scholarly journals Dynamics of SMA micro-actuator in biomechanical system

2018 ◽  
Vol 148 ◽  
pp. 09001
Author(s):  
Rafal Rusinek ◽  
Andrzej Weremczuk ◽  
Marcin Szymanski ◽  
Jerzy Warminski
Keyword(s):  
Middle Ear ◽  
Degrees Of Freedom ◽  
Primary Resonance ◽  
Resonance Curve ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Relative Temperature ◽  
Micro Actuator ◽  
Middle Ear Prosthesis ◽  
Increasing Temperature

In this paper the polynomial model of shape memory alloy is used to characterise properties of a micro-actuator which is applied as a new middle ear prosthesis. A two degrees of freedom model of the reconstructed middle ear is solve by means of multiple time scales method. The system has various behaviours near the primary resonance depending on ambient temperature. The special case when relative temperature θ = 1.0 characterises untypical resonance curve. Increasing temperature to the normal human body one the resonance curves are typical. Then the system has only one periodic solution if the excitation is not too strong.

scholarly journals On the Application of the Multiple Scales Method on Electrostatically Actuated Resonators

2019 ◽  
Vol 14 (4) ◽  
Author(s):  
Saad Ilyas ◽  
Feras K. Alfosail ◽  
Mohammad I. Younis
Keyword(s):  
Analytical Solution ◽  
Multiple Scales ◽  
Excitation Frequency ◽  
Primary Resonance ◽  
Equation Of Motion ◽  
Higher Order ◽  
Resonance Excitation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Electrostatically Actuated

We investigate modeling the dynamics of an electrostatically actuated resonator using the perturbation method of multiple time scales (MTS). First, we discuss two approaches to treat the nonlinear parallel-plate electrostatic force in the equation of motion and their impact on the application of MTS: expanding the force in Taylor series and multiplying both sides of the equation with the denominator of the forcing term. Considering a spring–mass–damper system excited electrostatically near primary resonance, it is concluded that, with consistent truncation of higher-order terms, both techniques yield same modulation equations. Then, we consider the problem of an electrostatically actuated resonator under simultaneous superharmonic and primary resonance excitation and derive a comprehensive analytical solution using MTS. The results of the analytical solution are compared against the numerical results obtained by long-time integration of the equation of motion. It is demonstrated that along with the direct excitation components at the excitation frequency and twice of that, higher-order parametric terms should also be included. Finally, the contributions of primary and superharmonic resonance toward the overall response of the resonator are examined.

scholarly journals Recent advances in periodic vibrations of the middle ear with a floating mass transducer

Meccanica ◽  
2020 ◽  
Vol 55 (12) ◽  
pp. 2609-2621
Author(s):  
Rafal Rusinek ◽  
Andrzej Weremczuk
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Middle Ear ◽  
Nonlinear Model ◽  
Degree Of Freedom ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Multiple Time Scales Method ◽  
Recent Advances ◽  
The Stability

AbstractThe paper investigates periodic solutions of a nonlinear model of the middle ear with a floating mass transducer. A multi degree of freedom model is used to obtain a solution near the first resonance. The model is solved analytically by means of the multiple time scales method. Next, the stability of obtained periodic solutions is analysed in order to identify the parameters of the floating mass transducer that affect the middle ear dynamics. Moreover, some parameters of the middle ear structure are investigated with respect to their impact on obtained periodic solutions.

Analytical solution and energy harvesting from nonlinear vibration of an asymmetric bimorph piezoelectric plate and optimizing the plate parameters by genetic algorithm

2017 ◽  
Vol 29 (6) ◽  
pp. 1120-1138 ◽  
Author(s):  
Hamed Shorakaei ◽  
Alireza Shooshtari
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Vibration ◽  
Piezoelectric Plate ◽  
Electrical Power ◽  
Electric Displacement ◽  
Primary Resonance ◽  
Load Resistance ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Piezoelectric Layers

In this article, harvesting of electrical power from nonlinear vibration of an asymmetric bimorph piezoelectric plate is presented based on the classical plate theory with von Kármán strain–displacement nonlinear relations in the presence of temperature change effect. Two piezoelectric layers with different thicknesses cover top and bottom layers of a substructure. The structure has been excited under harmonic transverse forces in case of primary resonance. Two coupled ordinary differential equations for displacement and voltage have been derived and solved via multiple time scales method. The voltage equation has been defined by electric displacement and Gauss’s law. Analytic relations for voltage and harvested electrical power have been derived. The analytic relation for power is based on different parameters of the plate such as thicknesses of the layers, dimensions of plate, load resistance, frequency of harmonic excitation, and mechanical properties of structure. The parameters are optimized using genetic algorithm method with consideration of power relation as cost function. To harvest the maximum energy from the plate, the thicknesses of two piezoelectric layers, load resistance, and detuning parameter have been optimized. To illustrate the effectiveness of the optimization, results are depicted in three different simulations.

Non-Stationary Oscillations at Slow Transitions Across Instabilities

2007 ◽  
Author(s):  
Rudolf R. Pusˇenjak ◽  
Maks M. Oblak ◽  
Jurij Avsec
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Time Scales ◽  
Primary Resonance ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Excitation Parameter ◽  
Linear Dynamical Systems ◽  
Weakly Nonlinear ◽  
Non Linear

The paper presents the study of non-stationary oscillations, which is based on extension of Lindstedt-Poincare (EL-P) method with multiple time scales for non-linear dynamical systems with cubic non-linearities. The generalization of the method is presented to discover the passage of weakly nonlinear systems through the resonance as a control or excitation parameter varies slowly across points of instabilities corresponding to the appearance of bifurcations. The method is applied to obtain non-stationary resonance curves of transition across points of instabilities during the passage through primary resonance of harmonically excited oscillators of Duffing type.

Vibration Analysis of a Shape Memory Oscillator by Harmonic Balance Method Verified Numerically

2019 ◽  
Vol 29 (03) ◽  
pp. 1930007 ◽  
Author(s):  
Rafal Rusinek ◽  
Joanna Rekas ◽  
Krzysztof Kecik
Keyword(s):  
Shape Memory ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
System Parameters ◽  
Irregular Motion

This paper focuses on periodic solutions for a one-degree-of-freedom oscillator with a spring made of shape memory alloy (SMA). However, when periodic solutions are unstable, irregular motion is identified numerically. The shape memory spring is described by a polynomial characteristic in this model. The harmonic balance method (HBM) is employed to find periodic solutions near the primary resonance. The solutions are confronted with results obtained by the multiple time scales method and numerical simulations. Finally, the effect of system parameters and temperature on the system dynamics is discussed.

An Alternative Perturbation Procedure of Multiple Scales for Nonlinear Dynamics Systems

1989 ◽  
Vol 56 (3) ◽  
pp. 667-675 ◽  
Author(s):  
S. L. Lau ◽  
Y. K. Cheung ◽  
Shuhui Chen
Keyword(s):  
Steady State ◽  
Nonlinear Systems ◽  
Degrees Of Freedom ◽  
Multiple Scales ◽  
Steady State Solution ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Almost Periodic ◽  
Perturbation Procedure ◽  
Incremental Harmonic Balance

An alternative perturbation procedure of multiple scales is presented in this paper which is capable of treating various periodic and almost periodic steady-state vibrations including combination resonance of nonlinear systems with multiple degrees-of-freedom. This procedure is a generalization of the Lindstedt-Poincare´ method. To show its essential features a typical example of cubic nonlinear systems, the clamped-hinged beam, is analyzed. The numerical results for the almost periodic-free vibration are surprisingly close to that obtained by the incremental harmonic balance (IHB) method, and the analytical formulae for steady-state solution are, in fact, identical with that of conventional method of multiple time scales. Moreover, detail calculations of this example revealed some interesting behavior of nonlinear responses, which is of significance for general cubic systems.

Nonlinear Forced Vibration of Curved Carbon Nanotube Resonators

2016 ◽  
Author(s):  
Hassan Askari ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Carbon Nanotube ◽  
Forced Vibration ◽  
Primary Resonance ◽  
Beam Theory ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Nonlinear Forced Vibration ◽  
Resonator System ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam

Nonlinear forced vibration of the nonlocal curved carbon nanotubes is investigated. The governing equation of vibration of a nonlocal curved carbon nanotube is developed. The nonlinear Winkler and Pasternak type foundations are chosen for the nanotube resonator system. Furthermore, the shape of the carbon nanotube system is assumed to be of a sinusoidal curvature form and different types of the boundary conditions are postulated for the targeted system. The Euler-Bernoulli beam theory in conjunction with the Eringen theory are implemented to obtain the partial differential equation of the system. The Galerkin method is applied to obtain the nonlinear ordinary differential equations of the system. For the sake of obtaining the primary resonance of the considered system the multiple time scales method is utilized. The influences of different parameters, namely, the position of the applied force, different forms of boundary condition, amplitude of curvature, and the coefficient of the Pasternak foundation, on the frequency response of the system were fully investigated.

Low- and High-Temperature Primary Resonance in Shape Memory Oscillator Observed by Multiple Time Scales and Harmonic Balance Method

2019 ◽  
Vol 14 (11) ◽  
Author(s):  
Andrzej Weremczuk ◽  
Joanna Rekas ◽  
Rafal Rusinek
Keyword(s):  
Shape Memory ◽  
Time Scales ◽  
Harmonic Balance ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Multiple Time Scales ◽  
Practical Implementation ◽  
Multiple Time ◽  
Fifth Order

Abstract This paper focuses on the primary resonance of a one degree-of-freedom (1DOF) oscillator with a spring made of shape memory alloy (SMA). The primary resonance is analyzed using the multiple time scales method (MTSM) and the harmonic balance method (HBM). The shape memory spring is described by a fifth-order polynomial function. The solutions are analyzed along with the results reported by another authors, and compared with numerical simulations. Three ranges of temperature are analyzed. Finally, the practical implementation aspect of the harmonic balance and MTSMs are discussed.

scholarly journals Vibrations of nonlinear elastic lattices: low- and high-frequency dynamic models, internal resonances and modes coupling

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190532 ◽  
Author(s):  
Igor V. Andrianov ◽  
Vladyslav V. Danishevskyy ◽  
Graham Rogerson
Keyword(s):  
High Frequency ◽  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Finite Size ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Internal Resonances ◽  
Energy Transfers ◽  
Fourth Order Method ◽  
Nonlinear Elastic

We aim to study how the interplay between the effects of nonlinearity and heterogeneity can influence on the distribution and localization of energy in discrete lattice-type structures. As the classical example, vibrations of a cubically nonlinear elastic lattice are considered. In contrast with many other authors, who dealt with infinite and periodic lattices, we examine a finite-size model. Supposing the length of the lattice to be much larger than the distance between the particles, continuous macroscopic equations suitable to describe both low- and high-frequency motions are derived. Acoustic and optical vibrations are studied asymptotically by the method of multiple time scales. For numerical simulations, the Runge–Kutta fourth-order method is employed. Internal resonances and energy exchange between the vibrating modes are predicted and analysed. It is shown that the decrease in the number of particles restricts energy transfers to higher-order modes and prevents the equipartition of energy between all degrees of freedom. The conditions for a possible reduction in the original nonlinear system are also discussed.

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