scholarly journals Nonlinear Oscillations of a Mass Attached to Linear and Nonlinear Springs in Series Using Approximate Solutions

2018 ◽  
pp. 201-207
Author(s):  
Beyza Bostancı ◽  
M. M. Fatih Karahan
Keyword(s):  
Nonlinear Oscillations ◽  
Approximate Solutions ◽  
Nonlinear Springs ◽  
In Series ◽  
Linear And Nonlinear

scholarly journals Nonlinear vibration of a lumped system with springs-in-series

Meccanica ◽  
2020 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Roman Starosta ◽  
Grażyna Sypniewska-Kamińska
Keyword(s):  
Multiple Scales ◽  
Approximate Solutions ◽  
Nonlinear Damping ◽  
Harmonic Excitation ◽  
Algebraic Equations ◽  
Lumped Mass ◽  
Nonlinear Springs ◽  
Differential Algebraic System ◽  
In Series ◽  
The Mathematical Model

AbstractThe paper deals with the dynamics of a lumped mass mechanical system containing two nonlinear springs connected in series. The external harmonic excitation, linear and nonlinear damping are included into considerations. The mathematical model contains both differential and algebraic equations, so it belongs to the class of dynamical systems governed by the differential–algebraic system of equations (DAEs). An approximate analytical approach is used to solve the initial value problem for the DAEs. We adopt the multiple scales method (MSM) that allows one to obtain the sufficiently correct approximate solutions both far from the resonance and at the resonance conditions. The steady and non-steady resonant vibrations are analyzed by employing the modulation equations of the amplitudes and phases which are yielded by the MSM procedure.

scholarly journals Mitigating the seismic pounding of multi-story buildings in series using linear and nonlinear fluid viscous dampers

2021 ◽  
Vol 21 (4) ◽  
Author(s):  
Hytham Elwardany ◽  
Robert Jankowski ◽  
Ayman Seleemah
Keyword(s):  
Substantial Improvement ◽  
Point Of View ◽  
Steel Buildings ◽  
Viscous Dampers ◽  
Element Analysis ◽  
Fluid Viscous Dampers ◽  
Adjacent Buildings ◽  
In Series ◽  
Linear And Nonlinear ◽  
Nonlinear Fluid

AbstractSeismic-induced pounding between adjacent buildings may have serious consequences, ranging from minor damage up to total collapse. Therefore, researchers try to mitigate the pounding problem using different methods, such as coupling the adjacent buildings with stiff beams, connecting them using viscoelastic links, and installing damping devices in each building individually. In the current paper, the effect of using linear and nonlinear fluid viscous dampers to mitigate the mutual pounding between a series of structures is investigated. Nonlinear finite-element analysis of a series of adjacent steel buildings equipped with damping devices was conducted. Contact surfaces with both contactor and target were used to model the mutual pounding. The results indicate that the use of linear or nonlinear dampers leads to the significant reduction in the response of adjacent buildings in series. Moreover, the substantial improvement of the performance of buildings has been observed for almost all stories. From the design point of view, it is concluded that dampers implemented in adjacent buildings should be designed to resist maximum force of 6.20 or 1.90 times the design independent force in the case of using linear or nonlinear fluid viscous dampers, respectively. Also, designers should pay attention to the design of the structural elements surrounding dampers, because considerable forces due to pounding may occur in the dampers at the maximum displaced position of the structure.

scholarly journals A Modified Techniques of Fractional-Order Cauchy-Reaction Diffusion Equation via Shehu Transform

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Mounirah Areshi ◽  
A. M. Zidan ◽  
Rasool Shah ◽  
Kamsing Nonlaopon
Keyword(s):  
Fractional Order ◽  
Reaction Diffusion ◽  
Approximate Solutions ◽  
Transformation Method ◽  
Reaction Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Closed Form Solutions ◽  
Homotopy Perturbation ◽  
In Series ◽  
The Given

In this article, the iterative transformation method and homotopy perturbation transformation method are applied to calculate the solution of time-fractional Cauchy-reaction diffusion equations. In this technique, Shehu transformation is combined of the iteration and the homotopy perturbation techniques. Four examples are examined to show validation and the efficacy of the present methods. The approximate solutions achieved by the suggested methods indicate that the approach is easy to apply to the given problems. Moreover, the solution in series form has the desire rate of convergence and provides closed-form solutions. It is noted that the procedure can be modified in other directions of fractional order problems. These solutions show that the current technique is very straightforward and helpful to perform in applied sciences.

scholarly journals SPICE Behaviors of Double Memristor Circuits Using Cosine Window Function

2021 ◽  
Vol 9 ◽  
Author(s):  
Kai-Da Xu ◽  
Donghao Li ◽  
Yannan Jiang ◽  
Qiang Chen
Keyword(s):  
Window Function ◽  
Charge Voltage ◽  
Hewlett Packard ◽  
Pspice Simulation ◽  
In Series ◽  
Linear And Nonlinear ◽  
High Flexibility ◽  
Flux Charge

In this paper, a Hewlett-Packard (HP) memristor model with a new window function and its versatile characteristics are presented. SPICE behaviors of the linear and nonlinear memristor model are studied through PSpice simulation. High flexibility is demonstrated for emulating the behaviors of the practical HP memristors. Furthermore, the characteristics of the composite SPICE behaviors are both investigated when two memristors are connected in series and in parallel. The polarity of each memristor is also taken into consideration. The relationships among flux, charge, voltage, current, and memristance of the double memristor circuits are simulated and analyzed.

Nonlinear oscillation system of mass with serial linear and nonlinear springs

2013 ◽  
Vol 87 (8) ◽  
pp. 787-792
Author(s):  
S. R. Seyedalizadeh Ganji ◽  
A. Barari ◽  
S. Karimpour ◽  
M. G. Sfahani
Keyword(s):  
Nonlinear Oscillation ◽  
Oscillation System ◽  
Nonlinear Springs ◽  
Linear And Nonlinear

scholarly journals Numerical Solution of Higher Order Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Shahid S. Siddiqi ◽  
Muzammal Iftikhar
Keyword(s):  
Boundary Value Problems ◽  
Homotopy Analysis Method ◽  
Present Method ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Higher Order ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Linear And Nonlinear

The aim of this paper is to use the homotopy analysis method (HAM), an approximating technique for solving linear and nonlinear higher order boundary value problems. Using HAM, approximate solutions of seventh-, eighth-, and tenth-order boundary value problems are developed. This approach provides the solution in terms of a convergent series. Approximate results are given for several examples to illustrate the implementation and accuracy of the method. The results obtained from this method are compared with the exact solutions and other methods (Akram and Rehman (2013), Farajeyan and Maleki (2012), Geng and Li (2009), Golbabai and Javidi (2007), He (2007), Inc and Evans (2004), Lamnii et al. (2008), Siddiqi and Akram (2007), Siddiqi et al. (2012), Siddiqi et al. (2009), Siddiqi and Iftikhar (2013), Siddiqi and Twizell (1996), Siddiqi and Twizell (1998), Torvattanabun and Koonprasert (2010), and Kasi Viswanadham and Raju (2012)) revealing that the present method is more accurate.

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