Vibration of FG nano-sized beams embedded in Winkler elastic foundation and with various boundary conditions

2020 ◽  
pp. 1-20
Author(s):  
Büşra Uzun ◽  
Ömer Civalek ◽  
Mustafa Özgür Yaylı
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Various Boundary Conditions ◽  
Winkler Elastic Foundation

scholarly journals Modeling of smart magnetically affected flexoelectric/piezoelectric nanostructures incorporating surface effects

2017 ◽  
Vol 7 ◽  
pp. 184798041771310 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Surface Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Surface Effects ◽  
Geometrical Parameters ◽  
Various Boundary Conditions ◽  
Buckling Behavior

In this article, electromechanical buckling behavior of size-dependent flexoelectric/piezoelectric nanobeams is investigated based on nonlocal and surface elasticity theories. Flexoelectricity represents the coupling between the strain gradients and electrical polarizations. Flexoelectric/piezoelectric nanostructures can tolerate higher buckling loads compared with conventional piezoelectric ones, especially at lower thicknesses. Nonlocal elasticity theory of Eringen is applied for analyzing flexoelectric/piezoelectric nanobeams for the first time. The flexoelectric/piezoelectric nanobeams are assumed to be in contact with a two-parameter elastic foundation which consists of infinite linear springs and a shear layer. The residual surface stresses which are usually neglected in modeling of flexoelectric nanobeams are incorporated into nonlocal elasticity to provide better understanding of the physics of the problem. Applying an analytical method which satisfies various boundary conditions, the governing equations obtained from Hamilton’s principle are solved. The reliability of the present approach is verified by comparing the obtained results with those provided in literature. Finally, the influences of nonlocal parameter, surface effects plate geometrical parameters, elastic foundation, and boundary conditions on the buckling characteristics of the flexoelectric/piezoelectric nanobeams are explored in detail.

Exact Solution for Free Vibration and Buckling of Sandwich S-FGM Plates on Pasternak Elastic Foundation with Various Boundary Conditions

2019 ◽  
Vol 19 (03) ◽  
pp. 1950028 ◽  
Author(s):  
S. J. Singh ◽  
S. P. Harsha
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Load Parameter ◽  
Various Boundary Conditions ◽  
Pasternak Elastic Foundation ◽  
Parametric Studies

In the present study, free vibration and buckling characteristics of a sandwich functionally graded material (FGM) plate resting on the Pasternak elastic foundation have been investigated. The formulation is based on non-polynomial higher-order shear deformation theory with inverse hyperbolic shape function. A new modified sigmoid law is presented to compute the effective material properties of sandwich FGM plate. The governing equilibrium equations have been derived using Hamilton’s principle. Non-dimensional frequencies and critical buckling loads are evaluated by considering different boundary conditions based on admissible functions satisfying the desired primary and secondary variables. Comprehensive parametric studies have been performed to analyze the influence of geometric configuration, volume fraction exponent, elastic medium parameter, and non-dimensional load parameter on the non-dimensional frequency and critical buckling load. These parametric studies have been done for various boundary conditions and different configurations of the sandwich plate. The computed results can be used as a benchmark for future comparison of sandwich S-FGM plates.

FREE VIBRATION OF FUNCTIONALLY GRADED THIN RECTANGULAR PLATES RESTING ON WINKLER ELASTIC FOUNDATION WITH GENERAL BOUNDARY CONDITIONS USING RAYLEIGH–RITZ METHOD

2014 ◽  
Vol 06 (04) ◽  
pp. 1450043 ◽  
Author(s):  
S. CHAKRAVERTY ◽  
K. K. PRADHAN
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Power Law ◽  
Ritz Method ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Aspect Ratios ◽  
Winkler Elastic Foundation ◽  
Special Cases

In this paper, free vibration of functionally graded (FG) rectangular plates subject to different sets of boundary conditions within the framework of classical plate theory is investigated. Rayleigh–Ritz method is used to obtain the generalized eigenvalue problem. Trial functions denoting the displacement components are expressed in simple algebraic polynomial forms which can handle any sets of boundary conditions. Material properties of the FG plate are assumed to vary continuously in the thickness direction of the constituents according to power-law form. The objective is to study the effects of constituent volume fractions, aspect ratios and power-law indices on the natural frequencies. New results for frequency parameters are incorporated after performing a test of convergence. Comparison with the results from the existing literature are provided for validation in special cases. Three-dimensional mode shapes are presented for FG square plates having various boundary conditions at the edges for different power-law indices. The present investigation also involves the rectangular FG plate to lay on a uniform Winkler elastic foundation. New results for the eigenfrequencies associated with foundation parameters are also reported here with the validation in special cases after checking a convergence pattern.

scholarly journals Dynamic Stability of Bi-Directional Functionally Graded Porous Cylindrical Shells Embedded in an Elastic Foundation

2020 ◽  
Vol 10 (4) ◽  
pp. 1345 ◽  
Author(s):  
Farshid Allahkarami ◽  
Hasan Tohidi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Boundary Conditions ◽  
Dynamic Stability ◽  
Elastic Foundation ◽  
Dynamic Instability ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Practical Applications ◽  
Energy Devices ◽  
Various Boundary Conditions

This paper investigates the dynamic buckling of bi-directional (BD) functionally graded (FG) porous cylindrical shells for various boundary conditions, where the FG material is modeled by means of power law functions with even and uneven porosity distributions of ceramic and metal phases. The third-order shear deformation theory (TSDT) is adopted to derive the governing equations of the problem via the Hamilton’s principle. The generalized differential quadrature (GDQ) method is applied together with the Bolotin scheme as numerical strategy to solve the problem, and to draw the dynamic instability region (DIR) of the structure. A large parametric study examines the effect of different boundary conditions at the extremities of the cylindrical shell, as well as the sensitivity of the dynamic stability to different thickness-to-radius ratios, length-to-radius ratios, transverse and longitudinal power indexes, porosity volume fractions, and elastic foundation constants. Based on results, the dynamic stability of BD-FG cylindrical shells can be controlled efficiently by selecting appropriate power indexes along the desired directions. Furthermore, the DIR is highly sensitive to the porosity distribution and to the extent of transverse and longitudinal power indexes. The numerical results could be of great interest for many practical applications, as civil, mechanical or aerospace engineering, as well as for energy devices or biomedical systems.

scholarly journals Nonlocal FEM Formulation for Vibration Analysis of Nanowires on Elastic Matrix with Different Materials

2019 ◽  
Vol 24 (2) ◽  
pp. 38 ◽  
Author(s):  
Büşra Uzun ◽  
Ömer Civalek
Keyword(s):  
Boundary Conditions ◽  
Nonlocal Elasticity Theory ◽  
Silver Nanowire ◽  
Small Scale ◽  
Weighted Residual Method ◽  
Simply Supported ◽  
Scale Parameters ◽  
Various Boundary Conditions ◽  
Winkler Elastic Foundation ◽  
Foundation Model

In this study, free vibration behaviors of various embedded nanowires made of different materials are investigated by using Eringen’s nonlocal elasticity theory. Silicon carbide nanowire (SiCNW), silver nanowire (AgNW), and gold nanowire (AuNW) are modeled as Euler–Bernoulli nanobeams with various boundary conditions such as simply supported (S-S), clamped simply supported (C-S), clamped–clamped (C-C), and clamped-free (C-F). The interactions between nanowires and medium are simulated by the Winkler elastic foundation model. The Galerkin weighted residual method is applied to the governing equations to gain stiffness and mass matrices. The results are given by tables and graphs. The effects of small-scale parameters, boundary conditions, and foundation parameters on frequencies are examined in detail. In addition, the influence of temperature change on the vibrational responses of the nanowires are also pursued as a case study.

Benchmark Vibration Frequencies of Square Thin Plates with all Possible Combinations of Classical Boundary Conditions

2019 ◽  
Vol 19 (11) ◽  
pp. 1950131
Author(s):  
Aharon Deutsch ◽  
Joseph Tenenbaum ◽  
Moshe Eisenberger
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Point Load ◽  
Thin Plates ◽  
Vibration Frequencies ◽  
Winkler Elastic Foundation ◽  
Edge Conditions ◽  
Classical Boundary

In this work, a new method is used for the exact vibration analysis of plates with classical boundary conditions. Four classical edge conditions are included: C — clamped, S — Simply supported, F — free, and G — guided. For square plates, all the possibilities add up to 55 cases. The solutions for the natural frequencies of the plates are found in this paper using static analysis. Starting from the equations of motion of an isotropic rectangular thin plate supported on Winkler elastic foundation, with a positive or negative value, the solution for the vibration frequencies of the plate is equivalent to finding the values of the negative elastic foundation that will yield infinite deflection under a point load on the plate. The solution is composed of three parts, the sum of which satisfies exactly both the field equation and the boundary conditions. For zero force, the vibration frequencies are found up to the desired accuracy. Benchmark results of the first six normalized natural frequencies, of isotropic square plates, for all possible 55 combinations of classical boundary conditions are given, many for the first time.

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