In this study, the chaotic behavior of a viscoelastic plate under integrated non-Gaussian additive and multiplicative bounded noise is investigated with an analytical approach. First, the governing equation of motion of the system was derived by introducing a set of dimensionless parameters. After that, the modified version of Melinkov’s function in terms of statistical indices was obtained, and then, for a spectrum of bounded noises, the boarder curves of chaotic areas were obtained. The model of sine/cosine Wiener was chosen for the bounded noise which enables the researcher to produce a range of wide and narrowband noises. For the case that the excitation is only additive, or only multiplicative, and that both excitations exist simultaneously, the effect of variations in structural properties and noise characteristics on the chaos area were investigated. It was shown that at frequencies close to the natural frequency of the corresponding linear system, narrowband excitations affected the chaotic behavior more than the wideband ones and vice versa. To validate the results, a numerical simulation was also made.

在这项研究中，通过分析方法研究了粘弹性板在非高斯积分加性和乘性有界噪声的作用下的混沌行为。首先，通过引入一组无量纲参数来推导系统的运动控制方程。此后，获得梅林科夫函数在统计指标方面的修改版本，然后，对于有界噪声谱，获得混沌区域的边界线。选择正弦/余弦维纳模型作为有界噪声，这使研究人员能够产生一系列宽带和窄带噪声。对于仅是加性或乘性的激励，并且两个激励同时存在的情况，研究了结构特性和噪声特性的变化对混沌区域的影响。结果表明，在接近相应线性系统固有频率的频率下，窄带激励对混沌行为的影响要大于宽带激励，反之亦然。为了验证结果，还进行了数值模拟。