Abstract In this note, some remarks on the modelling of a multi-degree-of-freedom system, a three-story shear-building structure, is presented. The modelling of a mechanical system is one of the most important aspects in engineering and physics, since is crucial for the understanding of the system. Besides, the model, if properly made, can be also useful to predict some phenomenon that might appear on the system itself and is unknown to researchers. In many situations, the system studied is simplified as a physical model, where the main characteristics regarding the dynamics of the system are defined, such as inertia and stiffness. This facilitates the obtainment of the mathematical model, which is used to obtain quantitative results that can be checked in some experimental procedure. This work presents the modeling of a shear-building structure, where the equations of motion and the natural frequencies of oscillation are obtained. The numeric values are validated by the comparison with experimental results from a previous work.

Abstract This paper presents a methodology for the measurement of strain by means of strain-gauges, where the data acquisition is done by using an Arduino Uno board, due to the low-cost and the easy manipulation of this microcontrollers. The measured signal conditioning is performed by means of a Wheatstone Bridge and then discretized by an Analog-Digital Converter (ADC) external to the Arduino. For the validation of the proposed measurement system, experiments are performed on a cantilever beam and on a cantilever-supported shaft, where the experimental results are compared with those obtained analytically and by simulation using the finite element method. The results obtained are in agreement with the literature and demonstrate that the proposed system has satisfactory accuracy.

This paper is aimed at undergraduate students of physics, engineering and mathematics, where a methodology for mechanical vibration analysis of a multi degree of freedom (DOF) excited by an harmonic force in the time and frequency domain is presented. The Arduino microcontroller is used as an acquisition system and low-cost MEMS accelerometers for the instrumentation of the system. System of multi DOF are studied in a great number of problems in mechanical sciences, however its experimental study is not always present in the courses due to the high costs and complexity. These problems are overpassed with the study proposed in this work. Besides, the application presented has an interface with several disciplines in undergraduation and graduation level. The method proposed can be easy implemented and the results obtained had good precision and are in agreement with the literature.

Neste estudo, utiliza-se a plataforma Arduino em conjunto com sensores, como acelerômetro, giroscópio e ultrassom, para medição de vibrações em sistemas mecânicos. O principal objetivo deste trabalho é a montagem de um sistema para aquisição de sinais de fácil manuseio, baixo custo e boa precisão para fins didáticos. Utiliza-se também a linguagem Python e suas bibliotecas numéricas para processamento dos sinais. Neste trabalho propõem-se o estudo de vibrações em uma viga, em que se mede a sua posição, velocidade e aceleração. Uma montagem experimental foi implementada. Os resultados obtidos são comparados com modelos analíticos e de simulação computacional através de elementos finitos. Os resultados estão em concordância com a literatura.

In this paper, we use the Arduino platform together with sensors as accelerometer, gyroscope and ultrasound, to measure vibrations in mechanical systems. The main objective is to assemble a signals acquisition system easy to handle, of low cost and good accuracy for teaching purposes. It is also used the Python language and its numerical libraries for signal processing. This paper proposes the study of vibrations of a beam, which is measured by position, velocity and acceleration. An experimental setup was implemented. The results obtained are compared with analytical models and computer simulations using finite elements. The results are in agreement with the literature.