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971.
Analysis of free non-linear vibrations of a viscoelastic plate under the conditions of different internal resonances 总被引:1,自引:0,他引:1
Yu. A. Rossikhin 《International Journal of Non》2006,41(2):313-325
Non-linear free damped vibrations of a rectangular plate described by three non-linear differential equations are considered when the plate is being under the conditions of the internal resonance one-to-one, and the internal additive or difference combinational resonances. Viscous properties of the system are described by the Riemann-Liouville fractional derivative of the order smaller than unit. The functions of the in-plane and out-of-plane displacements are determined in terms of eigenfunctions of linear vibrations with the further utilization of the method of multiple scales, in so doing the amplitude functions are expanded into power series in terms of the small parameter and depend on different time scales, but the fractional derivative is represented as a fractional power of the differentiation operator. It is assumed that the order of the damping coefficient depends on the character of the vibratory process and takes on the magnitude of the amplitudes’ order. The time-dependence of the amplitudes in the form of incomplete integrals of the first kind is obtained. Using the constructed solutions, the influence of viscosity on the energy exchange mechanism is analyzed which is intrinsic to free vibrations of different structures being under the conditions of the internal resonance. It is shown that each mode is characterized by its damping coefficient which is connected with the natural frequency of this mode by the exponential relationship with a negative fractional exponent. It is shown that viscosity may have a twofold effect on the system: a destabilizing influence producing unsteady energy exchange, and a stabilizing influence resulting in damping of the energy exchange mechanism. 相似文献
972.
In this paper, we present recent efforts conducted to investigate the dynamic behavior of a sensor diaphragm under initial
tension. A comprehensive mechanics model based on a plate with in-plane tension is presented and analyzed to examine the transition
from plate behavior to membrane behavior. It is shown that for certain tension parameter values, it is appropriate to model
the diaphragm as a plate-membrane structure rather than as a membrane. The model predictions are found to compare well with
experimental results. The analysis and results should be valuable for carrying out the design of circular sensor diaphragms
for various applications. 相似文献
973.
基于放松单元间协调条件的大变形变分原理和全局拉格朗日方法,推导了几何非线性精化三角形薄板单元。对几何刚度矩阵,通过引入特殊的单元位移函数,有效地消除了薄板弯曲问题中伴生的膜闭锁现象。数值结果表明该单元在几何非线性分析中既能消除膜闭锁又具有较高精度。 相似文献
974.
V. V. Vedeneev 《Fluid Dynamics》2005,40(5):805-817
The stability of an elastic plate in the form of a wide strip in a supersonic inviscid gas flow is investigated in the linear approximation. An expression for the dependence of the pressure on the plate deflection, asymptotically exact for wide plates, is used. Two qualitatively different instability types are obtained: flutter with respect to a single oscillatory mode due to negative aerodynamic damping and flutter of a related type due to the interaction of oscillatory modes. For each type the stability criterion and the frequency at which the oscillation amplitude grows most intensely are found. 相似文献
975.
采用SemiLoof型约束条件的薄板三角形广义协调元 总被引:1,自引:0,他引:1
本文综合广义协调元和SemiLoof元的优点,消除其缺点,建立一个九自由度三角形薄板单元。单元自由度只含常规的角点自由度,不采用SemiLoof元还包含边点自由度的复杂作法。着眼于广义协调,克服了某些非协调元不能通过分片检验的致命弱点。采用SemiLoof型约束条件,即全部采用离散型(点型)协调条件,不采用广义协调元通常采用的积分型协调条件的复杂作法。从简便实用、高精度和收敛可靠进行全面衡量,本单元是同类低阶薄板单元中的最优单元。 相似文献
976.
本文通过拉普拉斯变换,将最小二乘法应用于薄板的塑性动力响应问题。文中分别以承受均布冲击荷载(中载情形)的简支圆板和方板的塑性动力响应问题为例,说明本文方法的计算方法及步骤,并显示出本文方法的优越性。 相似文献
977.
一个基于膜板比拟理论的四节点二十四自由度的平板壳单元 总被引:3,自引:0,他引:3
应用膜板比拟关系 ,可以避开 c1 连续性的困难 ,为板单元的构造提供了一种新的途径 ,并已成功地构造出一系列相应的板单元。本文构造了一个四节点二十四自由度的平板壳单元 ,该单元由平面四节点理性元 RQ4(膜部分 )和由膜板比拟理论构造的一个四节点十二自由度的板单元 (弯曲部分 )构成。该单元构造简单 ,数值结果表明具有很好的收敛性和精度。 相似文献
978.
IntroductionBecauseoftherequirementofc1continuity ,itisverydifficulttoconstructconformingKirchhoffplatebendingelements.Inordertoovercomethedifficulty ,manyapproacheshavebeenpresented .Intheseapproaches,therequirementofc1isreleasedonconditionoftheconvergen… 相似文献
979.
980.
Maria S. Nerantzaki John T. Katsikadelis 《Archive of Applied Mechanics (Ingenieur Archiv)》2007,77(6):381-391
The BEM is developed for nonlinear free and forced vibrations of circular plates with variable thickness undergoing large
deflections. General boundary conditions are considered, which may be also nonlinear. The problem is formulated in terms of
displacements. The solution is based on the concept of the analog equation, according to which the two coupled nonlinear differential
equations with variable coefficients pertaining to the in-plane radial and transverse deformation are converted to two uncoupled
linear ones of a substitute beam with unit axial and unit bending stiffness, respectively, under fictitious quasi-static load
distributions. Numerical examples are presented which illustrate the method and demonstrate its accuracy. 相似文献