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For pinned-pinned, pinned-sliding and sliding-sliding beams, this variation may exactly be expressed as Ω− = √1 + U−.
The beam is tested for two end restraint conditions, pinned-pinned and fixed-fixed.
Spatial dependence is suppressed using Galerkin's method with the time dependent pinned-pinned overhanging beam modes.
Analytical results indicate that the variation of normalized natural frequency with normalized axial force is exactly the same for pinned-pinned, pinned-sliding and sliding-sliding beams and can be expressed in a closed form.
In this work a pinned-pinned beam interacting with a viscoelastic foundation which can react both in tension and compression, or in compression alone is considered.
Two types of load velocity profiles are considered, along with clamped-clamped and pinned-pinned support conditions.
However, equilibrium equations for such arches become intractable for analytical solution unlike the extreme cases of fixed-fixed and pinned-pinned arches.
Arches with revolute flexures at the ends retain bistable characteristics of the pinned-pinned arches while being amenable for easy fabrication.
Further, in this mode, apart from a region close to buckling, the above variation is almost the same for clamped-pinned, pinned-free and free-free beams.
Then, numerical results of the natural frequency are obtained via the Galerkin method, both for pinned-pinned and clamped-clamped supports.
The beam has immovable, namely clamped-clamped and pinned-pinned boundary conditions, which leads to midplane stretching in the course of vibrations.
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