相关论文: Exact shape of an ideal heavy spring suspended at …

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…

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…

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…

We analyze a simple problem in elasticity: the \emph{initial} motion of an elastic bar that after being hanged from an end is suddenly released. In a second problem a point mass is attached on the top of the bar. The analytical solutions…

We discuss the classical motion of a spring of arbitrary mass coupled to two arbitrary massive blocks attached at its ends. A general approach to the problem is presented and some general results are obtained. Examples for which a simple…

Most research papers that exploit conical springs focus only on conical springs with a constant pitch. In order to increase the range of possibilities for designers, this paper proposes a study of conical springs with other types of spirals…

A new equation is proposed to explain the curvature of spent sparklers. We found the state of a segment of the sparkler to depend strongly on the state of its spent segments. The equation is nearly able to produce the sparkler shape for a…

A weak spring is connected at one end to a rotor turning at constant angular velocity. The spring extends to a stretched length as determined by the spring mass, rest length, spring constant, rotor radius and rotor angular velocity. When…

We present dynamical effects on conformation in a simple bead-spring model consisting of three beads connected by two stiff springs. The conformation defined by the bending angle between the two springs is determined not only by a given…

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…

We show that during normal modes of an oscillatory system consisting of a hoop and a cylinder joining their centers by an ideal spring, its central mass does not remain at rest. This effect is due to the resultant external static friction…

A folded chain, with one end fixed at the ceiling and the other end released from the same elevation, is commonly modeled as an energy-conserving system in one-dimension. However, the analytical paradigms in previous literature is…

Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the…

This article shows how to use calculus to find the center of mass position of a soft cylindrical helical spring that is suspended vertically. The spring is non-uniformly stretched by the action of gravity. A general expression for the…

The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the…

In this study we experimentally show that a stretched rainbow spring under gravity or extra weight may exhibit unconventional fall motion. Specially, when the rainbow spring is released from a high place, its lower end remains stationary…

The standing wave solution on an idealized mass spring system can be found using straight forward algebra. The solution is found when this system makes jump rope like rotations around an axis.The standing wave forms a constant shape in a…

We consider conformation dynamics of a chain-like three-body bead-spring model, in which three point masses are connected in series by two springs and the conformation is defined by the bending angle between the two springs. Previous…

We obtain an exact strain consistency equation for full, elastic, and plastic strain characteristics that have a clear physical meaning and are naturally related to stresses. The dynamic equations are represented in a form that does not use…

In this paper we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational…