Knitted spacer fabrics can be an alternative material to typical rubber sponges and polyurethane foams for the protection of the human body from vibration exposure, such as automotive seat cushions and anti-vibration gloves. To provide a theoretical basis for the understanding of the nonlinear vibration behavior of the mass-spacer fabric system under harmonic excitation, experimental, analytical and numerical methods are used. Different from a linear mass-spring-damper vibration model, this study builds a phenomenological model with the asymmetric elastic force and the fractional derivative damping force to describe the periodic solution of the mass-spacer fabric system under harmonic excitation. Mathematical expression of the harmonic amplitude versus frequency response curve (FRC) is obtained using the harmonic balance method (HBM) to solve the equation of motion of the system. Parameter values in the model are estimated by performing curve fit between the modeled FRC and the experimental data of acceleration transmissibility. Theoretical analysis concerning the influence of varying excitation level on the FRCs is carried out, showing that nonlinear softening resonance turns into nonlinear hardening resonance with the increase of excitation level, due to the quadratic stiffness term and the cubic stiffness term in the model, respectively. The quadratic stiffness term also results in biased vibration response and causes an even order harmonic distortion. Besides, the increase of excitation level also results in elevated peak transmissibility at resonance.

中文翻译：

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谐波激励下针织间隔织物的非线性振动

针织间隔织物可以作为典型橡胶海绵和聚氨酯泡沫的替代材料，用于保护人体免受振动影响，例如汽车座垫和防震手套。为了为理解质量间隔织物系统在谐波激励下的非线性振动行为提供理论​​基础，使用了实验、解析和数值方法。与线性质量-弹簧-阻尼器振动模型不同，本研究建立了非对称弹性力和分数阶导数阻尼力的唯象模型来描述谐波激励下质量-间隔织物系统的周期解。使用谐波平衡法（HBM）求解系统的运动方程，得到谐波幅度与频率响应曲线（FRC）的数学表达式。模型中的参数值是通过在建模的 FRC 和加速度传递率的实验数据之间进行曲线拟合来估计的。对不同激励水平对FRCs影响的理论分析表明，随着激励水平的增加，非线性软化共振转变为非线性硬化共振，分别是由于模型中的二次刚度项和三次刚度项。二次刚度项还会导致有偏差的振动响应并导致偶次谐波失真。除了，