Damping is largely increasing with the vibration amplitude during nonlinear vibrations of rectangular plates. At the same time, soft materials present an increase in their stiffness with the vibration frequency. These two phenomena appear together and are both explained in the framework of the viscoelasticity. While the literature on nonlinear vibrations of plates is very large, these aspects are rarely touched. The present study applies the fractional linear solid model to describe the viscoelastic material behavior. This allows to capture at the same time (i) the increase in the storage modulus with the vibration frequency and (ii) the frequency-dependent nonlinear damping in nonlinear vibrations of rectangular plates. The solution to the nonlinear vibration problems is obtained through Lagrange equations by deriving the potential energy of the plate and the dissipated energy, both geometrically nonlinear and frequency dependent. The model is then applied to a silicone rubber rectangular plate tested experimentally. The plate was glued to a metal frame and harmonically excited by stepped sine testing at different force levels, and the vibration response was measured by a laser Doppler vibrometer. The comparison of numerical and experimental results was very satisfactorily carried out for: (i) nonlinear vibration responses in the frequency and time domain at different excitation levels, (ii) dissipated energy versus excitation frequency and excitation force, (iii) storage energy and (iv) loss factor, which is particularly interesting to evaluate the plate dissipation versus frequency at different excitation levels. Finally, the linear and nonlinear damping terms are compared.

在矩形板的非线性振动过程中，阻尼随着振动幅度的增加而大大增加。同时，软材料的刚度随振动频率而增加。这两种现象同时出现，并且都在粘弹性的框架内得到解释。尽管关于板的非线性振动的文献非常多，但很少涉及这些方面。本研究应用分数线性实体模型来描述粘弹性材料的行为。这允许同时捕获（i）储能模量随振动频率的增加，以及（ii）矩形板非线性振动中随频率变化的非线性阻尼。通过拉格朗日方程，通过推导板的势能和耗散能，可以得出非线性振动问题的解决方案，这些能量在几何上是非线性的，并且与频率有关。然后将模型应用于实验测试的硅橡胶矩形板。将该板胶粘到金属框架上，并通过分步正弦测试在不同的力水平下进行谐波激励，并通过激光多普勒振动计测量振动响应。数值和实验结果的比较非常令人满意：（i）在不同激励水平下在频域和时域中的非线性振动响应;（ii）耗能与激励频率和激励力的关系;（iii）储能和（ iv）损失系数，在不同激励水平下评估极板耗散与频率的关系尤其有趣。最后，比较了线性和非线性阻尼项。