i think we should know which is the reason and which is the result. K is the property of materials or components, we can get it by testing force and displacement. of course, the force can't be constant in the experiment. that's to say, the force will increase with the increase of displacement...
many references tell that the dynamic stiffness will reduce when vibration amplitude increases. And the experimental result is just so. But why there is such rule?who can explain it theoretically?