共查询到20条相似文献,搜索用时 125 毫秒
1.
2.
本文根据实验拟事出流固耦联系统的非一函数和模态参数。建立了此系统的非线性振地系统的数值和解析分析,论证了充液旋转壳的流固耦联自激振动特性,求出了流固耦联系统的霍普分叉解,阐明了只结文物鱼洗的振动机理。本文结论对同类自激振动的研究具有重要的参考价值 相似文献
3.
4.
缪经良 《非线性动力学学报》1994,1(3):276-282
本文首次用摄动法获得了具有非线性复刚度的复阻尼振动系统的自由振动和强迫振动的解,并对这类问题作出了较为详尽的讨论,计算结果与试验结果几乎一致。 相似文献
5.
经典粘测理论的(定常)螺旋流动早已系统地被研究过.专著[1]提供了这方面的详尽介绍.固体圆筒的有限变形螺旋运动较晚才被人们注意.文献[2]分别讨论了不可压缩超弹性体(即具有弹性势的)圆筒螺旋运动的两个极端情形:绕和沿轴线的剪切振动,并且对Mooney材料得到了分析解.本文旨在探讨更一般的Cauchy弹性体圆筒的 相似文献
6.
7.
涡激振动是造成海洋立管疲劳损伤的重要因素, 抑制振动能够保障结构安全, 延长使用寿命. 多数涡激振动抑制方法基于干扰流场的方式, 但在复杂环境条件下, 仅通过干扰流场对振动的抑制效果有限. 因此, 从结构层面考虑开展了海洋立管涡激振动抑制研究. 基于能量传递的理论, 阐述了立管涡激振动过程中的能量传递规律. 振动能量以行波形式由能量输入区传播至能量耗散区, 主要在能量耗散区被消耗. 通过局部增大能量耗散区的阻尼, 增加振动能量在传播过程中的消耗, 实现涡激振动抑制. 为了求解立管涡激振动响应, 构建了尾流振子预报模型, 并根据实验结果验证了理论模型的可靠性. 基于理论计算得到的能量系数, 判定立管涡激振动的能量输入区和能量耗散区. 通过对比立管增大阻尼前后的响应, 分析了涡激振动抑制效果. 研究结果表明: 在能量输入区增大阻尼对涡激振动的抑制效果并不显著; 在能量耗散区增大阻尼使能量衰减系数达到临界值之后, 能够显著降低立管上部和底部的涡激振动位移; 当能量衰减系数超过临界值后, 继续增大耗散区阻尼对涡激振动抑制效果的提升不明显. 相似文献
8.
柱体涡激振动是典型的流固耦合问题,其响应规律标识码在升速流动和远离壁面条件下获得的. 而自然环境流动通常不断经历升速和降速过程,近壁面柱体的涡激振动可呈现与远离标识码体不同的响应特征. 本研究结合大型波流水槽,设计了具有微结构阻尼的柱体涡激振动装置. 基于量纲分析,开展系列水槽标识码验,通过同步测量柱体涡激振动位移时程和绕流流场变化,研究了升降流速作用下柱体涡激振动触发和停振的临界速度(即上临标识码临界速度)变化规律,探究了近壁面柱体涡激振动迟滞效应. 采用自下向上激光扫射的 PIV 流场测量系统,对比分析了固定柱体标识码振动柱体的绕流特征. 实验观测表明,近壁面柱体涡激振动触发的临界速度呈现随壁面间距比减小而逐渐减小的变化趋势;但标识码速条件下的涡激振动停振所对应的下临界速度却明显小于升速时的涡激振动触发所对应的上临界速度. 采用上临界与下临界约标识码差值可定量表征涡激振动迟滞程度,研究发现该值随着柱体间距比减小呈线性增大趋势. 涡激振动迟滞现象通常伴随振幅阶跃标识码阶跃值则随着间距比减小而非线性减小. 相似文献
9.
《力学学报》2019,(6)
柱体涡激振动是典型的流固耦合问题,其响应规律大多是在升速流动和远离壁面条件下获得的.而自然环境流动通常不断经历升速和降速过程,近壁面柱体的涡激振动可呈现与远离壁面柱体不同的响应特征.本研究结合大型波流水槽,设计了具有微结构阻尼的柱体涡激振动装置.基于量纲分析,开展系列水槽模型实验,通过同步测量柱体涡激振动位移时程和绕流流场变化,研究了升降流速作用下柱体涡激振动触发和停振的临界速度(即上临界和下临界速度)变化规律,探究了近壁面柱体涡激振动迟滞效应.采用自下向上激光扫射的PIV流场测量系统,对比分析了固定柱体和涡激振动柱体的绕流特征.实验观测表明,近壁面柱体涡激振动触发的临界速度呈现随壁面间距比减小而逐渐减小的变化趋势;但流动降速条件下的涡激振动停振所对应的下临界速度却明显小于升速时的涡激振动触发所对应的上临界速度.采用上临界与下临界约减速度差值可定量表征涡激振动迟滞程度,研究发现该值随着柱体间距比减小呈线性增大趋势.涡激振动迟滞现象通常伴随振幅阶跃,振幅阶跃值则随着间距比减小而非线性减小. 相似文献
10.
11.
Dominic G. B. Edelen 《Archive for Rational Mechanics and Analysis》1962,11(1):117-121
Summary The most general element of the null set of the Euler-Lagrange operator is shown to be a polynomial in the derivatives of the independent variables of degree less than or equal to the minimum of the number of independent and dependent variables. The coefficients of such polynomials are solutions to an exhibited system of linear algebraic and first-order partial differential equations. It is then shown that these polynomials may be represented in terms of the divergence of a vector-ordered polynomial, provided similar linear algebraic and differential conditions are satisfied by the coefficients. Thus, an arbitrary divergence is not variationally deletable.Although the calculus of variations often provides elegant and fruitful means of attacking a wide range of problems, it carries with its use certain intrinsic difficulties. The origin of these difficulties lies in the fact that there is a continuum of variational statements which leads to one and the same system of Euler-Lagrange equations. This in turn implies that any solution of the EulerLagrange equations satisfies a continuum of laws of balance. The mathematical reason for the non-uniqueness of the variational statements and the laws of balance is the well known fact that there exist Lagrangian functions for which the Euler-Lagrange equations are identically satisfied. For the case of one independent variable, such Lagrangian functions are known to be total derivatives. When several independent variables are involved, the form that Lagrangian functions must have in order to be members of the null class of the Euler-Lagrange operator is more complicated. While examining a related problem in the theory of liquid crystals, Ericksen [1] obtained results which indicated that the characterization of the null set given in Theorem 3.2 of [2] was in error. A reexamination of the theorem in question showed that this was indeed the case. This note is presented to correct the error in Theorem 3.2 and its implications. 相似文献
12.
The stored energy functional of a homogeneous isotropic elastic body is invariant with respect to translation and rotation
of a reference configuration. One can use Noether's Theorem to derive the conservation laws corresponding to these invariant
transformations. These conservation laws provide an alternative way of formulating the system of equations governing equilibrium
of a homogeneous isotropic body. The resulting system is mathematically identical to the system of equilibrium equations and
constitutive relations, generally, of another material. This implies that each solution of the system of equilibrium equations
gives rise to another solution, which describes the reciprocal deformation and solves the system of equilibrium equations
of another material. In this paper we derive conservation laws and prove the theorem on conjugate solutions for two models
of elastic homogeneous isotropic bodies – the model of a simple material and the model of a material with couple stress (Cosserat
continuum).
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
13.
14.
Youssef Z. Boutros Mina B. Abd-el-Malek Nagwa A. Badran Hossam S. Hassan 《Meccanica》2006,41(6):681-691
The boundary-layer equations for two-dimensional steady flow of an incompressible, viscous fluid near a stagnation point at
a heated stretching sheet placed in a porous medium are considered. We apply Lie-group method for determining symmetry reductions
of partial differential equations. Lie-group method starts out with a general infinitesimal group of transformations under
which the given partial differential equations are invariant. The determining equations are a set of linear differential equations,
the solution of which gives the transformation function or the infinitesimals of the dependent and independent variables.
After the group has been determined, a solution to the given partial differential equations may be found from the invariant
surface condition such that its solution leads to similarity variables that reduce the number of independent variables of
the system. The effect of the velocity parameter λ, which is the ratio of the external free stream velocity to the stretching
surface velocity, permeability parameter of the porous medium k
1, and Prandtl number Pr on the horizontal and transverse velocities, temperature profiles, surface heat flux and the wall
shear stress, has been studied. 相似文献
15.
In existing studies, the well-known Hencky problem, i.e. the large deflection problem of axisymmetric deformation of a circular membrane subjected to uniformly distributed loads, has been analyzed generally on small-rotation-angle assumption and solved by using the common power series method. In fact, the problem studied and the method adopted may be effectively expanded to meet the needs of larger deformation. In this study, the classical Hencky problem was extended to the problem without small-rotation-angle assumption and resolved by using the perturbation idea combining with power series method. First, the governing differential equations used for the solution of stress and deflection in the perturbed system were established. Taking the load as a perturbation parameter, the stress and deflection were expanded with respect to the parameter. By substituting the expansions into the governing equations and corresponding boundary conditions, the perturbation solution of all levels were obtained, in which the zero-order perturbation solution exactly corresponds to the small-rotation-angle solution, i.e. the solution of the unperturbed system. The results indicate that if the perturbed and unperturbed systems as well as the corresponding differential equations may be distinguished, the perturbation method proposed in this study can be extended to solve other nonlinear differential equations, as long as the differential equation of unperturbed system may be obtained by letting a certain parameter be zero in the corresponding equation of perturbed system. 相似文献
16.
物理信息神经网络(physics-informed neural network, PINN)是将模型方程编码到神经网络中,使网络在逼近定解条件或观测数据的同时最小化方程残差,实现偏微分方程求解.该方法虽然具有无需网格划分、易于融合观测数据等优势,但目前仍存在训练成本高、求解精度低等局限性.文章提出频域物理信息神经网络(frequency domain physics-informed neural network, FD-PINN),通过从周期性空间维度对偏微分方程进行离散傅里叶变换,偏微分方程被退化为用于约束FD-PINN的频域中维度更低的微分方程组,该方程组内各方程不仅具有更少的自变量,并且求解难度更低.因此,与使用原始偏微分方程作为约束的经典PINN相比, FD-PINN实现了输入样本数目和优化难度的降低,能够在降低训练成本的同时提升求解精度.热传导方程、速度势方程和Burgers方程的求解结果表明, FD-PINN普遍将求解误差降低1~2个数量级,同时也将训练效率提升6~20倍. 相似文献
17.
Yunfei Lv Rong Yuan Yongzhen Pei Tongtong Li 《Journal of Dynamics and Differential Equations》2017,29(2):501-521
This article deals with a stage-structured model with state-dependent delay which is assumed to be an increasing function of the population density with lower and upper bound. Firstly, according to the principle of linearized stability (Theorem 3.6, Hartung et al. in Handbook of differential equations: ordinary differential equations, 2006), we study the local stability of system in combination with the positivity and boundedness of solutions. By using the comparison principle obtained and an iterative method, the global stability of the equilibria is completely analyzed. Our results show how the interaction between interspecific and intraspecific competition affects the coexistence of both species. 相似文献
18.
Diffusional growth of cloud particles is commonly described by a coupled system of parabolic equations and ordinary differential equations. The Dirichlet boundary condition for the parabolic equation is obtained from the solution of the ordinary differential equations, but this solution itself depends on the solution of the parabolic equations. We first present the governing equations describing diffusional growth of cloud particles. In a second step, we consider a simplified model problem, motivated by the diffusional growth equations. The main difference between the simplified model problem and the diffusional growth equations consists in neglecting the dependence of the domain for the parabolic equations on the solution. For the model problem, we show unique solvability using a fixed point method. Finally, we discuss application of the main result for the model problem to the diffusional growth equations and illustrate these equations with the help of a numerical solution. 相似文献
19.
Based on the Timoshenko beam theory, the finite-deflection and the axial inertia are taken into account, and the nonlinear partial differential equations for flexural waves in a beam are derived. Using the traveling wave method and integration skills, the nonlinear partial differential equations can be converted into an ordinary differential equation. The qualitative analysis indicates that the corresponding dynamic system has a heteroclinic orbit under a certain condition. An exact periodic solution of the nonlinear wave equation is obtained using the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function tends to one in the degenerate case, a shock wave solution is given. The small perturbations are further introduced, arising from the damping and the external load to an original Hamilton system, and the threshold condition of the existence of the transverse heteroclinic point is obtained using Melnikov's method. It is shown that the perturbed system has a chaotic property under the Smale horseshoe transform. 相似文献