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When putting two springs in their equilibrium positions in series attached at the end to a block and then displacing it from that equilibrium, each of the springs will experience corresponding displacements x 1 and x 2 for a total displacement of x 1 + x 2. We will be looking for an equation for the force on the block that looks like ...
Classic model used for deriving the equations of a mass spring damper model. The mass-spring-damper model consists of discrete mass nodes distributed throughout an object and interconnected via a network of springs and dampers. This model is well-suited for modelling object with complex material properties such as nonlinearity and viscoelasticity.
A spring system can be thought of as the simplest case of the finite element method for solving problems in statics. Assuming linear springs and small deformation (or restricting to one-dimensional motion) a spring system can be cast as a (possibly overdetermined) system of linear equations or equivalently as an energy minimization problem.
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
A mass m attached to a spring of spring constant k exhibits simple harmonic motion in closed space. The equation for describing the period: = shows the period of oscillation is independent of the amplitude, though in practice the amplitude should be small. The above equation is also valid in the case when an additional constant force is being ...
Materials undergoing strain are often modeled with mechanical components, such as springs (restorative force component) and dashpots (damping component). Connecting a spring and damper in series yields a model of a Maxwell material while connecting a spring and damper in parallel yields a model of a Kelvin–Voigt material. [2]
Diagram of a Maxwell material. The Maxwell model is represented by a purely viscous damper and a purely elastic spring connected in series, [4] as shown in the diagram. If, instead, we connect these two elements in parallel, [4] we get the generalized model of a solid Kelvin–Voigt material.
Stress resultants are simplified representations of the stress state in structural elements such as beams, plates, or shells. [1] The geometry of typical structural elements allows the internal stress state to be simplified because of the existence of a "thickness'" direction in which the size of the element is much smaller than in other directions.