A tutorial review on time-frequency analysis of non-stationary vibration signals with nonlinear dynamics applications

Time-frequency analysis (TFA) for mechanical vibrations in non-stationary operations is the main subject of this article, concisely written to be an introducing tutorial comparing different time-frequency techniques for non-stationary signals. The theory was carefully exposed and complemented with sample applications on mechanical vibrations and nonlinear dynamics. A particular phenomenon that is also observed in non-stationary systems is the Sommerfeld effect, which occurs due to the interaction between a non-ideal energy source and a mechanical system. An application through TFA for the characterization of the Sommerfeld effect is presented. The techniques presented in this article are applied in synthetic and experimental signals of mechanical systems, but the techniques presented can also be used in the most diverse applications and also in the numerical solution of differential equation

MATHEMATICAL MODEL OF A COLLISION BASED ON A SPRING-MASS-DAMPER SYSTEMWITH A NONLINEAR SPRING BEHAVIOR

This paper presents a mathematical model of a collision were the phenomenon will be simplified by a spring-mass-damper model. The spring will be considered to have an elastoplastic behavior, which states that the spring suffers a permanent deformation after a force application. The responses of the model will be obtained analytically and by numerical approximation.The model proposed in this paper allows one to obtain parameters of the system, and then compare to a full-scale experiment to test its suitability with it. The nonlinear behavior of the system will be characterized by analyzing the phase space diagram

Mathematical model of a vehicle crash: A case study

Case studies are very useful when it comes to students’ education. They show to them the issues that are faced by the mechanical engineers and what the students should do to resolve those issues during their professional career. In that sense, this paper presents a case study that can be presented in undergraduate and graduate courses where a vehicle crash collision is modeled by a spring-mass-damper system. The spring of the system will be considered to have a nonlinear force–deflection characteristic. The model proposed in this paper allows one to obtain the parameters of the system, and then compare them with the ones obtained experimentally to test the suitability of the model with the vehicle crash. The responses of the system will be obtained by numerical approximation by using the Runge–Kutta algorithm. </jats:p

Análise de vibrações em sistemas discretos de massas concentradas e com dois graus de liberdade através da transformada wavelet

O estudo de vibrações diz respeito aos movimentos oscilatórios de corpos e às forças que lhes são associadas. Todos os corpos dotados de massa e elasticidade são capazes de vibrar. Deste modo, a maior parte das máquinas e estruturas estão sujeitas a certos graus de vibração A maioria das atividades humanas envolve alguma forma de vibração. O estudo do comportamento dinâmico dessas oscilações mecânicas é o objetivo deste trabalho e para isto propomos um sistema de massas concentradas e com dois graus de liberdade. O sistema será excitado por forças externas, entre elas ondas de terremoto. Com simulações numéricas estudamos o sistema, usando a transformada rápida de Fourier, transformada wavelet.The study of vibration concerns oscillatory movement of bodies and the forces they are associated. All bodies that have mass and elasticity are able to vibrate. Thus, most of the machines and structures are subject to certain degrees of vibration most human activities involve some form of vibration. The study of the dynamic behavior of these mechanical oscillations is the objective of this work and to propose that a system of weights and concentrated with two degrees of freedom. The system will be excited by external forces, including waves of earthquake. With numerical simulations studied the system, using the fast Fourier transform, wavelet transform

Análise de vibrações em sistemas discretos de massas concentradas e com dois graus de liberdade através da transformada wavelet

O estudo de vibrações diz respeito aos movimentos oscilatórios de corpos e às forças que lhes são associadas. Todos os corpos dotados de massa e elasticidade são capazes de vibrar. Deste modo, a maior parte das máquinas e estruturas estão sujeitas a certos graus de vibração A maioria das atividades humanas envolve alguma forma de vibração. O estudo do comportamento dinâmico dessas oscilações mecânicas é o objetivo deste trabalho e para isto propomos um sistema de massas concentradas e com dois graus de liberdade. O sistema será excitado por forças externas, entre elas ondas de terremoto. Com simulações numéricas estudamos o sistema, usando a transformada rápida de Fourier, transformada wavelet.The study of vibration concerns oscillatory movement of bodies and the forces they are associated. All bodies that have mass and elasticity are able to vibrate. Thus, most of the machines and structures are subject to certain degrees of vibration most human activities involve some form of vibration. The study of the dynamic behavior of these mechanical oscillations is the objective of this work and to propose that a system of weights and concentrated with two degrees of freedom. The system will be excited by external forces, including waves of earthquake. With numerical simulations studied the system, using the fast Fourier transform, wavelet transform