Nonlinear Analysis of Shape Memory Devices With Duffing and Quadratic Oscillators

In this paper, we investigate the linear and nonlinear response of shape memory alloy (SMA)-based Duffing and quadratic oscillator under large deflection conditions. In this study, we first present thermomechanical constitutive modeling of SMA with a single degree-of-freedom system. Subsequently, we solve equation to obtain linear frequency and nonlinear frequency response using the method of harmonic balance and validate it with numerical solution as well as averaging method under the isothermal condition. However, for nonisothermal condition, we analyze the influence of cubic and quadratic nonlinearity on nonlinear response based on method of harmonic balance. Analysis of results leads to various ways of controlling the nature and extent of nonlinear response of SMA-based oscillators. Such findings can be effectively used to control external vibration of different systems.

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Nonlinear Frequency Response Analysis of a Multistage Clutch Damper With Multiple Nonlinearities

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4026036 ◽

2014 ◽

Vol 9 (3) ◽

Cited By ~ 8

Author(s):

Jong-Yun Yoon ◽

Hwan-Sik Yoon

Keyword(s):

Frequency Response ◽

Harmonic Balance ◽

Piecewise Linear ◽

Dynamic Performance ◽

Harmonic Balance Method ◽

Balance Method ◽

Response Analysis ◽

Nonlinear Frequency ◽

System Equation ◽

Nonlinear Frequency Response

This paper presents the nonlinear frequency response of a multistage clutch damper system in the framework of the harmonic balance method. For the numerical analysis, a multistage clutch damper with multiple nonlinearities is modeled as a single degree-of-freedom torsional system subjected to sinusoidal excitations. The nonlinearities include piecewise-linear stiffness, hysteresis, and preload all with asymmetric transition angles. Then, the nonlinear frequency response of the system is numerically obtained by applying the Newton–Raphson method to a system equation formulated by using the harmonic balance method. The resulting nonlinear frequency response is then compared with that obtained by direct numerical simulation of the system in the time domain. Using the simulation results, the stability characteristics and existence of quasi-harmonic response of the system are investigated. Also, the effect of stiffness values on the dynamic performance of the system is examined.

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Frequency Response Characteristics of a Revolute Impact Pair

14th Biennial Conference on Mechanical Vibration and Noise: Nonlinear Vibrations ◽

10.1115/detc1993-0043 ◽

1993 ◽

Author(s):

Y. Wang

Keyword(s):

Frequency Response ◽

Harmonic Balance ◽

Harmonic Balance Method ◽

Analytical Techniques ◽

Single Frequency ◽

Nonlinear Frequency ◽

Response Characteristics ◽

State Response ◽

Existence And Stability ◽

Nonlinear Frequency Response

Abstract Clearances in mechanical joints have deteriorating effects on the dynamic behavior of a machine in increasing noise and vibration and reducing the performance. In order to properly characterize these effects and to develop analytical techniques for machine design, it is necessary to investigate the dynamics associated with basic models of impacting systems. In this paper, we develop a method of harmonic balance to study a revolute impact pair. We focus on the characteristics of nonlinear frequency response of the system for a single frequency excitation. These characteristics include multiply-valued steady state response, multiple jump resonances, and existence and stability of these solutions. The effectiveness of the harmonic balance method combined with the Fast Fourier Transform technique is shown through numerical examples.

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Recent advances and comparisons between harmonic balance and Volterra-based nonlinear frequency response analysis methods

Nonlinear Dynamics ◽

10.1007/s11071-017-3860-z ◽

2017 ◽

Vol 91 (1) ◽

pp. 131-145 ◽

Cited By ~ 2

Author(s):

J. C. Peyton Jones ◽

K. S. A. Yaser

Keyword(s):

Frequency Response ◽

Harmonic Balance ◽

Response Analysis ◽

Nonlinear Frequency ◽

Frequency Response Analysis ◽

Analysis Methods ◽

Recent Advances ◽

Nonlinear Frequency Response

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Nonlinear Response and Suppression of Chaos by Weak Harmonic Perturbation Inside a Triple Well Φ6-Rayleigh Oscillator Combined to Parametric Excitations

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.2198215 ◽

2006 ◽

Vol 1 (3) ◽

pp. 196-204 ◽

Cited By ~ 6

Author(s):

M. Siewe Siewe ◽

F. M. Moukam Kakmeni ◽

C. Tchawoua ◽

P. Woafo

Keyword(s):

Harmonic Balance ◽

Nonlinear Response ◽

Main Attention ◽

Response Curves ◽

Local Bifurcations ◽

Method Of Harmonic Balance ◽

Averaged Equations ◽

Harmonic Perturbation ◽

Dynamical Properties ◽

Suppression Of Chaos

The nonlinear response and suppression of chaos by weak harmonic perturbation inside a triple well Φ6-Rayleigh oscillator combined to parametric excitations is studied in this paper. The main attention is focused on the dynamical properties of local bifurcations as well as global bifurcations including homoclinic and heteroclinic bifurcations. The original oscillator is transformed to averaged equations using the method of harmonic balance to obtain periodic solutions. The response curves show the saddle-node bifurcation and the multi-stability phenomena. Based on the Melnikov’s method, horseshoe chaos is found and its control is made by introducing an external periodic perturbation.

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Study of plate vibrating in fluids having part-through crack at random angles and locations

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/09544062211012717 ◽

2021 ◽

pp. 095440622110127

Author(s):

Ruqia Ikram ◽

Asif Israr

Keyword(s):

Frequency Response ◽

Multiple Scales ◽

Peak Amplitude ◽

Nonlinear Frequency ◽

Response Curves ◽

Crack Location ◽

Cracked Plate ◽

Nonlinear Frequency Response ◽

Angle Crack ◽

Crack Angle

This study presents the vibration characteristics of plate with part-through crack at random angles and locations in fluid. An experimental setup was designed and a series of tests were performed for plates submerged in fluid having cracks at selected angles and locations. However, it was not possible to study these characteristics for all possible crack angles and crack locations throughout the plate dimensions at any fluid level. Therefore, an analytical study is also carried out for plate having horizontal cracks submerged in fluid by adding the influence of crack angle and crack location. The effect of crack angle is incorporated into plate equation by adding bending and twisting moments, and in-plane forces that are applied due to antisymmetric loading, while the influence of crack location is also added in terms of compliance coefficients. Galerkin’s method is applied to get time dependent modal coordinate system. The method of multiple scales is used to find the frequency response and peak amplitude of submerged cracked plate. The analytical model is validated from literature for the horizontally cracked plate submerged in fluid as according to the best of the authors’ knowledge, literature lacks in results for plate with crack at random angle and location in the presence of fluid following validation with experimental results. The combined effect of crack angle, crack location and fluid on the natural frequencies and peak amplitude are investigated in detail. Phenomenon of bending hardening or softening is also observed for different boundary conditions using nonlinear frequency response curves.

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