任意变厚度的旋转扁薄壳非线性稳定的幂函数解法

以幂函数为试函数,两次使用配点法成功地分离了耦合的大挠度方程,从而导出变厚度旋转扁壳非线性稳定的计算式。支座可以是弹性的。本文给出了均布或多项式分布荷载作用下,线性或多项式型变厚度的圆锥壳、球壳、余弦壳或四次多项式型旋转壳的上、下临界荷载。均布荷载作用下指数型变厚度球壳的上临界荷载同其他方法的结果作了比较。用配点法编写的程序具有收敛范围大、精度高、通用性强和计算时间少的优点。     

夹层扁球壳的非线性稳定性

基于Reissner假设和变分原理,给出夹层扁球壳在均布压力作用下的大挠度方程,采用修正迭代法求得了夹层扁球壳非线性稳定问题的解析解,得到两类边界条件下临界屈曲载荷的表达式,讨论了几何参数和物理参数对临界屈曲载荷的影响.     

The dynamic stability and nonlinear resonance of a flexible connecting rod: Continuous parameter model

The transverse vibrations of a flexible connecting rod in an otherwise rigid slider-crank mechanism are considered. An analytical approach using the method of multiple scales is adopted and particular emphasis is placed on nonlinear effects which arise from finite deformations. Several nonlinear resonances and instabilities are investigated, and the influences of important system parameters on these resonances are examined in detail.     

Stress-strain state of shallow shells with rectangular planform and varying thickness: Refined formulation

The stress-strain state of a shallow shell with rectangular planform and varying thickness is analyzed in a refined formulation for different boundary conditions. A numerical-and-analytic method is developed based on the spline-approximation and discrete-orthogonalization methods. The stress-strain state of shallow shells with thickness varied without change in weight is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 80–91, October 2007.     

弹性地基上圆底扁球壳的非线性动力问题

本文从Krmn非线性基本微分方程出发,提出了将修正迭代法和伽辽金法联合运用,分析了弹性地基上圆底扁球壳在均布荷载作用下周边固定边界条件的非线性动力响应问题,给出了中心振幅与时间t之间关系的二次近似解析表达式;同时还讨论了Winkler地基参数K对中心最大振幅的影响。此外将本文的部分结果和已有文献结果作了比较,二者吻合较好。     

APPLICATION OF THE MODIFIED METHOD OF MULTIPLE SCALES TO THE BENDING PROBLEMS FOR CIRCULAR THIN PLATE AT VERY LARGE DEFLECTION AND THE ASYMPTOTICS OF SOLUTIONS(Ⅱ)

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APPLICATION OF THE MODIFIED METHOD OF MULTIPLE SCALES TO THE BENDING PROBLEMS FOR CIRCULAR THIN PLATE AT VERY LARGE DEFLECTION AND THE ASYMPTOTICS OF SOLUTIONS(Ⅱ)

This paper is a continuation of part (Ⅰ), on the asymptotics behaviors of the series solutions investigated in (Ⅰ). The remainder terms of the series solutions are estimated by the maximum norm.     

Stress state of nonthin orthotropic shells with varying thickness and rectangular planform

The stress-strain state of a shallow orthotropic shell with rectangular planform and thickness varying in two coordinate directions is studied. A refined problem formulation is used. Different boundary conditions are considered. A numerical analytic approach based on the spline approximation and discrete orthogonalization is developed. The stress-strain state of shallow orthotropic shells whose thickness is varied keeping its mass constant is studied Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 91–102, August 2008.     

含孔扁薄球壳的复变函数解法

本文建立了含孔扁薄球壳的复变函数求解方法,从而为这一类问题的求解提供了一条有效而规范的途径.     

Effect of gravity on nonlinear oscillations of a horizontal,immovable-end beam

A critical problem in designing large structures for space applications, such as space stations and parabolic antennas, is the limitation of testing these structures and their substructures on earth. These structures will exhibit very high flexibilities due to the small loads expected to be encountered in orbit. It has been reported in the literature that the gravitational sag effect under dead weight is of extreme importance during ground tests of space-station structural components [1–4]. An investigation of a horizontal, pinned-pinned beam with complete axial restraint and undergoing large-amplitude oscillations about the statically deflected position is presented here. This paper presents a solution for the frequency-amplitude relationship of the nonlinear free oscillations of a horizontal, immovable-end beam under the influence of gravity.The governing equation of motion used for the analysis is the Bernoulli-Euler type modified to include the effects of mid-plane stretching and gravity. Boundary conditions are simply supported such that at both ends there is no bending moment and no transverse and axial displacements. These boundary conditions give rise to an initial tension in the statically deflected shape. The displacement function consists of an assumed space mode using a simple sine function and unknown amplitude which is a function of time. This assumption provides for satisfaction of the boundary conditions and leads to an ordinary differential equation which is nonlinear, containing both quadratic and cubic functions of the amplitude. The perturbation method of multiple scales is used to provide an approximate solution for the fundamental frequency-amplitude relationship.Since the beam is initially deflected the small-amplitude fundamental natural frequency always increases relative to the free vibration situation provided in zero gravity. The nonlinear equation provides for interactions between frequency and amplitude in that both hardening and softening effects arise. The coefficient of the quadratic term in the nonlinear equation arises from the static (dead load) portion of the deflection. This quadratic term, depending upon its magnitude, introduces a softening effect that overcomes the hardening term (due to initial axial tension developed by deflection) for large slenderness ratios.For very large slender, immovable-end beams, the fundamental natural frequency is greater than that of beams without axial constraints undergoing small amplitude oscillations. This phenomenon is attributed to the stiffening effect of the statically-induced axial tension. However, the stiffening effect of axial tension in beams with slenderness ratios greater than approximately 392 undergoing large-amplitude symmetric-mode oscillations is overpowered by the presence of gravitational loading.Nomenclature A amplitude of the first harmonic - A ₁ cross-sectional area of beam - a(t) vibratory amplitude - E Young's modulus - g acceleration due to gravity - g ₁,g ₂,g ₃ constants defined in equations (8) - I area moment of inertia of cross-section - L length of beam - N axial tension force induced by gravitational loading