Analyzing dynamic response of non-homogeneous string fixed at both ends

Hu, Weipeng; Han, Songmei; Deng, Zichen

doi:10.1016/j.ijnonlinmec.2011.09.008

Cited by 6 publications

(3 citation statements)

References 9 publications

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“…Moreover, if damping of the structure is considered, the dissipative effect cannot be simulated by these numerical methods. The generalized multi-symplectic method [Hu et al, 2012a;Hu et al, 2013a;Hu et al, 2013b;Hu et al, 2012b] derived from the multi-symplectic idea [Bridges, 1997;Bridges and Reich, 2001;Moore and Reich, 2003a;Moore and Reich, 2003b;Reich, 2000], proved to be a high-efficiency structure-preserving method for analyzing the moving load system and the dissipative problem [Hu et al, 2012a;Hu et al, 2012b], is now used to study the dynamic responses of a nonuniform continuous beam with small damping coefficient under moving loads in this paper. The results of the numerical experiments are presented for the beam under a single load moving at a constant speed or a variable speed.…”

Section: Introductionmentioning

confidence: 99%

Generalized Multi-Symplectic Method for Dynamic Responses of Continuous Beam Under Moving Load

Deng

Ouyang

2013

Int. J. Appl. Mechanics

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Based on the multi-symplectic idea, a generalized multi-symplectic integrator method is presented to analyze the dynamic response of multi-span continuous beams with small damping coefficient. Focusing on the local conservation properties, the generalized multisymplectic formulations are introduced and a fifteen-point implicit structure-preserving scheme is constructed to solve the first-order partial differential equations derived from the dynamic equation governing the dynamic behavior of continuous beams under moving load. From the results of the numerical experiments, it can be concluded that, for the cases considered in this paper, the structure-preserving scheme is generalized multisymplectic if the viscous damping c ≤ 0.3751 when the continuous beam is under a constant-speed moving load and the structure-preserving scheme is generalized multisymplectic if the viscous damping c ≤ 0.3095 when the continuous beam is under a variable-speed moving load with fixed step lengths ∆t = 0.05 and ∆x = 0.025. Similar to a multi-symplectic scheme, the generalized multi-symplectic scheme also has two remarkable advantages: the excellent long-time numerical behavior and the good conservation property.

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Section: Introductionmentioning

confidence: 99%

Generalized Multi-Symplectic Method for Dynamic Responses of Continuous Beam Under Moving Load

Deng

Ouyang

2013

Int. J. Appl. Mechanics

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“…To investigate the energy loss in PDE by generalized multisymplectic method [16,17], the generalized multisymplectic scheme for the symmetric form (2) must be constructed firstly.…”

Section: Generalized Multisymplectic Schemementioning

confidence: 99%

“…Thus, the energy loss due to the viscosity of the fuel in the PDE is presented by studying the energy loss due to the viscosity of the fluid in Burgers model excited by periodic impulses. Focusing on the energy loss due to the viscosity of the fluid in the PDE, a Burgers model excited by periodic impulses is introduced to describe the flow field in the PDE firstly; and then based on the generalized multisymplectic theory [16][17][18], the expression of the energy loss due to the viscosity of the fluid is derived from the first-order symmetric form of the Burgers model; finally, the numerical results of the energy loss are reported.…”

Section: Introductionmentioning

confidence: 99%

Energy Loss in Pulse Detonation Engine due to Fuel Viscosity

Deng

Xie

2014

Mathematical Problems in Engineering

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Fluid viscosity is a significant factor resulting in the energy loss in most fluid dynamical systems. To analyze the energy loss in the pulse detonation engine (PDE) due to the viscosity of the fuel, the energy loss in the Burgers model excited by periodic impulses is investigated based on the generalized multisymplectic method in this paper. Firstly, the single detonation energy is simplified as an impulse; thus the complex detonation process is simplified. And then, the symmetry of the Burgers model excited by periodic impulses is studied in the generalized multisymplectic framework and the energy loss expression is obtained. Finally, the energy loss in the Burgers model is investigated numerically. The results in this paper can be used to explain the difference between the theoretical performance and the experimental performance of the PDE partly. In addition, the analytical approach of this paper can be extended to the analysis of the energy loss in other fluid dynamic systems due to the fluid viscosity.

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