## 1 Introduction
In this method, quadratic programming with a bivalent constraint at each time point was applied to determine the response limit of the structure. Uncertainties-but-bounded external loads were analyzed in [20], in which a nonprobability modal superposition method was proposed. The obtained solution area was wider than that in the case of using the probabilistic approach, but this method was definitely less laborious. In [21], Chebyshev polynomials were used to estimate the limits of the dynamic response of systems with uncertain parameters. Furthermore, the lower and upper limits of the structure response can be obtained by expanding the expected value into a Taylor series, as shown in [22], in which the Taylor series expansion was used to estimate the range of the nonlinear response of the structure with uncertainties. The second-order Taylor series expansion was used in [23] to determine the limits of natural frequencies. In [24], the second-order Taylor series expansion was used to determine the critical combination of uncertain parameters, i.e., the combination for which the structure response takes the minimum and maximum values. In addition, this method does not require much computational effort. The first- and second-order Taylor series expansion was also used in [25], where the solution of the eigenvalue problem and frequency response functions for systems with viscoelastic dampers were analyzed. In [26], uncertainties of a system with viscoelastic dampers were analyzed using a probabilistic approach. In [27], stochastic analysis was applied to systems with uncertain-but-bounded parameters. This method adopted a first-order approximation of the random response obtained by improving the interval analysis based on affine arithmetic. In [28], a hybrid stochastic and interval approach was used to analyze systems with mixed random and interval parameters. The expressions of mean values and the variance of the considered quantity were derived using the perturbation method and the random interval moment method. Interval analysis was used to determine the limits of these probabilistic quantities. The advantage of this approach is that it can be applied to all of the following scenarios: only random, only interval, and mixed parameters. Interval analysis can also be applied to problems related to the structure design process. In [29; 30], it was used to optimize systems with uncertainties, whereas in [31], it was used to analyze the nodes of the structure subjected to dynamic effects. Interval analysis was also used to model the nodes of the structure and hence to find the connections whose stiffness change would have a positive effect on the structure response. Furthermore, it was used in the analysis of systems with uncertainties that use an active vibration control system [32]. In Table 1, a brief overview as well as the advantages and disadvantages of three main groups of methods used for analyzing systems with uncertainties are presented. It is worth noting that the choice of an appropriate method depends on the nature of the problem and the available data. In this study, a composite beam with viscoelastic layers was considered. It is assumed that design parameters change within certain specified limits. Interval analysis was used to determine the dynamic response of the structure in the form of dynamic characteristics. Their limits were expressed as the first- and second-order Taylor series expansions. The solutions obtained were compared with those calculated using the vertex method, which can be adopted as a comparative method. This study also presented an algorithm that can obtain a critical combination of uncertain parameters, just like the vertex method, but it is much less laborious. In addition, this algorithm can also be used for large uncertainties and when the number of uncertain parameters is large. Only a few studies have been conducted on composite structures with viscoelastic layers in which parameters are uncertain. In [33], such a structure was analyzed, but using the Monte Carlo method.