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We consider axial movements of elastic web performing small transversal vibrations. We take into account thermal loadings on the moving web (panel) and determine the critical temperature providing the divergence (instability) of thermoelastic panel. We perform an analysis of non-stationary vibrations of the panel. Solving dynamical problem is based on application of Galerkin’s method. As an example, we present the analytical solution to the problem of nonstationary thermoelastic panel vibrations for the case of two shape functions. 相似文献
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Nikolay Banichuk Alexander Barsuk S. Y. Ivanova Juha Jeronen Evgeni Makeev 《基于设计的结构力学与机械力学》2018,46(1):1-17
We consider an infinite, homogenous linearly elastic beam resting on a system of linearly elastic supports, as an idealized model for a paper web in the middle of a cylinder-based dryer section. We obtain closed-form analytical expressions for the eigenfrequencies and the eigenmodes. The frequencies increase as the support rigidity is increased. Each frequency is bounded from above by the solution with absolutely rigid supports, and from below by the solution in the limit of vanishing support rigidity. Thus in a real system, the natural frequencies will be lower than predicted by commonly used models with rigid supports. 相似文献
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This research is devoted to the modeling of high-speed rectilinear penetration of a rigid axisymmetric body (impactor with a flat bluntness) into an elastic–plastic media with account for its rotation about the axis of symmetry. The body has an arbitrary shape of the meridian. The resistance to the motion is represented as the sum of the body drag and the contribution of friction. The dynamic system governing the body motion is derived and the qualitative and numerical analysis of the projectile movement and perforation of a slab are performed. The problem of shape optimization of impactor with a flat bluntness is studied using evolutionary algorithm. 相似文献
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N.V. Banichuk 《International Journal of Solids and Structures》1976,12(4):275-286
The paper considers the problem of optimization of mechanical systems described by partial differential equations. The shape of the region of integration of these equations is not specified beforehand but is to determined from the condition that a certain integral functional attains an extremal value. The mathematical optimization problem is reduced to a variational one having no differential constraints and the necessary optimality conditions are derived. The latter are used for seeking the cross-sectional shape of elastic bars of maximum torsional rigidity. Exact and approximate analytical solutions are given and the effectiveness of the optimal solutions is estimated. 相似文献
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The optimization problem is considered for a partial differential equation of elliptic type. The boundary of the domain in which the equation is given emerges as the control function and is to be determined from the condition of the extremum of the integral of the solution of the boundary value problem. Seeking the extremals is reduced to solving a va national problem without differential constraints. Necessary conditions for optimality are obtained, and shapes of elastic bars possessing the maximum stiffness under torsion are found with their aid. 相似文献
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We derive a complete set of necessary optimality conditions for a class of variational problems whose extremal solutions are associated with singularities. The use of these conditions is illustrated by two examples involving the optimization of the shapes of elastic bodies with stiffness and stability constraints. 相似文献
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