## 1 Introduction  
Laminated glass (LG) is largely used in several ways, and mostly increasing is its application for load-bearing structural members for buildings and constructions. There, special care is required for the optimal and safe design of structural elements that are able to ensure resistance, robustness, stiffness, redundancy, etc., even under extreme loads [1, 2].  
From a structural point of view, critical design conditions can include explosive events [3, 4, 5] and impacts [6, 7, 8], natural hazards and earthquakes [9, 10], and dynamic loads in general (including moving loads, in the case of pedestrian systems [11, 12, 13, 14, 15, 16]), whose effects need dedicated calculation methods.  
While the research community is spending efforts for the refinement or development of analytical/graphical design procedures that are able to capture the limit states of interest for design, the actual dynamic behaviour of even simple laminated glass elements is often described by means of approximate methods/working assumptions [17]. Such a strategy can be beneficial at the preliminary design stage. However, the same approaches are often not able to properly capture the real dynamic performance of in-service LG structures. This is especially the case of LG systems that are subjected to severe operational conditions, where mechanical properties and boundary conditions might be strongly affected by installation methods, ambient, etc. (i.e., Figure 1).  
In this context, the paper aims at investigating the dynamic behaviour of the in-service LG members in free vibrations. Following earlier studies of literature, special care is focused on the sensitivity analysis of their fundamental frequency to a multitude of aspects of technical interest, including the type of interlayer (and its frequency-dependent shear stiffness), the aspect ratio of LG beams, the presence of flexible restraints that can provide only partial translational/rotational constraints (with respect to ideal boundaries), or the effects of possible delaminations in the bonding interlayers.  
To this aim, classical analytical methods are first recalled in Section 2, so as to introduce the literature concept of \"adjusted dynamic\" effective thickness for LG beams [17]. Hence, preliminary analytical calculations are carried out on a wide set of LG beams, giving evidence of the expected sensitivity of frequency estimates to some variations in the LG beam composition and/or geometrical configuration.  
As shown, major uncertainties in frequency estimates can derive from the actual stiffness of restraints, as well as from the dynamic response of the interlayers in use, to the imposed vibration frequency. Even further sensitivity is related--for in-service structures--to the possible presence of damage, like delaminations or material degradations, which should be properly taken into account for safe vibration assessments, with respect to early-stage design calculations. Such an aspect is further explored with the support of on-site vibration experiments (Section 3) that were carried out on selected LG beams belonging to an existing structure. The sensitivity of test predictions to major influencing parameters is discussed in Section 4, with the support of refined Finite Element (FE) numerical models (ABAQUS [18]) and parametric analytical calculations. Based on experimental observations and refined FE numerical models (ABAQUS [18]), practical analytical expressions are proposed in the paper, so that the expected vibration frequencies of a general (double) LG beam with flexible restraints could be rationally calculated. Dedicated analytical methods are also adapted to LG members and proposed to include possible delaminations in the bonding interlayers, thus resulting in more accurate dynamic estimations for in-service glass structures, based on past literature studies on composite laminates.  
Figure 1: Example of glass structures under severe operational conditions, due to (**a**) temperature variations or (**b**) overcrowding.