
Author(s):  
Piotr Cupiał
Keyword(s):  
Rectangular Plate ◽  
Vibration Analysis ◽  
Natural Vibration ◽  
Three Dimensional

scholarly journals Modelling Method of Dynamic Characteristics of Marine Thin-Walled Structure

2019 ◽  
Vol 26 (4) ◽  
pp. 39-46
Author(s):  
Do Van Doan ◽  
Adam Szeleziński ◽  
Lech Murawski ◽  
Adam Muc
Keyword(s):  
Numerical Model ◽  
Rectangular Plate ◽  
Thin Plate ◽  
Vibration Analysis ◽  
Three Dimensional ◽  
Rectangular Thin Plate ◽  
Thin Rectangular Plate ◽  
Thin Walled Structures ◽  
Modelling Method ◽  
Thin Walled

AbstractThin-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 structure-rectangular 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.

scholarly journals Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions

Materials ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 7088
Author(s):  
Wenhao Huang ◽  
Kai Xue ◽  
Qiuhong Li
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Three Dimensional ◽  
Functionally Graded ◽  
General Boundary ◽  
Global Coordinate System ◽  
General Boundary Conditions ◽  
Characteristic Analysis

Functionally graded materials (FGMs) structures are increasingly used in engineering due to their superior mechanical and material properties, and the FGMs plate with cutouts is a common structural form, but research on the vibration characteristics of FGMs plate with cutouts is relatively limited. In this paper, the three-dimensional exact solution for the vibration analysis of FGMs rectangular plate with circular cutouts subjected to general boundary conditions is presented based on the three-dimensional elasticity theory. The displacement field functions are expressed as standard cosine Fourier series plus auxiliary cosine series terms satisfying the boundary conditions in the global coordinate system. The plate with circular cutout is discretized into four curve quadrilateral sub-domains using the p-version method, and then the blending function method is applied to map the closed quadrilateral region to the computational space. The characteristic equation is obtained based on the Lagrangian energy principle and Rayleigh–Ritz method. The efficiency and reliability of proposed method are verified by comparing the present results with those available in the literature and FEM methods. Finally, a parametric study is investigated including the cutout sizes, the cutout positions, and the cutout numbers from the free vibration characteristic analysis and the harmonic analysis. The results can serve as benchmark data for other research on the vibration of FGMs plates with cutouts.

Three Dimensional Crankshaft Vibration Analysis Including Gyroscopic Effect

1994 ◽  
Author(s):  
Chang-Seok Han ◽  
Kang-Woo Lee ◽  
Don-Boo Cho ◽  
Young-Jin Cheon ◽  
Seung-Dong Yeo
Keyword(s):  
Vibration Analysis ◽  
Three Dimensional ◽  
Gyroscopic Effect

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

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