Many important vibration phenomena which simultaneously contain quadratic nonlinear stiffness and damping exist in the complicated vibrating systems under practical circumstances. In this paper, we established a 2-deg...Many important vibration phenomena which simultaneously contain quadratic nonlinear stiffness and damping exist in the complicated vibrating systems under practical circumstances. In this paper, we established a 2-degree-of-freedom (DOF) nonlinear vibration model for such a system, deduced the differential equations of motion which govern its dynamics, and worked out the solutions for the governing equations by the principle of superposition of nonlinear normal modes (NLNM) based on Shaw’s theory of invariant manifolds. We conducted numerical simulations with the established model, using superposition of nonlinear normal modes and direct numerical methods, respectively. The obtained results demonstrate the feasibility of the proposed method in that its calculated data varies in a similar tendency to that of the direct numerical solutions.展开更多
Environmental micro-vibration is one of the key factors impacting the running of electronic workshop.Low frequency micro-vibration has a significant influence on the normal operation of high precision machining and te...Environmental micro-vibration is one of the key factors impacting the running of electronic workshop.Low frequency micro-vibration has a significant influence on the normal operation of high precision machining and testing equipment,and even causes irreversible damage to the equipment.Micro-vibration testing and response analysis are important to guide the vibration isolation design and ensure the stable operation of various precision equipment in the workshop.Parameters of Davidenkov model are fitted based on whale swarm optimization algorithm,and its applicability is verified.At the same time,taking the testing project of an electronic workshop raw land as an example,the micro-vibration response is analyzed.The results show that the nonlinear constitutive model constructed by whale optimization algorithm can simulate the dynamic nonlinear behavior of soil under the action of micro-vibration better.Compared with the traditional equivalent linearization method,the nonlinear constitutive model based on the whale optimization algorithm has a smaller acceleration response value.It can effectively suppress the“virtual resonance effect”produced by the equivalent linearization method.展开更多
基金Funded by the National Science Foundation of China (No. 50075029).
文摘Many important vibration phenomena which simultaneously contain quadratic nonlinear stiffness and damping exist in the complicated vibrating systems under practical circumstances. In this paper, we established a 2-degree-of-freedom (DOF) nonlinear vibration model for such a system, deduced the differential equations of motion which govern its dynamics, and worked out the solutions for the governing equations by the principle of superposition of nonlinear normal modes (NLNM) based on Shaw’s theory of invariant manifolds. We conducted numerical simulations with the established model, using superposition of nonlinear normal modes and direct numerical methods, respectively. The obtained results demonstrate the feasibility of the proposed method in that its calculated data varies in a similar tendency to that of the direct numerical solutions.
文摘Environmental micro-vibration is one of the key factors impacting the running of electronic workshop.Low frequency micro-vibration has a significant influence on the normal operation of high precision machining and testing equipment,and even causes irreversible damage to the equipment.Micro-vibration testing and response analysis are important to guide the vibration isolation design and ensure the stable operation of various precision equipment in the workshop.Parameters of Davidenkov model are fitted based on whale swarm optimization algorithm,and its applicability is verified.At the same time,taking the testing project of an electronic workshop raw land as an example,the micro-vibration response is analyzed.The results show that the nonlinear constitutive model constructed by whale optimization algorithm can simulate the dynamic nonlinear behavior of soil under the action of micro-vibration better.Compared with the traditional equivalent linearization method,the nonlinear constitutive model based on the whale optimization algorithm has a smaller acceleration response value.It can effectively suppress the“virtual resonance effect”produced by the equivalent linearization method.
