Nonlinear vibration of cracked rectangular Mindlin plate with in-plane preload

被引:25
作者
Xue, Jian [1 ,2 ]
Wang, Yuefang [1 ,2 ]
Chen, Lihua [3 ]
机构
[1] Dalian Univ Technol, Dalian 116024, Peoples R China
[2] State Key Lab Struct Anal Ind Equipment, Dalian 116024, Peoples R China
[3] Beijing Univ Technol, Beijing 100124, Peoples R China
关键词
Nonlinear vibration; Mindlin plate; Side crack; Preload; Ritz method; LARGE-AMPLITUDE VIBRATIONS;
D O I
10.1016/j.jsv.2020.115437
中图分类号
O42 [声学];
学科分类号
070206 ; 082403 ;
摘要
In this paper, the nonlinear vibration of a Mindlin plate with a side crack is investigated considering an in-plane preload. Special corner functions are incorporated into the admissible functions of displacements to describe the singularity in stress at the crack tip as well the discontinuities in displacements and rotations across the crack. Based on the Mindlin plate theory and von Karman's nonlinear plate theory, the potential and kinetic energies of the cracked loaded plated are constructed. The Ritz method with the special admissible functions is employed to determine the initial in-plane stress resultants. The natural frequencies and modes of the plate with or without in-plane preload are also determined through the Ritz method. The nonlinear dynamical equations of the plate are derived using the Hamilton's principle, and are discretized into second-order ordinary differential equations through the Galerkin's method with the three lowest order modes obtained by the Ritz method in free vibration. These equations are transformed into of first-order ordinary differential equations and are solved via the Runge-Kutta algorithm. The nonlinear dynamical response of the plate with various parameters of crack and in-plane preload under transverse harmonic excitation is presented through time history of responses, phase portraits and bifurcation diagrams in conjunction with the maximum Lyapunov exponent. It is demonstrated that the nonlinear dynamics of the plate is complicated due to the crack and in-plane compressive preload. (c) 2020 Elsevier Ltd. All rights reserved.
引用
收藏
页数:22
相关论文
共 50 条
[21]   Free Vibration of Stiffened Plate with Cracked Stiffeners [J].
Xue, Jian ;
Chen, Lihua ;
Sun, Yue ;
Zhang, Wei .
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2024, 16 (01) :253-278
[22]   Nonlinear vibration control effects of membrane structures with in-plane PVDF actuators: A parametric study [J].
Lu, Yifan ;
Shao, Qi ;
Amabili, Marco ;
Yue, Honghao ;
Guo, Hongwei .
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2020, 122
[23]   Nonlinear In-plane Vibration of a Rotating Beam with Spring-mass System Attached to the Beam [J].
Pohit, G. ;
Das, S. K. ;
Ray, P. C. .
JOURNAL OF VIBRATION ENGINEERING & TECHNOLOGIES, 2015, 3 (01) :65-82
[24]   DSC ANALYSIS FOR BUCKLING AND VIBRATION OF RECTANGULAR PLATES WITH ELASTICALLY RESTRAINED EDGES AND LINEARLY VARYING IN-PLANE LOADING [J].
Lai, S. K. ;
Xiang, Y. .
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS, 2009, 9 (03) :511-531
[25]   An Analytical Solution for Nonlinear Vibration Analysis of Functionally Graded Rectangular Plate in Contact with Fluid [J].
Hashemi, Soheil ;
Jafari, Ali Asghar .
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2021, 13 (04) :914-941
[26]   Study of Vibration Characteristics of Cantilever Rectangular Plate with Side Crack [J].
Chen, Li Hua ;
Sun, Yue ;
Zhang, Wei .
VIBRATION, STRUCTURAL ENGINEERING AND MEASUREMENT II, PTS 1-3, 2012, 226-228 :113-118
[27]   An Extended Separation-of-Variable Method for Free Vibration of Rectangular Mindlin Plates [J].
Li, Gen ;
Xing, Yufeng ;
Wang, Zekun .
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS, 2021, 21 (11)
[28]   Optimal location of a cutout in rectangular Mindlin plates for maximum fundamental frequency of vibration [J].
Wang, CM ;
Wu, WQ .
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, 2002, 24 (05) :400-404
[29]   Dynamic response of a Mindlin elastic rectangular plate under a distributed moving mass [J].
Gbadeyan, JA ;
Dada, MS .
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, 2006, 48 (03) :323-340
[30]   Free vibration of Mindlin plates based on the relative displacement plate element [J].
Ma, Y. Q. ;
Ang, K. K. .
FINITE ELEMENTS IN ANALYSIS AND DESIGN, 2006, 42 (11) :1021-1028