This paper investigates buckling response of higher-order shear deformable nanobeams made of functionally graded piezoelectric (FGP) materials embedded in an elastic foundation. Material properties of FGP nanobeam change continuously in thickness direction based on power-law model. To capture small size effects, Eringen’s nonlocal elasticity theory is adopted. Employing Hamilton’s principle, the nonlocal governing equations of FGP nanobeams embedded in elastic foundation are obtained. To predict buckling behavior of embedded FGP nanobeams, the Navier-type analytical solution is applied to solve the governing equations. Numerical results demonstrate the influences of various parameters such as elastic foundation, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on the buckling loads of size-dependent FGP nanobeams.

Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium

Nonlinear vibration of a nanobeam elastically bonded with a piezoelectric nanobeam via strain gradient theory

Micro scale experiments demonstrated that the material deformation behaviors of some metals and polymers deformed elasticity are size dependence, and the modified couple stress theory (MCST), which introduce an additional material length scale parameter, could capture the size dependences. The article reviews the available size-dependent models of micro-beam and micro-plate based on the MCST. For the representative micro-beams and micro-plates, the relevant mechanical models of micro-structures for static bending, vibration, buckling and pull-in instability, have been established based on the MCST, and the analytical and numerical solutions have been obtained. The results show that the size effects on the mechanical properties of the micro-structures are obvious and significant. Further possible researches on the size-dependent behaviors of the micro-structures are proposed.

A Review on the Size-Dependent Models of Micro-beam and Micro-plate Based on the Modified Couple Stress Theory

Buckling and post-buckling analyses of piezoelectric hybrid microplates subject to thermo–electro-mechanical loads based on the modified couple stress theory

In this paper, the modified couple stress theory has been employed to analyze the size-dependent behavior of a multilayer micro-plate with piezoelectric layers in the presence of electrical voltage as a model for the Atomic Force Microscope cantilever. By using the Hamilton's principle, the equations of motion considering the material length scale parameter and the effects of voltage for the piezoelectric micro-plate have been derived based on the Kirchhoff's plate model. The equations have been solved by applying the GDQR as a semi-analytical method for different boundary conditions. The static and free vibration behaviors of the micro-cantilever are investigated to signify the size effect, piezoelectric properties and external voltage. The results indicate when the material length scale parameter is comparable with plate thickness; the size effect will be significant. By separating the effects of the induced electrical field to the voltage effects and the structural effects of the piezoelectric material, the influence of the applied voltage on vibration frequency as well as the size effects at different boundary conditions have been investigated. Also it is shown that in the piezoelectric micro-cantilever the voltage effect on the size-dependent natural frequency differs significantly for the positive and negative applied voltage.

The size-dependent analysis of multilayer micro-cantilever plate with piezoelectric layer incorporated voltage effect based on a modified couple stress theory

In this paper, surface and piezoelectric effects on the vibration behavior of nanowires (NWs) are investigated by using a Timoshenko beam model. The electric field equations and the governing equations of motion for the piezoelectric NWs are derived with the consideration of surface effects. By the exact solution of the governing equations, an expression for the natural frequencies of NWs with simply-supported boundary conditions is obtained. The effects of piezoelectricity and surface effects on the vibrational behavior of Timoshenko NWs are graphically illustrated. A comparison is also made between the predictions of Timoshenko beam model and those of its Euler-Bernoulli counterpart. Additionally, the present results are validated through comparison with the available data in the literature.

https://jns.kashanu.ac.ir/article_7782_5d588755f48a758725629598540cae5a.pdf

Vibration of Piezoelectric Nanowires Including Surface Effects

The vibration behavior of piezoelectric microbeams is studied on the basis of the modified couple stress theory. The governing equations of motion and boundary conditions for the Euler-Bernoulli and Timoshenko beam models are derived using Hamilton’s principle. By the exact solution of the governing equations, an expression for natural frequencies of microbeams with simply supported boundary conditions is obtained. Numerical results for both beam models are presented and the effects of piezoelectricity and length scale parameter are illustrated. It is found that the influences of piezoelectricity and size effects are more prominent when the length of microbeams decreases. A comparison between two beam models also reveals that the Euler-Bernoulli beam model tends to overestimate the natural frequencies of microbeams as compared to its Timoshenko counterpart.

https://downloads.hindawi.com/journals/sv/2014/598292.pdf

Vibration Characteristics of Piezoelectric Microbeams Based on the Modified Couple Stress Theory

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

S. Hosseinzadeh

Author Tools

Chat about Author

Papers

Vibration of Piezoelectric Nanowires Including Surface Effects

Vibration Characteristics of Piezoelectric Microbeams Based on the Modified Couple Stress Theory