VIBRATIONS OF ONE-WAY RECTANGULAR STEPPED THIN PLATES ON WINKLER’S FOUNDATION

Applied Mathematics and Mechanics (English Edition) ›› 1998, Vol. 19 ›› Issue (2): 169-177.

VIBRATIONS OF ONE-WAY RECTANGULAR STEPPED THIN PLATES ON WINKLER’S FOUNDATION

张英世¹, 王燮山²

1. Division 508. Department of Flight Vehicle Design and Applied Mechanics, Peking University ofAeronautics and Astronauties, Beijing 100083, P.R.China;
2. North China Electric Power University, Beijing 102206, P.R.China

收稿日期:1995-11-03 修回日期:1997-08-11 出版日期:1998-02-18 发布日期:1998-02-18
通讯作者: Chen Yushu

VIBRATIONS OF ONE-WAY RECTANGULAR STEPPED THIN PLATES ON WINKLER’S FOUNDATION

Zhang Yingshi¹, Wang Xieshan²

1. Division 508. Department of Flight Vehicle Design and Applied Mechanics, Peking University ofAeronautics and Astronauties, Beijing 100083, P.R.China;
2. North China Electric Power University, Beijing 102206, P.R.China

Received:1995-11-03 Revised:1997-08-11 Online:1998-02-18 Published:1998-02-18

摘要/Abstract

摘要： Differential equations of free forced vibrations of one-way rectangular stepped thin plated on Winkler’s foundation are established by using singular functions,their general solutions are solved:exprssion of vibration mode function and frequency equations on usual supports are derived from W operator:forced responses of such plates under different-type loads are discussed with generalized functions.

关键词: Winkler’s foundation, one-way rcctangular stepped thin plate, free vibration, forced response

Abstract: Differential equations of free forced vibrations of one-way rectangular stepped thin plated on Winkler’s foundation are established by using singular functions,their general solutions are solved:exprssion of vibration mode function and frequency equations on usual supports are derived from W operator:forced responses of such plates under different-type loads are discussed with generalized functions.

Key words: Winkler’s foundation, one-way rcctangular stepped thin plate, free vibration, forced response

张英世;王燮山. VIBRATIONS OF ONE-WAY RECTANGULAR STEPPED THIN PLATES ON WINKLER’S FOUNDATION[J]. Applied Mathematics and Mechanics (English Edition), 1998, 19(2): 169-177.

Zhang Yingshi;Wang Xieshan. VIBRATIONS OF ONE-WAY RECTANGULAR STEPPED THIN PLATES ON WINKLER’S FOUNDATION[J]. Applied Mathematics and Mechanics (English Edition), 1998, 19(2): 169-177.

[1]	H. M. FEIZABAD, M. H. YAS. Free vibration and buckling analysis of polymeric composite beams reinforced by functionally graded bamboo fibers[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(3): 543-562.
[2]	Xiaodong GUO, Zhu SU, Lifeng WANG. Dynamic characteristics of multi-span spinning beams with elastic constraints under an axial compressive force[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(2): 295-310.
[3]	Xueqian FANG, Qilin HE, Hongwei MA, Changsong ZHU. Multi-field coupling and free vibration of a sandwiched functionally-graded piezoelectric semiconductor plate[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(8): 1351-1366.
[4]	U. N. ARIBAS, M. AYDIN, M. ATALAY, M. H. OMURTAG. Cross-sectional warping and precision of the first-order shear deformation theory for vibrations of transversely functionally graded curved beams[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(12): 2109-2138.
[5]	Changsong ZHU, Xueqian FANG, Jinxi LIU. Nonlinear free vibration of piezoelectric semiconductor doubly-curved shells based on nonlinear drift-diffusion model[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(10): 1761-1776.
[6]	Lingkang ZHAO, Peijun WEI, Yueqiu LI. Free vibration of thermo-elastic microplate based on spatiotemporal fractional-order derivatives with nonlocal characteristic length and time[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(1): 109-124.
[7]	Qingdong CHAI, Yanqing WANG, Meiwen TENG. Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(8): 1203-1218.
[8]	M. H. YAS, F. AKHLAGHI, S. KAMARIAN, A. H. YAS. Static and free vibration analysis of four-parameter continuous grading elliptical sandwich plates[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(4): 523-536.
[9]	M. KOHANSAL-VAJARGAH, R. ANSARI, M. FARAJI-OSKOUIE, M. BAZDID-VAHDATI. Vibration analysis of two-dimensional structures using micropolar elements[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(7): 999-1012.
[10]	Shaowu YANG, Yuxin HAO, Wei ZHANG, Li YANG, Lingtao LIU. Nonlinear vibration of functionally graded graphene plateletreinforced composite truncated conical shell using first-order shear deformation theory[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(7): 981-998.
[11]	V. V. THAM, H. Q. TRAN, T. M. TU. Vibration characteristics of piezoelectric functionally graded carbon nanotube-reinforced composite doubly-curved shells[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(6): 819-840.
[12]	Peiliang BIAN, Hai QING. Torsional static and vibration analysis of functionally graded nanotube with bi-Helmholtz kernel based stress-driven nonlocal integral model[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(3): 425-440.
[13]	Pei ZHANG, Hai QING. Two-phase nonlocal integral models with a bi-Helmholtz averaging kernel for nanorods[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(10): 1379-1396.
[14]	S. AFSHIN, M. H. YAS. Dynamic and buckling analysis of polymer hybrid composite beam with variable thickness[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(5): 785-804.
[15]	Zhiwei ZHOU, Meixia CHEN, Kun XIE. Non-uniform rational B-spline based free vibration analysis of axially functionally graded tapered Timoshenko curved beams[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(4): 567-586.

VIBRATIONS OF ONE-WAY RECTANGULAR STEPPED THIN PLATES ON WINKLER’S FOUNDATION

VIBRATIONS OF ONE-WAY RECTANGULAR STEPPED THIN PLATES ON WINKLER’S FOUNDATION

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价