... Computational mechanics Structural dynamics Numerical Integration methods where λ is an eigenvalue of the matrix A and the coefficients A 1 , A 2 , and A 3 are found to be (14) A 1 = − ( β 1 + 2 β 2 ) Ω 2 + 2 ( 1 − β 0 ) ξ Ω...

... received July 11, 2018; published online August 27, 2018. Assoc. Editor: Dumitru Baleanu. 10 10 2017 11 07 2018 Algorithms Computational mechanics Fractional calculus Integration methods Fractional differential equations (FDEs) have drawn increasing attention and interest...

... . Manuscript received January 6, 2018; final manuscript received July 21, 2018; published online August 22, 2018. Assoc. Editor: Brian Feeny. 06 01 2018 21 07 2018 Algorithms Fractional calculus Nonlinear dynamical systems Numerical Integration methods Fractional differential...

... systems Nonlinear phenomena Numerical Integration methods Diffusion is a widespread physical phenomenon in nature. On micro scale, diffusion is caused by the Brownian motion of atoms or molecules that leads to complete mixing. While on macro level, it is described by the famous Fick's laws...

... are implicit, and some are explicit. They are relatively more stable than the explicit method for convection–diffusion equation [ 11 ]. Aerospace applications Algorithms Algorithms Computational mechanics Stability Numerical Integration methods Integration methods 29 11 2017 20 06...

... Multibody system dynamics Nonlinear dynamical systems Design optimization Robotics Impact Contact Friction modeling Numerical Integration methods Bio-mechanical systems Biological systems Dynamics Stability of nonlinear systems Design sensitivity Nonlinear systems Mechanism systems...

... Algorithms Fractional calculus Integration methods During the last several decades, fractional calculus has been developed very quickly due to its various applications in fields of engineering, mechanics, physics, economics, and biology; see Refs. [ 1 – 9 ]. It is known that there have existed...

.... As mentioned earlier, DR uses a time integration method to solve an artificially damped dynamic system. However, there are several types of time integration methods (e.g., Euler, central finite difference, trapezoidal, Runge–Kutta, and generalized- α [ 8 ]). It is obvious that the integrator type influences...

... . Manuscript received August 29, 2017; final manuscript received May 10, 2018; published online June 18, 2018. Assoc. Editor: Anindya Chatterjee. 29 08 2017 10 05 2018 Algorithms Fractional calculus Nonlinear dynamical systems Numerical Integration methods Fractional...

...; final manuscript received May 15, 2018; published online June 18, 2018. Assoc. Editor: Dumitru Baleanu. 08 12 2017 15 05 2018 Algorithms Fractional calculus Numerical Integration methods Recently, fractional calculus (FC), the theory of differentiation and integration...

... issues of convergence to local minima [ 6 ]. Algorithms Experimental dynamics Numerical Integration methods 03 10 2017 02 05 2018 Contributed by the Design Engineering Division of ASME for publication in the J OURNAL OF C OMPUTATIONAL AND N ONLINEAR D YNAMICS...

... Railroad dynamics Vehicular dynamics Numerical Dynamics Integration methods The dynamic behaviors of a railway vehicle subject to the guiding tracks possessing structural deformations have long been an interesting topic for researchers engaged in railway engineering. Though the topic...

... Algorithms Computational mechanics Nonlinear oscillations Reduced-order models Structural dynamics Numerical Integration methods Vibration The use of finite element (FE)-based structural dynamic models to simulate structural response has become a standard practice in many fields of application...

.... 14 11 2017 06 03 2018 Algorithms Fractional calculus Design optimization Parameter estimation System identification Numerical Design sensitivity Nonlinear systems Integration methods During the past decades, much attention has been drawn for the study of fractional...

... November 2, 2016; final manuscript received November 1, 2017; published online December 7, 2017. Assoc. Editor: Firdaus Udwadia. 02 11 2016 01 11 2017 Algorithms Chaotic dynamics Nonlinear dynamical systems Numerical Integration methods Recently, the chaotic behavior...

... manuscript received July 24, 2015; published online November 29, 2017. Assoc. Editor: D. Dane Quinn. 05 06 2014 24 07 2015 Algorithms Integration methods Parameter estimation is a very broad and complex research field. In general, it presents a high degree of difficulty...

.... Algorithms Computational kinematics Flexible-cody dynamics Parameter estimation System identification Numerical Dynamics Integration methods Copyright © 2017 by ASME 2017 1555-1415/2018/13(2)/021009/9/ $25.00 ...

... Numerical Symbolic solution systems Integration methods Linear ordinary differential equations with time-periodic coefficients have a wide range of applications in various fields of science and engineering. Some of their applications include structures subjected to periodic loads [ 1 ], helicopter...

... manuscript received July 17, 2017; published online October 31, 2017. Assoc. Editor: Javier Cuadrado. 14 02 2017 17 07 2017 Algorithms Multibody system dynamics Non-smooth dynamics Impact Contact Friction modeling Numerical Integration methods The time-evolution...

... received September 7, 2017; published online October 9, 2017. Assoc. Editor: Hiroshi Yabuno. 22 09 2016 07 09 2017 Algorithms Continuation Methods Fractional calculus Numerical Integration methods In the past few decades, fractional calculus has been used in several areas...