Steady Collision Vibration in Spring-Mass System Excited by Periodic Displacement with Arbitrary Function : 1st Report, Analysis of Response Vibrations for Harmonic, Superharmonic and Subharmonic Resonances(Mechanical Systems)

This paper deals with the collision vibration in continuous system excited by periodic displacement with arbitrary functions. The analytical model is steady collision vibration in simply-supported-beam having an attached mass which collides elastically to symmetric faces with restoring force of hysteresis loops. In order to clarify the main resonance of the system subjected to excitation by displacement, the resulting vibration is analyzed applying the Fourier series method for this system. Following this theoretical analysis, the numerical calculations are also performed, and the resonance curves are constructed using the resulting vibrations. Effects of the stiffness of clamped spring, the ratio of attached mass and the amplitude of excitation on the resonance curves are shown as an example of numerical results.

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Analysis of collision vibration in two-degree-of-freedom system without damping subjected to periodic excitation (Derivation of analytical solutions for 2nd order super harmonic resonance)

Aihara

Kumano

2016

Transactions of the JSME (In Japanese)

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Collision vibration systems are usually modeled as a nonlinear spring whose characteristics are described by the broken line model. These systems are called piecewise-linear systems. A piecewise-linear system is highly nonlinear, and it is usually difficult to predict the system response using any general analytical solution. If the effects of design parameters such as clearance size and dynamic nonlinearity of the systems are known, the structures can be designed to be safer and more comfortable. This paper deals with forced collision vibration in a mass-spring system for two-degree-of-freedom. The analytical model is mass-spring system having two masses in which one mass is subjected to an exciting vibration with arbitrary functions. Then the restoring force, which has characteristics of an asymmetric piecewise-linear system, collides elastically to another mass when amplitude of the mass increases farther than clearance. In order to analyze resulting vibration for the super harmonic resonance, the Fourier series method is applied and analytical solutions for this system are derived. Next, following the analytical solutions, numerical calculations are performed, and the resonance curves are constructed by using resulting vibration. Effects of amplitude ratio of excitation, nonlinearity of the system and mass ratio on the resonance curves are shown numerically. For verification of the analytical solutions, numerical simulations are performed by the Runge-Kutta method, and numerical results based on analytical solutions are compared with numerical simulation results on the resonance curves. The analytical results are in a fairy good agreement with the numerical simulation results.

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Steady Collision Vibration in Spring-Mass System Excited by Periodic Displacement with Arbitrary Function : 1st Report, Analysis of Response Vibrations for Harmonic, Superharmonic and Subharmonic Resonances(Mechanical Systems)

Cited by 4 publications

References 4 publications

Steady Collision Vibration in Spring-Mass System Excited by Periodic Displacement with Arbitrary Function : 2nd Report, Analysis of Stability Criterions for Harmonic, Superharmonic and Subharmonic Resonances(Mechanical Systems)

Steady Collision Vibration in Spring-Mass System Excited by Periodic Displacement with Arbitrary Function : 2nd Report, Analysis of Stability Criterions for Harmonic, Superharmonic and Subharmonic Resonances(Mechanical Systems)

Analysis of Steady Collision Vibration in Simply-Supported-Beam Having an Attached Mass with Restoring Force of Hysteresis Loops

Analysis of collision vibration in two-degree-of-freedom system without damping subjected to periodic excitation (Derivation of analytical solutions for 2nd order super harmonic resonance)

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