Seismic vulnerability of Santa Maria Novella Basilica in Florence

This paper presents the evaluation of the seismic vulnerability of Santa Maria Novella Basilica in Florence. Santa Maria Novella is one of the most important historical churches in Italy and, for this reason, different studies on the structural behavior of this monument were conducted during the last decades. Particularly, this work is focused on the dynamic behavior of the church. Mechanical properties of masonries were determined through "in situ" and laboratory tests, according to the National Italian Code (Norme Tecniche per le Costruzioni, 2018). An eigenvalue analysis on a finite element model of the Basilica was performed to obtain the fundamental vibration mode shapes.Finally, to evaluate the seismic risk index in terms of ratio between the minimum peak ground acceleration which leads to the first collapse of a structural element and the design peak ground acceleration, a response spectrum analysis was carried out to evaluate the stress fields in both columns and walls

SIMILARITY SOLUTIONS AND CONSERVATION LAWS FOR THE BEAM EQUATIONS: A COMPLETE STUDY

We study the similarity solutions and we determine the conservation laws of various forms of beam equations, such as Euler-Bernoulli, Rayleigh and Timoshenko-Prescott. The travelling-wave reduction leads to solvable fourth-order odes for all the forms. In addition, the reduction based on the scaling symmetry for the Euler-Bernoulli form leads to certain odes for which there exists zero symmetries. Therefore, we conduct the singularity analysis to ascertain the integrability. We study two reduced odes of second and third orders. The reduced second-order ode is a perturbed form of Painlevé-Ince equation, which is integrable and the third-order ode falls into the category of equations studied by Chazy, Bureau and Cosgrove. Moreover, we derived the symmetries and its corresponding reductions and conservation laws for the forced form of the abovementioned beam forms. The Lie Algebra is mentioned explicitly for all the cases

Dynamic interfacial fracture of a double cantilever beam

Assessment of the energy release rate (ERR) of layered material structures with account for dynamic and vibration effects is important for understanding and predicting fracture behavior in various engineering applications. In this work, the pure-mode-I interfacial fracture behavior of a symmetric double cantilever beam (DCB) under constant-rate opening displacement is studied using a dynamics and vibration analysis of Euler-Bernoulli beams, and the ERR is derived. Furthermore, a ‘dynamic factor’ that quantifies the dynamic effect in relation to the static component of ERR is defined. The resulting expressions are relatively short, mathematically elegant and convenient-to-use by engineers and researchers, which increases their usefulness. It is found that the dynamic factor is a function of the characteristic time only, and that this is an intrinsic property of DCB structures. An approximate method is also proposed to predict the crack extension. Predictions of ERR and crack extension are in good agreement with results from numerical results with finite-element method (FEM) simulations. Using only the first vibration mode is sufficient to capture the amplitude and frequency of ERR variation predicted by the FEM. Using higher-order vibration modes causes divergence in the amplitude of ERR oscillation; this is due to the limitation of Euler-Bernoulli beams in vibration analysis

Matching experimental and three dimensional numerical models for structural vibration problems with uncertainties

© 2017 The Author(s) The simulation model which examines the dynamic behavior of real structures needs to address the impact of uncertainty in both geometry and material parameters. This article investigates three-dimensional finite element models for structural dynamics problems with respect to both model and parameter uncertainties. The parameter uncertainties are determined via laboratory measurements on several beam-like samples. The parameters are then considered as random variables to the finite element model for exploring the uncertainty effects on the quality of the model outputs, i.e. natural frequencies. The accuracy of the output predictions from the model is compared with the experimental results. To this end, the non-contact experimental modal analysis is conducted to identify the natural frequency of the samples. The results show a good agreement compared with experimental data. Furthermore, it is demonstrated that geometrical uncertainties have more influence on the natural frequencies compared to material parameters and material uncertainties are about two times higher than geometrical uncertainties. This gives valuable insights for improving the finite element model due to various parameter ranges required in a modeling process involving uncertainty

Important considerations in optimising the structural aspect of a SDOF electromagnetic vibration energy harvester

This study investigates several important considerations to be made when optimising the structural aspects of a single-degree-of-freedom (SDOF) electromagnetic vibration energy harvester. Using the critically damped stress method, the damping and power output of the harvester were modelled and verified, displaying an excellent agreement with the experimental results. The SDOF harvester was structurally optimised under a certain set of constraints and it was found that under the fixed beam’s thickness condition, the harvester displayed an insignificant increase in power output as a function of volume when the device’s size was relatively larger. This highlights the importance of considering a smaller practical volume for this case. Additionally, when optimising the device using a low stress constraint and a low damping material, it was observed that considering the load resistance as an input parameter to the objective function would lead to a higher power output compared to the optimum load resistance condition. Further analysis indicated that there exists a power limit when the electromagnetic coupling coefficient approaches infinity. For the case of a high electromagnetic coupling coefficient value and a small volume constraint, it is possible to achieve approximately 80.0% of the harvester’s power limit. Finally, it was demonstrated that a high power output can be achieved for a SDOF electromagnetic harvester by considering a high-density proof mass centred at the free end of the beam

Estimating Natural Frequencies of Cartesian 3D Printer Based on Kinematic Scheme

Nowadays, 3D printers based on Cartesian kinematics are becoming extremely popular due to their reliability and inexpensiveness. In the early stages of the 3D printer design, once it is chosen to use the Cartesian kinematics, it is always necessary to select relative positions of axes and linear drives (prismatic joints), which would be optimal for the particular specification. Within the class of Cartesian mechanics, many designs are possible. Using the Euler–Lagrange formalism, this paper introduces a method for estimating the natural frequencies of Cartesian 3D printers based on the kinematic scheme. Comparison with the finite element method and experimental validation of the proposed method are given. The method can help to develop preliminary designs of Cartesian 3D printers and is especially useful for emerging 3D-printing technologies

The cantilever beams analysis by the means of the first-order shear deformation and the Euler-Bernoulli theory

The effect of the Timoshenko theory and the Euler-Bernoulli theory are investigated in this paper through numerical and analytical analyses. The investigation was required to obtain the optimized position of the pipes support. The Timoshenko beam theory or the first order shear deformation theory was used regarding thick beams where the shearing effect of the beam is considered. The study of the thin beams was performed with the Euler-Bernoulli theory. The analysis was done for stainless steel AISI-440C beams with the rectangular cross-section. The steel beams were a cantilever and stressed under varying point-centred load