Random Response Analysis Of Non-Smooth Systems With Friction,Collision Or Variable-Mass

Non-smooth factors are ubiquitous in modern engineering structures.Non-smooth factors can change the dynamic mechanical behaviors dramatically,and even induce structural insecurity.So far,the researches on non-smooth systems concentrate on the cases with deterministic excitations,and the studies on the cases with stochastic excitations are very few.Stationary response and optimal control are investigated for stochastic systems with three classes of non-smooth factors,such as friction,contact/impact and mass disturbance.According to the different mechanisms of non-smooth factors,the non-smooth systems are reclassified:dynamic friction and contact are classified into the conservative-and dissipative-mechanisms non-smooth system and mass disturbance is classified into the inertia-mechanism non-smooth system,respectively.Unified approaches for each subclass are established in this thesis.Dynamic friction is described by auxiliary differential equation,and we have developed an approach to reduce the dimensions of the system equation by solving the auxiliary equation directly and the generalized harmonic transformation.The dynamic friction is equivalent to a nonlinear stiffness term and a nonlinear damping term.The stationary responses could be solved by stochastic averaging method.For systems with hard contact,which is described by restitution coefficient dependent on impact velocity,the description on barrier location could be integrated into the equation of vibration by Zhuralev transformation.The energy loss by contact is described by an added damping term and the approximated analytical solution could be solved next.For systems with Hertzdamp-type contact,the non-smooth factors in their piecewise description could be solved in the point view of energy.It is distinguished by energy whether the collision could happen or not and the analytical solutions for the two cases are given respectively.For systems with mass disturbance,the original equation,which is hard to transformed into state equations,could be approximated by Taylor expansion.The response solution is solved by applying stochastic averaging to the approximated system instead of the original one.The applicability and accuracy of the proposed analytical and semi-analytical procedures will be validated through numerical simulation for the original non-smooth systems.Research results can guide the engineering application of the typical non-smooth systems,and in theoretical aspect,extend the research field of stochastic dynamics.The successful analysis always means that the system is acknowledged well.Generally speaking,the optimal control strategy could be made by combining stochastic dynamic programming principle to suppress the stochastic response.In this thesis,the optimal control strategy is well set out for systems with mass disturbance.And it could be a good example to deal with other stochastic non-smooth systems.As one of basic scientific methods,experiment gains increasing attention by researchers in these years.The writer has made great efforts in building the lab of control of smart materials.In this process,an energy harvester for beam-type structure is designed based on the idea that the local responses could be enhanced if the beam is point-driven by wideband noises.An experiment device is built and it verifies our theoretical calculation qualitatively.