Related papers: Analytical and Experimental Study of Conical Teles…
A general expression for the elastic potential energy of a helical spring is derived using the basic concepts of elasticity theory and geometry. Both the translational and the rotational displacement of the spring's moving ends are…
We show that when a gradually increasing tensile force is applied to the ends of a helical spring with sufficiently large ratios of radius to pitch and twist to bending rigidity, the end-to-end distance undergoes a sequence of discontinuous…
In the present article we determine the exact shape of an ideal spring suspended at both ends. Historically, this goes under the name of Elastica problem. The total energy of the suspended spring is a functional depending on two independent…
The static equilibrium deformation of a heavy spring due to its own weight is calculated for two cases. First for a spring hanging in a constant gravitational field, then for a spring which is at rest in a rotating system where it is…
Helical torsion springs with tangential legs are used for many applications: from simple everyday use systems, like clothes peg, to advanced systems, as sectional doors. Torsion springs are usually exploited with an inner rod as a guide.…
In the present article the linear mass Density for vertically suspended heavy springs is calculated for two different cases. First for a spring of invariable length suspended at the top and fixed at the bottom of the spring, then for a…
Cylindrical extension springs have been commonly exploited in mechanical systems for years and their behavior could be considered as well identified. Nevertheless, it appears that the influence of the loops on the global stiffness is not…
We study the force vs extension behaviour of a helical spring made of a thin torsionally-stiff anisotropic elastic rod. Our focus is on springs of very low helical pitch. For certain parameters of the problem such a spring is found not to…
Aeroelastic model testing is essential for evaluating the wind resistance performance of long-span suspension bridges. In these models, truss girders are commonly modelled by a discrete-stiffness system incorporating U-shaped springs to…
The Slinky is a well-known example of a highly flexible helical spring, exhibiting large, geometrically nonlinear deformations from minimal applied forces. By considering it as a system of coils that act to resist axial, shearing, and…
This paper discusses the oscillations of a spring (slinky) under its own weight. A discrete model, describing the slinky by $N$ springs and $N$ masses, is introduced and compared to a continuous treatment. One interesting result is that the…
Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous application focused on two-dimensional homogeneous fluid, this study examines the geometric…
We study slender, helical elastic rods subject to distributed forces and moments. Focussing on the case when the helix axis remains straight, we employ the method of multiple scales to systematically derive an 'equivalent-rod' theory from…
Springs are used for a wide range of applications in physics and engineering. Possibly, one of its most common uses is to study the nature of restoring forces in oscillatory systems. While experiments that verify the Hooke's law using…
This paper investigates the behavior of a heavy soft spring in steady circular motion. Since the spring is inhomogeneous due to centrifugal force, one can rigorously prove that it follows the one-dimensional static Willis-form equations.…
The authors investigate the ideal, nondriven multifluid equations of motion to identify consistent (i.e., truly stationary), mechanically static models for composition profiles within the thermosphere. These physically faithful functions…
The problem of finding the frequencies of small longitudinal oscillations of a spring having a finite mass and stiffness, attached at one end to a wall and at the other end to a body of finite mass, is discussed. This problem was repeatedly…
The non-evanescent vibration, evanescent vibration and forced vibration of an oscillator attached to the massless spring are always discussed in general mechanics courses. In this article, we focus on the heavy-spring conditions. We first…
A decomposition of the energy and helicity fluxes in a turbulent hydrodynamic flow is proposed. The decomposition is based on the projection of the flow to a helical basis that allows to investigate separately the role of interactions among…
The spring-mass system studied in undergraduate physics laboratories may exhibit complex dynamics due to the simultaneous action of gravitational and elastic forces in addition to air friction. In the first part of this paper, we describe a…