Free Vibration Response of FG Porous Sandwich Micro-Beam with Flexoelectric Face-Sheets Resting on Modified Silica Aerogel Foundation

2019 ◽  
Vol 11 (09) ◽  
pp. 1950087 ◽  
Author(s):  
Ali Ghorbanpour Arani ◽  
Hassan Baba Akbar Zarei ◽  
Pouya Pourmousa
Keyword(s):  
Free Vibration ◽  
Electric Field ◽  
External Electric Field ◽  
Silica Aerogel ◽  
Free Vibration Analysis ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Dimensionless Frequency ◽  
Modified Silica

The free vibration analysis of sandwich micro-beam (SMB) which is subjected to electrical field is investigated by adopting the Euler–Bernoulli beam theory (EBBT) and modified strain gradient theory (MSGT). SMB is made of three layers, including a functionally graded (FG) porous core and two flexoelectric face-sheets. The porosities are assumed to be distributed over the beam thickness based on the two distribution functions. Also, due to the electric properties of flexoelectric materials, face-sheets of SMB are subjected to the external electric field. The modified Silica Aerogel foundation model is employed to consider the effects of elastic foundation on SMB. The size-dependent governing equations of motion are derived using Hamilton’s principle and solved by Navier’s solution method for a case of simply supported SMB. The effects of various parameters, such as length to thickness ratio, porosity index, flexoelectric loadings (the load applied to the flexoelectric face-sheets caused by external electric field), small scale parameter and foundation parameters on dimensionless frequency of SMB, are assessed. The results of this work can be used for optimum design and control of micro-electro-mechanical devices.

scholarly journals Free Vibration Analysis of Triclinic Nanobeams Based on the Differential Quadrature Method

2019 ◽  
Vol 9 (17) ◽  
pp. 3517 ◽  
Author(s):  
Behrouz Karami ◽  
Maziar Janghorban ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Strain Gradient ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Vibration Response ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Beam Model

In this work, the nonlocal strain gradient theory is applied to study the free vibration response of a Timoshenko beam made of triclinic material. The governing equations of the problem and the associated boundary conditions are obtained by means of the Hamiltonian principle, whereby the generalized differential quadrature (GDQ) method is implemented as numerical tool to solve the eigenvalue problem in a discrete form. Different combinations of boundary conditions are also considered, which include simply-supports, clamped supports and free edges. Starting with some pioneering works from the literature about isotropic nanobeams, a convergence analysis is first performed, and the accuracy of the proposed size-dependent anisotropic beam model is checked. A large parametric investigation studies the effect of the nonlocal, geometry, and strain gradient parameters, together with the boundary conditions, on the vibration response of the anisotropic nanobeams, as useful for practical engineering applications.

scholarly journals Free Vibration of Functionally Graded Carbon Nanotube-reinforced Doubly-curved Shells

2020 ◽  
Vol 01 ◽  
Author(s):  
Maziar Janghorban ◽  
Behrouz Karami
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Strain Gradient ◽  
Shear Deformation Theory ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Size Dependency ◽  
Wide Range ◽  
Doubly Curved

Background:: Carbon nanotubes (CNTs) reinforced structures are the main elements of structural equipment. Hence a wide range of investigations has been performed on the response of these structures. A lot of studies covered the static and dynamic phenomenon of CNTs reinforced beams, plates and shells. However, there is no study on the free vibration analysis of a doubly-curved nano-size shell made of CNTs reinforced composite materials. Methods:: This work utilized a general third-order shear deformation theory to model the nanoshell where the general strain gradient theory is used in order to capture both nonlocality and strain gradient size-dependency. The Navier solution solving procedure is adopted to solve the partial differential equations (PDEs) and get the natural frequency of the system which is obtained through the Hamilton principle. Results:: The current study shows the importance of small-scale coefficients. The natural frequency increases with rising the strain gradient-size dependency which is because of stiffness enhancement, while the natural frequency decreases by increasing the nonlocality. In addition, the numerical examples covered the CNTs distribution patterns. Conclusion:: This work also studied the importance of shell panel’s shape. It has been observed that spherical shell panel has a higher frequency compared to the hyperbolic one. Furthermore, the frequency of the system increases with growing length-to-thickness ration.

Free vibration of piezoelectric boron nitride nanotube-based composite cylindrical micropanel embedded in an elastic medium subjected to electric potential via modified strain gradient theory

2020 ◽  
Vol 234 (12) ◽  
pp. 2309-2328
Author(s):  
Ahmad Ghasemi Ghalebahman ◽  
Meysam Bigdeli-Yeganeh ◽  
Elham Cheloeian ◽  
Morteza Khademi-Kouhi
Keyword(s):  
Boron Nitride ◽  
Aspect Ratio ◽  
Free Vibration ◽  
Electric Field ◽  
Elastic Medium ◽  
Strain Gradient ◽  
Volume Fraction ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory

This paper deals with the free vibration analysis of a smart polymeric composite sandwich micropanel made of polyvinylidene fluoride reinforced by single-walled boron nitride nanotubes resting on an elastic substrate under an electric field. The analysis procedure is based on the first-order shear deformation theory and modified strain gradient theory to investigate the size-dependent effect. The nanotubes are assumed to be uniformly distributed within the polymeric matrix. The elastomeric substrate is modeled using Winkler springs and a Pasternak shear layer. First, the constitutive equations of the nanocomposite are derived for a unit cell using a micro-electromechanics modeling technique, and the stress–strain relations are subsequently obtained with regard to mechanical and electrical terms. The equations of motion of the micropanel are obtained based on the Hamilton principle. Finally, the natural frequencies of the micropanel are obtained by extracting the mass and stiffness matrices through the method of variational calculus. A parametric study is further performed to investigate the effect of various parameters such as the stiffness of the elastic medium, the effect of electric field, different modes of vibration, aspect ratio, and so on. It is observed that the panel’s stiffness and, consequently, the natural frequency decrease as the aspect ratio increases and the nanotube volume fraction reduces. A comparison is also conducted with the classical continuum theory and modified coupled stress theory.

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