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Purpose <p>The current work utilizes analytical methods to examine the response of nanobeams to static bending, free vibration, and forced&#xa0;vibrations in a moist temperature environment, taking into account the impact of the flexoelectric effect. The primary objective of this&#xa0;study is to investigate the implications of nanobeam design, production, and utilization in engineering applications.</p> Method <p>The calculation formulae are derived from the integration of nonlocal theory and strain gradient theory in order to account for the&#xa0;influence of small dimensions. This study utilizes analytical methods to provide solutions for the difficulties related to static bending,&#xa0;particular vibrations, and forced vibrations of nanobeams in a thermally humid environment.</p> Results <p>The verification of calculation theory is accomplished by means of comparing it with existing literature. Additionally, this study explores&#xa0;the impact of several elements, such as material properties, environmental conditions (e.g., temperature and moisture), and applied&#xa0;load, on the vibration frequency values, as well as the static and dynamic bending displacements of nanobeams. Thus, by considering&#xa0;the flexoelectric effect and disregarding its impact on the mechanical responses of the nanobeams, one might derive significant and&#xa0;insightful findings.</p>

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Bending, Free, and Forced Vibration Responses of Nanobeams Taking Flexoelectricity and Temperature Into Account

  • 期刊论文

  • 发表日期：

    2025年9月6日

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  • Vu Hoa Binh,
  • Pham Ba Khien,
  • Bui Van Tuyen

摘要

Purpose

The current work utilizes analytical methods to examine the response of nanobeams to static bending, free vibration, and forced vibrations in a moist temperature environment, taking into account the impact of the flexoelectric effect. The primary objective of this study is to investigate the implications of nanobeam design, production, and utilization in engineering applications.

Method

The calculation formulae are derived from the integration of nonlocal theory and strain gradient theory in order to account for the influence of small dimensions. This study utilizes analytical methods to provide solutions for the difficulties related to static bending, particular vibrations, and forced vibrations of nanobeams in a thermally humid environment.

Results

The verification of calculation theory is accomplished by means of comparing it with existing literature. Additionally, this study explores the impact of several elements, such as material properties, environmental conditions (e.g., temperature and moisture), and applied load, on the vibration frequency values, as well as the static and dynamic bending displacements of nanobeams. Thus, by considering the flexoelectric effect and disregarding its impact on the mechanical responses of the nanobeams, one might derive significant and insightful findings.