Free Vibration of Prestressed Plates and Shallow Shells with Piezoelectric Elements

Author:

Kamenskikh Alexander1ORCID,Lekomtsev Sergey1ORCID,Matveenko Valerii1ORCID

Affiliation:

1. Laboratory of Functional Materials Mechanics, Institute of Continuous Media Mechanics, Ural Branch of the Russian Academy of Sciences, 1, Acad. Korolev Street, Perm 614068, Russian Federation, Russia

Abstract

In this paper, the possibility of using piezoelectric elements to create a prestress state in a plate and a shallow shell leading to a change in the natural frequencies is demonstrated numerically and experimentally. Strains in the thin-walled structure are determined using the non-linear relations based on the Reissner–Mindlin theory, which are linearized with respect to the state with a small deviation from the initial equilibrium caused by the inverse piezoeffect. A mathematical formulation of the dynamics problem is based on the variational principle of virtual displacements, taking into account the prestress state. The solution was developed by the finite element method. The validity of the obtained results is confirmed by comparing the natural frequencies and mode shapes of a rectangular plate with a piezoelectric element obtained numerically and experimentally at different values of electrical voltage. A series of calculations has been carried out to analyze the influence of the elasticity modulus, length, thickness, curvature of the shallow shell and voltage on the spectrum of natural frequencies of vibration. It was found that the effectiveness of using this technique decreases with increasing stiffness of the structure as a whole.

Funder

Ministry of Science and Higher Education of the Russian Federation

Publisher

World Scientific Pub Co Pte Ltd

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3