The dynamic analysis of nonlinear viscoelastic systems in the frequency domain is not an easy task. In most cases, it is due to the frequency- and temperature-dependent properties of the viscoelastic part. Additionally, due to the inherent uncertainties affecting the viscoelastic efficiency in practical situations, their handling in the nonlinear modeling methodology becomes essential nowadays. However, it is still an issue. Thus, this paper presents a numerical modeling methodology intended to perform dynamic analyses in the frequency domain of thin sandwich plates under large displacements. The uncertainties characterizing the nonlinear dynamics of the viscoelastic system are introduced on the random linear and nonlinear finite element matrices by performing the Karhunen–Loève expansion technique. The Latin hypercube sampling method is used herein as the stochastic solver, and the nonlinear frequency responses are computed using the harmonic balance method combined with the Galerkin bases. To overcome the difficulty in solving the resulting complex nonlinear eigenproblem with a frequency-dependent viscoelastic stiffness, making the stochastic nonlinear analyses in the frequency domain very costly, sometimes unfeasible, an efficient and accurate iterative reduction method is proposed to approximate the complex eigenmodes. The envelopes of nonlinear frequency responses demonstrate clearly the relevance of considering the uncertainties in design variables of viscoelastic systems having nonlinear behavior to deal with more realistic situations.

中文翻译：

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具有非线性行为的粘弹性夹层板的不确定性传播和数值评估

在频域中对非线性粘弹性系统进行动态分析并非易事。在大多数情况下，这是由于粘弹性零件的频率和温度相关特性。另外，由于在实际情况下影响粘弹性效率的内在不确定性，如今在非线性建模方法中对其进行处理变得至关重要。但是，这仍然是一个问题。因此，本文提出了一种数值建模方法，旨在在大位移下在薄夹心板的频域中进行动态分析。通过执行Karhunen-Loève展开技术，在随机线性和非线性有限元矩阵中引入了表征粘弹性系统非线性动力学的不确定性。拉丁超立方采样方法在本文中用作随机求解器，并且非线性谐波响应是使用谐波平衡方法结合Galerkin基来计算的。为了克服求解具有频率依赖的粘弹性刚度的复杂非线性本征问题的困难，使频域中的随机非线性分析非常昂贵，有时不可行，提出了一种有效且准确的迭代约简方法来逼近复杂本征模。非线性频率响应的包络清楚地表明了考虑具有非线性行为的粘弹性系统的设计变量中的不确定性以应对更现实情况的相关性。利用谐波平衡法结合Galerkin基计算非线性频率响应。为了克服求解具有频率依赖的粘弹性刚度的复杂非线性本征问题的困难，使频域中的随机非线性分析非常昂贵，有时不可行，提出了一种有效且准确的迭代约简方法来逼近复杂本征模。非线性频率响应的包络清楚地表明了考虑具有非线性行为的粘弹性系统的设计变量中的不确定性以应对更现实情况的相关性。利用谐波平衡法结合Galerkin基计算非线性频率响应。为了克服求解具有频率依赖的粘弹性刚度的复杂非线性本征问题的困难，使频域中的随机非线性分析非常昂贵，有时不可行，提出了一种有效且准确的迭代约简方法来逼近复杂本征模。非线性频率响应的包络清楚地表明了考虑具有非线性行为的粘弹性系统的设计变量中的不确定性以应对更现实情况的相关性。为了使频域中的随机非线性分析非常昂贵，有时不可行，提出了一种有效且准确的迭代约简方法来逼近复杂的本征模。非线性频率响应的包络清楚地表明了考虑具有非线性行为的粘弹性系统的设计变量中的不确定性以应对更现实情况的相关性。为了使频域中的随机非线性分析非常昂贵，有时甚至不可行，提出了一种有效且准确的迭代约简方法来逼近复杂的本征模。非线性频率响应的包络清楚地表明了考虑具有非线性行为的粘弹性系统设计变量中的不确定性以应对更现实情况的相关性。