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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 mass suspended from a spring, for example, might, if pulled and released, bounce up and down. On each bounce, the system tends to return to its equilibrium position, but overshoots it. Sometimes losses (e.g. frictional) damp the system and can cause the oscillations to gradually decay in amplitude towards zero or attenuate. The damping ratio ...
The mass-spring model is converted into a system of constraints, which demands that the distance between the connected nodes be equal to the initial distance. This system is solved sequentially and iteratively, by directly moving nodes to satisfy each constraint, until sufficiently stiff cloth is obtained.
The graph shows the effect of a tuned mass damper on a simple spring–mass–damper system, excited by vibrations with an amplitude of one unit of force applied to the main mass, m 1. An important measure of performance is the ratio of the force on the motor mounts to the force vibrating the motor, F 0 / F 1 . This assumes that the ...
In a real spring–mass system, the spring has a non-negligible mass. Since not all of the spring's length moves at the same velocity v {\displaystyle v} as the suspended mass M {\displaystyle M} (for example the point completely opposed to the mass M {\displaystyle M} , at the other end of the spring, is not moving at all), its kinetic energy ...
For example, calculating the FRF for a mass–spring–damper system with a mass of 1 kg, spring stiffness of 1.93 N/mm and a damping ratio of 0.1. The values of the spring and mass give a natural frequency of 7 Hz for this specific system. Applying the 1 Hz square wave from earlier allows the calculation of the predicted vibration of the mass.
A passive isolation system, such as a shock mount, in general contains mass, spring, and damping elements and moves as a harmonic oscillator. The mass and spring stiffness dictate a natural frequency of the system. Damping causes energy dissipation and has a secondary effect on natural frequency. Passive Vibration Isolation
The first applications of computer simulations for dynamic systems was in the aerospace industry. [5] Commercial uses of dynamic simulation are many and range from nuclear power, steam turbines, 6 degrees of freedom vehicle modeling, electric motors, econometric models, biological systems, robot arms, mass-spring-damper systems, hydraulic systems, and drug dose migration through the human body ...