Acta mathematica scientia, Series B >
NONLINEAR ANALYSIS ON THE VIBRATION OF ELASTIC PLATES
Received date: 2016-03-14
Revised date: 2016-05-23
Online published: 2017-04-25
Supported by
Min Ding was supported in part by Innovation Award by Wuhan University of Technology under a project Grant 20410771; Shengbo Gong was supported in part by China Scholarship Council under Grant 201306230035.
We consider the vibration of elastic thin plates under certain reasonable assump-tions. We derive the nonlinear equations for this model by the Hamilton Principle. Under the conditions on the hyperbolicity for the initial data, we establish the local time well-posedness for the initial and boundary value problem by Picard iteration scheme, and obtain the estimates for the solutions.
Min DING , Shengbo GONG . NONLINEAR ANALYSIS ON THE VIBRATION OF ELASTIC PLATES[J]. Acta mathematica scientia, Series B, 2017 , 37(2) : 511 -526 . DOI: 10.1016/S0252-9602(17)30018-8
[1] Chen S H, Huang J L, Sze K Y. Multidimensional Lindstedt Poincarmethod for nonlinear vibration of axially moving beams. Journal of Sound and Vibration, 2007, 306(1):1-11
[2] Sze K Y, Chen S H, Huang J L. The incremental harmonic balance method for nonlinear vibration of axially moving beams. Journal of Sound and Vibration, 2005, 281(3):611-626
[3] Pellicano F, Vestroni F. Nonlinear dynamics and bifurcations of an axially moving beam. Journal of Vibra-tion and Acoustics, 2000, 122(1):21-30
[4] Riedel C H, Tan C A. Coupled forced response of an axially moving strip with internal resonance. Interna-tional Journal of Non-Linear Mechanics, 2002, 37(1):101-116
[5] Schochet S. Initial-boundary-value Problems for Quasilinear Symmetric Hyperbolic Systems, Existence of Solutions to the Compressible Euler Equations, and Their Incompressible Limit. Diss New York University, Graduate School of Arts and Science, 1984
[6] Schmeisser, Hans-Jrgen, Winfried S. Traces, Gagliardo-Nirenberg inequalities and Sobolev type embeddings for vector-valued function spaces. Friedrich-Schiller-University, 2001
[7] Wickert J A. Non-linear vibration of a traveling tensioned beam. International Journal of Non-Linear Mechanics, 1992, 27(3):503-517
[8] Wickert J A, Mote C D. Current research on the vibration and stability of axially-moving materials. Shock and Vibration Digest, 1988, 20:3-13
/
| 〈 |
|
〉 |