Natural frequencies and damping ratios of multi-layered laminated glass beams using a dynamic effective thickness

Multi-layered laminated glass panels are those with at least three monolithic glass layers and two viscoelastic interlayers. Multi-layered laminated glass panels are commonly used in floors, roofs and other horizontal glazing accessible to the public where a high level of security is required. Although the glass can be consider a linear-elastic material, the viscoelastic interlayers determine a non-linear behaviour of the laminated structure that must be taken into consideration. In this paper, an analytical model based on the effective thickness concept and the Ross, Kerwin and Ungar model is proposed to predict the dynamic behaviour of multi-layered laminated glass beam-like structures with different boundary conditions and at different temperatures. This analytical model allows the simplification of the calculus on this multi-layered laminated components opposite to use time-consuming numeric models. In this work, a study was carried out on a multi-layered laminated glass beam composed of three annealed glass layers and two polymeric interlayers. The analytical predictions are validated by numerical simulations and experimentally using operational modal analysis tests. The proposed model predicts the natural frequencies with errors less than 5% whereas the discrepancies in damping ratios are less than 50%

An effective thickness to estimate stresses in laminated glass beams under dynamic loadings

Finite element models for estimating stresses and displacements in laminated glass elements under dynamic loadings are very time-consuming because (1) many small 3D elements are needed to model accurately all the layers of the sandwich element and (2) the core usually shows a time and temperature dependent behaviour. In the last years, the concept of effective thickness using a quasi-elastic solution has got the attention of the research community because of its simplicity and reasonable level of accuracy achieved in the calculation of laminated glass elements under static loadings. In this paper, a dynamic effective thickness to estimate stresses in laminated glass beams under dynamic loadings in the frequency domain is derived using the correspondence principle. The analytical equations are validated by experimental tests carried out on simply supported and free–free laminated glass beams at different temperatures in the range 20–40 °

Dynamic effective thickness in laminated-glass beams and plates

In recent years, several equations have been proposed to calculate deflections and stresses in laminated-glass beams and plates under static loading using the concept of effective thickness, which consists of calculating the thickness of a monolithic element with equivalent bending properties to a laminated element. Recently, an effective thickness for the dynamic behavior of laminated-glass beams has been proposed to enable the modal parameters (natural frequencies, loss factors and mode shapes) to be determined using an equivalent monolithic model. In the present paper, the technique has been extended to the two-dimensional case of rectangular laminated-glass plates and the steps needed to estimate the modal parameters of laminated-glass elements using this methodology are presented. The dynamic effective thickness concept has been validated by experimental tests made on a laminated-glass beam and a laminated-glass plate. The results show that good accuracy is achieved in the natural frequencies and mode shapes but high scatter is encountered in the loss factor

Some Methods to Determine Scaled Mode Shapes in Natural Input Modal Analysis

IMAC-XXIII: Conference & Exposition on Structural Dynamics - Structural Health MonitoringWhen the modal model is going to be used for structural modification or for structural response simulation, the scaled mode shapes must be known. If natural input modal analysis is performed, only un-scaled mode shapes can be obtained and an extra method is necessary to obtain the scaling factor. In this paper, two new methods based on mass change are proposed. The first method involves small mass changes in two repeated tests allowing to achieve good accuracy. The second method involves only one mass change and enables the scaling factors of both the modified and unmodified mode shapes to be obtained. Finally, the effect of the normalization used in the mode shapes and the accuracy of each method are analyzed by simulatio

Scaling Factor Estimation by the Mass Change Method

International Operational Modal Analysis Conferencee (IOMAC), Copenhagen, DenmarkWhen natural input modal analysis is performed, the acting forces are unknown; by this reason only un-scaled mode shapes may be obtained so that the FRF matrix can not be constructed. If the structure is modified and a new modal testing is carried out, the scaling factors can be determined using the modal parameters (natural frequencies and mode shapes) from both the modified and the unmodified structure. Mass change is in many cases the simplest way to perform structural modification, which involves repeated testing implying mass change in different points of the structure where the mode shapes are known. In this paper, several methods to estimate the scaling factors, based on the mass change method, are presented. The accuracy obtained through the methods proposed depends on the type of normalization used in the mode shapes, the mass change magnitude and the number and the location of the masses attached to the structure, which effect is also analyzed. Finally, it is shown how the scaling factors can be used to improve the modal updating procedure

Scaling Factor Estimation Using an Optimized Mass Change Strategy, Part 1: Theory

In natural input modal analysis, only un-scaled mode shapes can be obtained. The mass change method is, in many cases, the simplest way to estimate the scaling factors, which involves repeated modal testing after changing the mass in different points of the structure where the mode shapes are known. The scaling factors are determined using the natural frequencies and mode shapes of both the modified and the unmodified structure. However, the uncertainty on the scaling factor estimation depends on the modal analysis and the mass change strategy (number, magnitude and location of the masses) used to modify the dynamic behavior of the structure. In this paper, a procedure to optimize the mass change strategy is proposed, which uses the modal parameters (natural frequencies and mode shapes) of the original structure as the basic informatio