Modal analysis of masonry structures

Abstract

This paper presents a new numerical tool for evaluating the vibration frequencies and mode shapes of masonry buildings in the presence of cracks. The algorithm has been implemented within the NOSA-ITACA code, which models masonry as a nonlinear elastic material with zero tensile strength. Some case studies are reported, and the differences between linear and nonlinear behaviour highlighted.

A New Numerical Procedure for Assessing the Dynamic Behaviour of Ancient Masonry Towers

“…This paper presents a numerical procedure implemented in the NOSA-ITACA code [12], which calculates the natural frequencies and mode shapes of masonry buildings in the presence of cracks [13]. In standard modal analysis the dynamic characteristics of a structure discretized into finite elements are determined by solving the constrained generalized eigenvalue problem…”

“…Matrix M is symmetric and positive-definite, K is symmetric and, in view of (2), positive-definite as well [16]. Given the masonry structure under examination, discretized into finite elements, and given the mechanical properties of the structure's constituent masonry-like material, together with the kinematic constraints and loads acting on it, the procedure proposed in [13] consists of the following steps.…”

“…A new numerical procedure for the modal analysis of masonry structures has been presented in [13] and implemented in the finite element code NOSA-ITACA. In standard modal analysis natural frequencies and mode shapes are calculated by solving the generalized eigenvalue problem involving the mass matrix M and the stiffness matrix K, with K determined under the assuption that the structure's constituent materials are linear elastic.…”

Dynamic characterization of progressively damaged segmental masonry arches with one settled support: experimental and numerical analyses

“…To this end, the FE NOSA-ITACA code [33], [34], developed by the Mechanics of Materials and Structures Laboratory of ISTI-CNR, adopts a numerical method based on linear perturbation and modal analysis, which takes into account the influence of existing damage on the dynamic properties of masonry buildings. The numerical method is widely described in [35,36]. The NOSA-ITACA code allows to study the nonlinear behavior of masonry structures by adopting the constitutive equation of masonry-like materials.…”

“…of the structure are estimated in the presence of cracks[35,36]. In particular, NOSA-ITACA provides the first k natural frequencies 1…”