Nonlinear vibrations of viscoelastic cylindrical shells taking into account shear deformation and rotatory inertia

The vibration problem of a viscoelastic cylindrical shell is studied in a geometrically nonlinear formulation using the refined Timoshenko theory. The problem is solved by the Bubnov–Galerkin procedure combined with a numerical method based on quadrature formulas. The choice of relaxation kernels is substantiated for solving dynamic problems of viscoelastic systems. The numerical convergence of the Bubnov–Galerkin procedure is examined. The effect of viscoelastic properties of the material on the response of the cylindrical shell is discussed. The results obtained by various theories are compared.     

Bending of multilayer transversally isotropic plates and beams

Ivano-Frankovskii Sector, IPPMM, National Academy of Sciences, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 30, No. 5, pp. 55–62, May, 1994.     

考虑剪切变形的薄壁箱梁畸变分析

采用广义坐标法,建立畸变位移模式和几何方程,推导出畸变剪应力;基于混合变分原理,建立了一种新的畸变理论和梁段单元模型,该理论充分考虑了剪切变形的影响。基于新理论,指出了在单箱室箱梁不存在布莱特纯畸变,明确了畸变中心的定义,研究了畸变剪应力成分对剪切变形的影响及其影响程度。结果表明,对于常见的箱梁是可以忽略剪切变形的对畸变效应的影响。     

On one model of a transversally isotropic elastic foundation

The method of expansion of the stress and displacement components into series in terms of functions of the transverse coordinate and the method of variation with respect to the state being determined are used to construct an iterative model of a transversally isotropic elastic foundation. This model allows for all the SSS components. The order of the equations does not depend on the number of terms of the expansions, which approximate the displacements and stresses. As an example, the problem on a concentrated force applied to an elastic foundation is considered. Pridneprovskaya State Academy of Building and Architecture, Dnepropetrovsk, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 36, No. 6, pp. 130–134, June, 2000.     

The influence of inplane deformation on the buckling loads of isotropic elastic plates

Archive of Applied Mechanics - The paper deals with buckling of isotropic, homogeneous elastic plates of constant thickness and shows that the effect of inplane deformation is of the same order of...     

Elastic deformation of a transversally isotropic paraboloid of revolution

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 25, No. 2, pp. 12–19, February, 1989.     

考虑剪切变形的矩形截面薄壁杆件畸变分析

在以往不考虑剪切变形的畸变分析理论基础上,假设翘曲位移及切向位移的分布函数,考虑剪切变形的影响,利用最小势能原理建立单位均布畸变荷载作用下的畸变角微分方程。采用一般解法对该畸变角微分方程进行求解,并推导求解的初参数法。随之,通过实例验证了本文理论的正确性,结果表明考虑剪切变形的影响大大提高了考虑畸变效应的计算精度。     

Superposition of low-amplitude shear vibrations on steady shear flow of an elastic fluid

The previously proposed theory of viscoelastic behavior of polymer fluids is compared with experiments on the superposition of low-amplitude shear vibrations on a steady flow. It is shown that the theory agrees satisfactorily with experiments on a single polymer solution. The superposition of a steady shear flow and low-amplitude vibrations can be used to investigate some nonlinear effects characteristic of elastic fluids by relatively simple methods. The literature devoted to this question is fairly extensive; we cite only investigations in which the main results have been obtained [1–3]. The most common experimental scheme is one-dimensional (parallel superposition), although there is also a two-dimensional scheme of orthogonal superposition of shear vibrations on steady flows. Since almost all the effects in the second scheme are qualitatively similar to the first [3], but are not so clearly manifested, we give the theoretical and experimental results relating to the parallel scheme in this paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–7, January–February, 1976.We are grateful to É. Kh. Lipkina for help in the calculations.     

Non-linear vibrations of transversely isotropic rectangular'' plates

The large amplitude free flexural vibration of transversely isotropic rectangular plate, incorporating the effects of transverse shear and rotatory inertia, is studied using the von Karman field equations. A mode shape, consisting of three generalised-coordinates together with the Galerkin technique, results in a system of three non-linear simultaneous ordinary differential equations which govern the motion of the plate. These equations are integrated using a fourth-order Runge-Kutta method to obtain the period for each amplitude of vibration. The non-linear period vs amplitude behaviour is of the hardening type and it is also found that transverse shear and rotary inertia effects increase the period and that this increase is quite significant even for thin transversely isotropic plates. The results are compared with earlier results which were based on a one-term or one generalised coordinate solution and using the Berger approximation or the von Karman field equations.