Research on New Types of Suspension Vibration Reduction Systems (SVRSs) with Geometric Nonlinear Damping

Jian Zhang,Xingjiu Luo,Meng Yang,Shuaishuai Sun

doi:10.1155/2021/6627693

Jian Zhang, Xingjiu Luo + Show 2 more

Open Access

https://doi.org/10.1155/2021/6627693

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Abstract

Firstly, this paper puts forward two new types of suspension vibration reduction systems (SVRSs) with geometric nonlinear damping based on general SVRS (GSVRS), which only has geometric nonlinear stiffness. Secondly, it derives the motion differential equations for the two new types of SVRS, respectively, and discusses the similarities and differences among the two types and GSVRS through the comparison of motion differential equations. Then, it conducts dimensionless processing of the motion differential equations for the two new types of SVRS and carries out a comparative study on the vibration isolation performance of the two types of SVRS under impact excitation and random excitation, respectively. At last, it performs the optimal computation of the chosen new type of SVRS through the ergodic optimization method and studies the influence rule of SVRS parameters on vibration isolation performance so as to realize the optimization of vibration isolation performance.

Highlights

Since linear damping is adopted in this paper, the nonlinear damping force generated mainly results from spatial geometrical factors. us, the damping force obtained in this paper can be deemed as a geometric nonlinear damping force. It can be known from 8C1((a0 + d0x2)/l20)x_that geometric nonlinear damping force of Type I comprises linear part and a nonlinear part which is related to the square displacement
According to (2C2x2x_/l21), the geometric nonlinear damping force of Type II comprises nonlinear part only, which is related to the square displacement
E variation rule of the geometric nonlinear damping forces is studied below. It can be known from the expression of geometric nonlinear damping force in Type I that, according to different suspension angles φ0, d0 can be either positive or negative. erefore, this paper provides two sets of parameters to calculate the curved surface of geometric nonlinear damping force 8C1((a0 + d0x2)/l20)x_: (I) φ0 π/4, C1 1000 N s/m, and l0 0.1 m; (II) φ0 π/7, C1 1000 N s/ m, and l0 0.1 m

Summary

Establishment of Motion Equation for the New Types of SVRS

Vertical damping force generated by each horizontal damping C2 can be expressed as follows: FVi FDi sin θ,. Take the first-order term of sinθ Taylor series into the formula of FVi, and FVi can be changed as follows: FVi. When the two horizontal dampings act together, total vertical damping force can be expressed as follows: FV (23). According to (2C2x2x_/l21), the geometric nonlinear damping force of Type II comprises nonlinear part only, which is related to the square displacement. According to the formula of geometric nonlinear damping force in Type I, when the displacement is 0 m, the damping force related to square displacement is 0 N, and the whole geometric nonlinear damping force comprises linear part only regardless of d0 (positive or negative). Due to lack of linear damping force, the whole geometric nonlinear damping force in Type II is smaller than that in Type I of which d0 is positive

Comparative Study

Conclusion