A Novel Exact Plate Theory for Bending Vibrations Based on the Partial Differential Operator Theory

Chuanping Zhou, Maofa Wang, Xiao Han, Huanhuan Xue, Jing Ni and Weihua Zhou
Additional contact information
Chuanping Zhou: School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China
Maofa Wang: School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China
Xiao Han: Hangzhou Changchuan Technology Co., Ltd., Hangzhou 310018, China
Huanhuan Xue: School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China
Jing Ni: School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China
Weihua Zhou: College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China

Mathematics, 2021, vol. 9, issue 16, 1-12

Abstract: Thick wall structures are usually applied at a highly reduced frequency. It is crucial to study the refined dynamic modeling of a thick plate, as it is directly related to the dynamic mechanical characteristics of an engineering structure or device, elastic wave scattering and dynamic stress concentration, and motion stability and dynamic control of a distributed parameter system. In this paper, based on the partial differential operator theory, an exact elasto-dynamics theory without assumptions for bending vibrations is presented by using the formal solution proposed by Boussinesq–Galerkin, and its dynamic equations are obtained under appropriate gauge conditions. The exact plate theory is then compared with other theories of plates. Since the derivation of the dynamic equation is conducted without any prior assumption, the proposed dynamic equation of plates is more exact and can be applied to a wider frequency range and greater thickness.

Keywords: exact plate theory; thick plate; bending vibration; partial differential operator theory; gauge condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/16/1920/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/16/1920/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:16:p:1920-:d:613156

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().