scholarly journals Vibration Analysis of Piezoelectric Composite Plate Resting on Nonlinear Elastic Foundations Using Sinc and Discrete Singular Convolution Differential Quadrature Techniques

2020 ◽  
Vol 2020 ◽  
pp. 1-22
Author(s):  
Ola Ragb ◽  
Mohamed Salah ◽  
M. S. Matbuly ◽  
R. B. M. Amer
Keyword(s):  
Composite Plate ◽  
Nonlinear Eigenvalue Problem ◽  
Differential Quadrature ◽  
Mode Shapes ◽  
Piezoelectric Composite ◽  
Sensors And Actuators ◽  
Elastic Foundations ◽  
Discrete Singular Convolution ◽  
Nonlinear Elastic ◽  
Foundation Parameters

In this work, free vibration of the piezoelectric composite plate resting on nonlinear elastic foundations is examined. The three-dimensionality of elasticity theory and piezoelectricity is used to derive the governing equation of motion. By implementing two differential quadrature schemes and applying different boundary conditions, the problem is converted to a nonlinear eigenvalue problem. The perturbation method and iterative quadrature formula are used to solve the obtained equation. Numerical analysis of the proposed schemes is introduced to demonstrate the accuracy and efficiency of the obtained results. The obtained results are compared with available results in the literature, showing excellent agreement. Additionally, the proposed schemes have higher efficiency than previous schemes. Furthermore, a parametric study is introduced to investigate the effect of elastic foundation parameters, different materials of sensors and actuators, and elastic and geometric characteristics of the composite plate on the natural frequencies and mode shapes.

Nonlinear Vibrations of Rectangular Mooney-Rivlin Membrane Resting on a Nonlinear Elastic Foundation

2014 ◽  
Author(s):  
Renata M. Soares ◽  
Paulo B. Gonçalves
Keyword(s):  
Elastic Foundation ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Incompressible Material ◽  
Mode Shapes ◽  
Element Formulation ◽  
Nonlinear Elastic Foundation ◽  
The Galerkin Method ◽  
Nonlinear Elastic ◽  
Foundation Parameters

The aim of the present work is to investigate the nonlinear vibration response of a pre-stretched rectangular hyperelastic membrane resting on a nonlinear elastic foundation. The membrane is composed of an isotropic, homogeneous and hyperelastic material, which is modeled as a Mooney-Rivlin incompressible material. The elastic foundation is described by a Winkler type nonlinear model with cubic nonlinearity. First the exact solution of the membrane under a biaxial stretch is obtained. Then the equations of motion of the pre-stretched membrane resting on the nonlinear foundation are derived. From the linearized equations, the natural frequencies and mode shapes of the membrane are obtained analytically. Then the natural modes are used to approximate the nonlinear deformation field using the Galerkin method. The results compare well with the results evaluated for the same membrane using a nonlinear finite element formulation. The results show the strong influence of the initial stretching ratio and foundation parameters on the linear and nonlinear oscillations and stability of the membrane.

scholarly journals Vibration Analysis of Magneto-Electro-Thermo NanoBeam Resting on Nonlinear Elastic Foundation Using Sinc and Discrete Singular Convolution Differential Quadrature Method

2019 ◽  
Vol 13 (7) ◽  
pp. 49 ◽  
Author(s):  
Ola Ragb ◽  
Mokhtar Mohamed ◽  
M.S. Matbuly
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Differential Quadrature Method ◽  
Nonlocal Parameter ◽  
Differential Quadrature ◽  
Mode Shapes ◽  
Electric Voltage ◽  
Nonlinear Elastic Foundation ◽  
Axial Forces ◽  
Nonlinear Elastic

Magneto-Electro-Thermo nanobeam resting on a nonlinear elastic foundation is presented. This beam is subjected to the external electric voltage and magnetic potential, mechanical potential and temperature change. Also, we added the new material PTZ-5H-COFe2O4. The governing equations and boundary conditions are derived using Hamilton principle. These equations are discretized by using three differential quadrature methods and iterative quadrature technique to determine the natural frequencies and mode shapes. Numerical analysis is introduced to explain the influence of computational characteristics of the proposed schemes on convergence, accuracy and efficiency of the obtained results. The obtained results agreed with the previous analytical and numerical ones. A detailed parametric study is conducted to investigate the influences of different boundary conditions, various composite materials, nonlinear elastic foundation, nonlocal parameter, the length-to-thickness ratio, external electric and magnetic potentials, axial forces, temperature and their effects on the vibration characteristics of Magneto-Electro-Thermo-Elastic nanobeam.

DQFEM Analyses of Static and Dynamic Nonlinear Elastic-Plastic Problems Using a GSR-Based Accelerated Constant Stiffness Equilibrium Iteration Technique

2001 ◽  
Vol 123 (3) ◽  
pp. 310-317 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Finite Element ◽  
Numerical Technique ◽  
Time Integration ◽  
Differential Quadrature ◽  
Element Discretization ◽  
Constant Stiffness ◽  
Structural Problems ◽  
Nonlinear Structural ◽  
Numerical Time Integration ◽  
Nonlinear Elastic

An integrated numerical technique for static and dynamic nonlinear structural problems adopting the equilibrium iteration is proposed. The differential quadrature finite element method (DQFEM), which uses the differential quadrature (DQ) techniques to the finite element discretization, is used to analyze the static and dynamic nonlinear structural mechanics problems. Numerical time integration in conjunction with the use of equilibrium iteration is used to update the response history. The equilibrium iteration can be carried out by the accelerated iteration schemes. The global secant relaxation-based accelerated constant stiffness and diagonal stiffness-based predictor-corrector equilibrium iterations which are efficient and reliable are used for the numerical computations. Sample problems are analyzed. Numerical results demonstrate the algorithm.

scholarly journals An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

2021 ◽  
Author(s):  
Ishan Ali Khan
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Wide Range ◽  
Walled Cnts

Since their discovery, immense attention has been given to carbon nanotubes (CNTs), due to their exceptional thermal, electronic and mechanical properties and, therefore, the wide range of applications in which they are, or can be potentially, employed. Hence, it is important that all the properties of carbon nanotubes are studied extensively. This thesis studies the vibrational frequencies of double-walled and triple-walled CNTs, with and without an elastic medium surrounding them, by using Finite Element Method (FEM) and Dynamic Stiffness Matrix (DSM) formulations, considering them as Euler-Bernoulli beams coupled with van der Waals interaction forces. For FEM modelling, the linear eigenvalue problem is obtained using Galerkin weighted residual approach. The natural frequencies and mode shapes are derived from eigenvalues and eigenvectors, respectively. For DSM formulation of double-walled CNTs, a nonlinear eigenvalue problem is obtained by enforcing displacement and load end conditions to the exact solution of single equation achieved by combining the coupled governing equations. The natural frequencies are obtained using Wittrick-Williams algorithm. FEM formulation is also applied to both double and triple-walled CNTs modelled as nonlocal Euler-Bernoulli beam. The natural frequencies obtained for all the cases, are in agreement with the values provided in literature.

scholarly journals Coupled flexural - torsional vibration and stability analysis of pre-loaded beams using conventional and dynamic finite element methods

2021 ◽  
Author(s):  
Heenkenda Jayasinghe
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Axial Force ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Compressive Force ◽  
Mode Shapes ◽  
Dynamic Finite Element ◽  
Starting Point

Dynamic Finite Element (DFE) and conventional finite element formulations are developed to study the flexural - torsional vibration and stability of an isotropic, homogeneous and linearly elastic pre-loaded beam subjected to an axial load and end-moment. Various classical boundary conditions are considered. Elementary Euler - Bernoulli bending and St. Venant torsion beam theories were used as a starting point to develop the governing equations and the finite element solutions. The nonlinear Eigenvalue problem resulted from the DFE method was solved using a program code written in MATLAB and the natural frequencies and mode shapes of the system were determined form the Eigenvalues and Eigenvectors, respectively. Similarly, a linear Eigenvalue problem was formulated and solved using a MATLAB code for the conventional FEM method. The conventional FEM results were validated against those available in the literature and ANSYS simulations and the DFE results were compared with the FEM results. The results confirmed that tensile forces increased the natural frequencies, which indicates beam stiffening. On the contrary, compressive forces reduced the natural frequencies, suggesting a reduction in beam stiffness. Similarly, when an end-moment was applied the stiffness of the beam and the natural frequencies diminished. More importantly, when a force and end-moment were acting in combination, the results depended on the direction and magnitude of the axial force. Nevertheless, the stiffness of the beam is more sensitive to the changes in the magnitude and direction of the axial force compared to the moment. A buckling analysis of the beam was also carried out to determine the critical buckling end-moment and axial compressive force.

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