## 1 Introduction  
The process of designing and analyzing structures involves the consideration of a wide range of factors that can influence their behavior under dynamic conditions. Uncertainties concerning design parameters, materials, production processes, and environmental conditions are significant factors that can greatly impact the safety, reliability, and performance of structures. Traditional approaches to dynamic structural analysis often overlook these uncertainties associated with design parameters, leading to inaccuracies in predicting structural behavior under real operating conditions. Therefore, addressing uncertainties is a crucial aspect of modern design processes. There are some main approaches to incorporating uncertainties associated with design parameters. The first is the probabilistic approach, which assumes that uncertainties in design parameters are modeled using statistical parameters. This allows for the determination of the probability of various scenarios, and examples of its application can be found in works by [PERSON] and [PERSON] [1], [PERSON] et al. [2], as well as [PERSON] et al. [3], including research within the context of structures with viscoelastic elements. However, many cases present challenges such as insufficient statistical data or difficulties in precisely determining probability distributions for all design parameters. In such cases, the second approach, involving interval analysis, is utilized. Here, design parameters are defined by interval values. This article employs interval analysis to investigate the impact of uncertainties in design parameters on the dynamic response of structures. One of the simplest tools that can be applied is the Monte Carlo method and the vertex method. The Monte Carlo method involves repeatedly sampling from specified intervals for individual design parameters and then conducting an analysis for each sample ([PERSON] et al. [4]). While effective, its main drawback is the high computational cost, especially for complex construction models and a large number of parameters. On the other hand, the vertex method relies on representing intervals using vertices and finding solutions for all their combinations ([PERSON] et al. in [5; 6]). This method is also time-consuming, which is why, in recent decades, efforts have been focused on finding other methods to reduce the computational burden. [PERSON] et al. in [7; 8] and [PERSON] in [9] presented a method for computing uncertain eigenvalues of systems with interval parameters. They proposed the utilization of matrix perturbation theory and interval extension theory. Both undamped and damped cases were considered. A similar approach was applied in [10] by [PERSON] and [PERSON] but for determining the dynamic response of structures. The authors also conducted a comparison of the obtained results with the probabilistic approach, based on both mathematical proofs and numerical simulations. The range of obtained results encompassed those obtained by the probabilistic method. An alternative to perturbational methods has been presented in [11] by [PERSON] et al. The authors introduced a method based on the vertex method, which was applied to the first-order deviation of dynamic response. They demonstrated that this proposed method reduces overestimation and is also more accurate than perturbational methods. However, it is worth noting that second-order components in the equations of motion were omitted in their considerations; hence, the method may not be suitable when parameter variability is high. [PERSON] et al. in [12] and [PERSON] and [PERSON] in [13] applied modal interval analysis, combining modal analysis and interval calculus. The authors presented a method for finding eigenfrequencies, modal shapes, and frequency response functions (FRFs). [PERSON] et al. in [14] determined the frequency response function for systems with uncertain parameters using the Laplace transform. This transformation converted dynamic equilibrium equations into a linear system of algebraic equations.