NON-LINEAR VIBRATIONS OF A BEAM-MASS SYSTEM UNDER DIFFERENT BOUNDARY CONDITIONS

To simulate the non-linear vibrations of a floating bridge of a continuous system on separate floating supports with additional limiting supports at the ends with a moving load solves the most complicated problem which is the problem of describing the behavior of a span structure. A technique for simulating the vibration of an elastically supported deformable rod with limiting supports at the ends, which is a design scheme of a span structure, under the action of a moving force is developed. A computational algorithm for solving partial differential equations with varying boundary conditions is proposed, which includes boundary conditions in the model equations and does not require the subordination of basis functions to the boundary conditions. During the calculation, the basis remains constant. Piecewise linear basis functions are used to solve the differential equation. The technique is tested using a computational program Matlab, which is implemented when performing numerical studies of the behavior of the dynamic system as a function of the parameter changes. The developed technique is universal for studying the dynamics of a number of constructively non-linear systems.

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Non-linear vibrations of a beam with cantilever-Hertzian contact boundary conditions

Journal of Sound and Vibration ◽

10.1016/s0022-460x(03)00791-0 ◽

2004 ◽

Vol 275 (1-2) ◽

pp. 177-191 ◽

Cited By ~ 50

Author(s):

J.A Turner

Keyword(s):

Boundary Conditions ◽

Hertzian Contact ◽

Contact Boundary ◽

Non Linear ◽

Linear Vibrations

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THERMAL POST-BUCKLING OF SLENDER ELASTIC RODS WITH DIFFERENT BOUNDARY CONDITIONS

Revista de Engenharia Térmica ◽

10.5380/reterm.v5i2.61842 ◽

2006 ◽

Vol 5 (2) ◽

pp. 50

Author(s):

R. F. Solano ◽

M. A. Vaz

Keyword(s):

Boundary Conditions ◽

Numerical Solutions ◽

Mathematical Formulation ◽

Different Boundary Conditions ◽

Linear Ordinary Differential Equations ◽

Linear Elastic ◽

Buckling Behavior ◽

Non Linear ◽

Post Buckling ◽

Complex Boundary

This paper presents mathematical formulation, critical buckling temperature and analytical and numerical solutions for the thermal post-buckling behavior of slender rods subjected to uniform thermal load. The material is assumed to be linear elastic, homogeneous and isotropic. Furthermore, large displacements are considered hence the formulation is geometrically non-linear. Three different boundary conditions are assumed: (i) double-hinged non-movable, (ii) hinged non-movable at one end, whereas at the other end longitudinal displacement is constrained by a linear spring, and (iii) double-fixed non-movable. The governing equations are derived from geometrical compatibility, equilibrium of forces and moments, constitutive equations and strain-displacement relation, yielding a set of six first-order non-linear ordinary differential equations with boundary conditions specified at both ends, which constitutes a complex boundary value problem. The buckling and post-buckling solutions are respectively accomplished assuming infinitesimal and finite rotations. The results are presented in non-dimensional graphs for a range of temperature gradients and different values of slenderness ratios, and it is shown that this parameter governs the rod post-buckling response. The influence of the boundary conditions is evaluated through graphic results for deformed configuration, maximum deflection, maximum inclination angle and maximum curvature in the rod.

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