The stationary response of viscoelastic dynamical system with the right unilateral nonzero offset barrier impacts subjected to stochastic excitations is investigated. First, the viscoelastic force is approximately tre...The stationary response of viscoelastic dynamical system with the right unilateral nonzero offset barrier impacts subjected to stochastic excitations is investigated. First, the viscoelastic force is approximately treated as equivalent terms associated with effects. Then, the free vibro-impact(VI) system is absorbed to describe the periodic motion without impacts and quasi-periodic motion with impacts based upon the level of system energy. The stochastic averaging of energy envelope(SAEE) is adopted to seek the stationary probability density functions(PDFs). The detailed theoretical results for Van der Pol viscoelastic VI system with the right unilateral nonzero offset barrier are solved to demonstrate the important effects of the viscoelastic damping and nonzero rigid barrier impacts condition. Monte Carlo(MC) simulation is also performed to verify the reliability of the suggested approach. The stochastic P-bifurcation caused by certain system parameters is further explored. The variation of elastic modulus from negative to zero and then to positive witnesses the evolution process of stochastic P-bifurcation. From the vicinity of the common value to a wider range, the relaxation time induces the stochastic P-bifurcation in the two interval schemes.展开更多
A human being is a complex type of creature whose existence depends on three components;the spirit, the soul and the body which interact in a reversible manner. I do believe that there comes a time when there is lack ...A human being is a complex type of creature whose existence depends on three components;the spirit, the soul and the body which interact in a reversible manner. I do believe that there comes a time when there is lack of a reversible interaction between the soul and the spirit in certain individuals which leads to a state of mental offset. For humans to live in sociality the world is governed by humans’ laws but the mentally offset human do not live according to these laws. Due to this, they are considered as being useless in the society but I do believe that they have complete natural human rights and are not useless for they are aware of each act they perform. It is observed that the mentally offset human hardly acquire a disease from natural origin, I do believe that due to this lack of a reversible interaction between the soul and the spirit, the immune system is reprogrammed such that there is a lack of recognition of exogenous and endogenous pathological substances and there is no means of interaction between these substances and the body cells.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11872305 and 11872307)the Excellent Doctorate Cultivating Foundation of Northwestern Polytechnical University,China
文摘The stationary response of viscoelastic dynamical system with the right unilateral nonzero offset barrier impacts subjected to stochastic excitations is investigated. First, the viscoelastic force is approximately treated as equivalent terms associated with effects. Then, the free vibro-impact(VI) system is absorbed to describe the periodic motion without impacts and quasi-periodic motion with impacts based upon the level of system energy. The stochastic averaging of energy envelope(SAEE) is adopted to seek the stationary probability density functions(PDFs). The detailed theoretical results for Van der Pol viscoelastic VI system with the right unilateral nonzero offset barrier are solved to demonstrate the important effects of the viscoelastic damping and nonzero rigid barrier impacts condition. Monte Carlo(MC) simulation is also performed to verify the reliability of the suggested approach. The stochastic P-bifurcation caused by certain system parameters is further explored. The variation of elastic modulus from negative to zero and then to positive witnesses the evolution process of stochastic P-bifurcation. From the vicinity of the common value to a wider range, the relaxation time induces the stochastic P-bifurcation in the two interval schemes.
文摘A human being is a complex type of creature whose existence depends on three components;the spirit, the soul and the body which interact in a reversible manner. I do believe that there comes a time when there is lack of a reversible interaction between the soul and the spirit in certain individuals which leads to a state of mental offset. For humans to live in sociality the world is governed by humans’ laws but the mentally offset human do not live according to these laws. Due to this, they are considered as being useless in the society but I do believe that they have complete natural human rights and are not useless for they are aware of each act they perform. It is observed that the mentally offset human hardly acquire a disease from natural origin, I do believe that due to this lack of a reversible interaction between the soul and the spirit, the immune system is reprogrammed such that there is a lack of recognition of exogenous and endogenous pathological substances and there is no means of interaction between these substances and the body cells.
