scholarly journals Nonlinear Vibration of the Blade with Variable Thickness

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
Xiaobo Jie ◽  
Wei Zhang ◽  
Jiajia Mao
Keyword(s):  
Variable Thickness ◽  
Conical Shell ◽  
Deformation Theory ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Dynamic Responses ◽  
Nonlinear Ordinary Differential Equations ◽  
Nonlinear Relationship ◽  
Governing Equations ◽  
First Order

In this paper, the nonlinear dynamic responses of the blade with variable thickness are investigated by simulating it as a rotating pretwisted cantilever conical shell with variable thickness. The governing equations of motion are derived based on the von Kármán nonlinear relationship, Hamilton’s principle, and the first-order shear deformation theory. Galerkin’s method is employed to transform the partial differential governing equations of motion to a set of nonlinear ordinary differential equations. Then, some important numerical results are presented in terms of significant input parameters.

scholarly journals A Semi-Analytical Solution for Elastic Analysis of Rotating Thick Cylindrical Shells with Variable Thickness Using Disk Form Multilayers

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammad Zamani Nejad ◽  
Mehdi Jabbari ◽  
Mehdi Ghannad
Keyword(s):  
Cylindrical Shell ◽  
Analytical Solution ◽  
Differential Equations ◽  
Variable Thickness ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
First Order ◽  
Thick Cylinder ◽  
Good Agreement

Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations. Given that the cylinder is divided intondisks,nsets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM) is also presented and good agreement was found.

Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak’s foundation

2017 ◽  
Vol 29 (5) ◽  
pp. 774-786 ◽  
Author(s):  
M Arefi ◽  
MH Zamani ◽  
M Kiani
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Governing Equations ◽  
First Order ◽  
Size Dependent ◽  
Inhomogeneity Parameter ◽  
Exponentially Graded

This work is devoted to the free vibration nonlocal analysis of an elastic three-layered nanoplate with exponentially graded graphene sheet core and piezomagnetic face-sheets. The rectangular elastic three-layered nanoplate is resting on Pasternak’s foundation. Material properties of the core are supposed to vary along the thickness direction based on the exponential function. The governing equations of motion are derived from Hamilton’s principle based on first-order shear deformation theory. In addition, Eringen’s nonlocal piezo-magneto-elasticity theory is used to consider size effects. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually, the natural frequency is scrutinized for different side length ratio, nonlocal parameter, inhomogeneity parameter, and parameters of foundation numerically. The comparison with various references is performed for validation of our analytical results.

Free vibration analysis of a porous rotor integrated with regular patterns of circumferentially distributed functionally graded piezoelectric patches on inner and outer surfaces

2020 ◽  
Vol 32 (1) ◽  
pp. 82-103
Author(s):  
Yaser Heidari ◽  
Mohsen Irani Rahaghi ◽  
Mohammad Arefi
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
External Work ◽  
First Order ◽  
Functionally Graded Piezoelectric

This article studies dynamic characteristics of a novel porous cylindrical hollow rotor based on the first-order shear deformation theory and Hamilton’s principle. The proposed model is made from a core including aluminum with porosity integrated with an arrangement of functionally graded piezoelectric patches placed on its inner and outer surfaces with a customized circumferential orientation. The piezoelectric patches are subjected to applied electric potential as sensor and actuator. The kinematic relations are developed based on the first-order shear deformation theory. Hamilton’s principle is used to derive governing equations of motion with calculation of strain and kinetic energies and external work. Solution procedure of the partial differential equations of motion is developed using Galerkin technique for simple boundary conditions. The accuracy and trueness of this work is justified using a comprehensive comparison with previous valid references. A large parametric study is presented to show influence of significant parameters such as dimensionless geometric parameters, porosity coefficient, angular speed, inhomogeneous index, and characteristics of patches on the mode shapes, natural frequencies, and critical speeds of the structure.

Free Vibration of Bimodulus Laminated Cross-Ply Conical Panels

2008 ◽  
Author(s):  
K. Khan ◽  
B. P. Patel ◽  
Y. Nath
Keyword(s):  
Free Vibration ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Equation Of Motion ◽  
Governing Equations ◽  
First Order ◽  
Lagrange’S Equation ◽  
Number Of Layers ◽  
Surface Location

The problem is formulated employing first order shear deformation theory. The governing equations, obtained using Lagrange’s equation of motion, are solved by finite element method. A detailed parametric study is carried out to study the influences of thickness ratio, aspect ratio, semicone angle, and number of layers on the free vibration natural frequencies and neutral surface location of bimodulus cross-ply composite laminated conical panels.

Chaos and Bifurcation of Composite Laminated Cantilever Rectangular Plate

2012 ◽  
Author(s):  
Wei Zhang ◽  
Minghui Zhao ◽  
Xiangying Guo
Keyword(s):  
Rectangular Plate ◽  
Deformation Theory ◽  
Complex Dynamics ◽  
Equations Of Motion ◽  
Plate Boundary ◽  
Shear Deformation Theory ◽  
Governing Equations ◽  
Chaotic Motions ◽  
Cantilever Rectangular Plate ◽  
Two Degree Of Freedom

According to the Reddy’s high-order shear deformation theory and the von-Karman type equations for the geometric nonlinearity, the chaos and bifurcation of a composite laminated cantilever rectangular plate subjected to the in-plane and moment excitations are investigated with the case of 1:2 internal resonance. A new expression of displacement functions which can satisfy the cantilever plate boundary conditions are used to make the nonlinear partial differential governing equations of motion discretized into a two-degree-of-freedom nonlinear system under combined parametric and forcing excitations, representing the evolution of the amplitudes and phases exhibiting complex dynamics. The results of numerical simulation demonstrate that there exist the periodic and chaotic motions of the composite laminated cantilever rectangular plate. Finally, the influence of the forcing excitations on the bifurcations and chaotic behaviors of the system is investigated numerically.

scholarly journals A New Beam Model for Simulation of the Mechanical Behaviour of Variable Thickness Functionally Graded Material Beams Based on Modified First Order Shear Deformation Theory

Materials ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 404 ◽  
Author(s):  
Vu Nam ◽  
Pham Vinh ◽  
Nguyen Chinh ◽  
Do Thom ◽  
Tran Hong
Keyword(s):  
Mechanical Behavior ◽  
Functionally Graded Material ◽  
Variable Thickness ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Beam Model ◽  
First Order ◽  
Graded Material ◽  
Fgm Beam

There are many beam models to simulate the variable thickness functionally graded material (FGM) beam, each model has advantages and disadvantages in computer aided engineering of the mechanical behavior of this beam. In this work, a new model of beam is presented to study the mechanical static bending, free vibration, and buckling behavior of the variable thickness functionally graded material beams. The formulations are based on modified first order shear deformation theory and interpolating polynomials. This new beam model is free of shear-locking for both thick and thin beams, is easy to apply in computation, and has efficiency in simulating the variable thickness beams. The effects of some parameters, such as the power-law material index, degree of non-uniformity index, and the length-to-height ratio, on the mechanical behavior of the variable thickness FGM beam are considered.

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