应用数学和力学

2014 Vol. 35, No. 1

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Symplectic Conservation Integration of Rigid Body Dynamics With Quaternion Parameters

XU Xiao-ming, ZHONG Wan-xie

2014, 35(1): 1-11. doi: 10.3879/j.issn.1000-0887.2014.01.001

Abstract(2330) PDF(2572)

Abstract:
A numerical method was proposed with the quaternion representation of rigid body dynamics. Based on the analytical structural mechanics, the action of differential system was introduced for the time integration of the approximated discrete system and the constraint that the norm of quaternion kept c...

Symplectic Runge-Kutta Method for Structural Dynamics

GUO Jing, XING Yu-feng

2014, 35(1): 12-21. doi: 10.3879/j.issn.1000-0887.2014.01.002

Abstract(1637) PDF(1252)

Abstract:
An explicit and efficient implementation of the symplectic implicit Gauss-Legendre Runge-Kutta (RK) method of stage s and order 2s,was presented for solution of the dynamical ordinary differential equation with physical damping and external loads. The analytical explicit spectral radii and single-st...

Structure-Preserving Algorithm for Steady-State Solution to the Infinite Dimensional Hamilton System

QIN Yu-yue, DENG Zi-chen, HU Wei-peng

2014, 35(1): 22-28. doi: 10.3879/j.issn.1000-0887.2014.01.003

Abstract(1793) PDF(1321)

Abstract:
Based on Hamilton variational principle and Bridges’ multi-symplectic integration theory, a new structure-preserving algorithm was proposed to simulate the steady-state solution to the complex infinite dimensional Hamilton system. With Zufiria’s Boussinesq-type equations as an example, the high-orde...

Research on the Vibration Property of the Beam on Elastic Foundation Based on the PCs Theory

CHEN Qi-yong, HU Shao-wei, ZHANG Zi-ming

2014, 35(1): 29-38. doi: 10.3879/j.issn.1000-0887.2014.01.004

Abstract(1476) PDF(1100)

Abstract:
Axial loads imposed on the structure influence the vibration properties and cause the change of vibration resistance functions. Theory about the band gap properties of phononic crystals (PCs) were used to study the flexural vibration band gaps of an Euler beam on elastic foundation. A flexural vibra...

Nonlinear Galloping of Iced Quad-Bundle Conductors With Internal Resonances

YAN Bo, LIU Xiao-hui, ZHAO Li, ZHOU Lin-shu

2014, 35(1): 39-49. doi: 10.3879/j.issn.1000-0887.2014.01.005

Abstract(1577) PDF(1050)

Abstract:
Galloping of iced quad-bundle conductors with internal resonance was numerically investigated by means of nonlinear finite element method. Based on the numerical simulation of galloping processes of the typical iced quad-bundle conductor lines in both the steady and the stochastic wind fields, gallo...

On Piecewise Nonlinear Dynamic Characteristics of a New-Type Quasi-Zero-Stiffness Vibration Isolator With Cam-Roller-Spring Mechanism

WANG Xin-long, ZHOU Jia-xi, XU Dao-lin

2014, 35(1): 50-62. doi: 10.3879/j.issn.1000-0887.2014.01.006

Abstract(2250) PDF(1121)

Abstract:
A piecewise nonlinear dynamic model for a new-type quasi-zero-stiffness (QZS) vibration isolation system with cam-roller-spring mechanism was developed. The dynamic characteristics of the QZS system under harmonic base motion were analyzed theoretically with the averaging method, and the primary res...

Non-Stationary Response of a Stochastic System With Fractional Derivative Damping Under Gaussian White-Noise Excitation

LI Wei, ZHAO Jun-feng, LI Rui-hong, Natasa Trisovic

2014, 35(1): 63-70. doi: 10.3879/j.issn.1000-0887.2014.01.007

Abstract(1928) PDF(997)

Abstract:
Non-stationary response of a nonlinear stochastically dynamical system with fractional derivative damping under Gaussian white-noise excitation was investigated. Based on the equivalent linearization method, the original nonlinear system was converted to a linear system with respect to the vibration...

Dynamic Responses of the Submerged Floating Tunnel Under Combined Internal Wave and Sea Current Effect

TIAN Xue-fei, DONG Man-sheng, PANG Huan-ping, LIN Zhi, NIU Zhong-rong

2014, 35(1): 71-80. doi: 10.3879/j.issn.1000-0887.2014.01.008

Abstract(1801) PDF(1139)

Abstract:
The stratified ocean internal wave flow field was established based on the potential flow function theory. The joint force by internal wave and sea current was considered with the Morison method to establish a nonlinear vibration mathematical-physical model of tunnel-fluid interaction. The correspon...

Free Vibration Analysis of Elastic Foundation Euler Beams With Different Discontinuities Based on Generalized Functions

CHEN Xiao-chao, MAO Qi-bo, XUE Xiao-li

2014, 35(1): 81-91. doi: 10.3879/j.issn.1000-0887.2014.01.009

Abstract(1750) PDF(872)

Abstract:
The general governing differential equations for the vibration of elastic foundation Euler-Bernoulli beams with different discontinuities subject to axial forces were established based on generalized functions. For each discontinuity at a given location, a basic modal displacement function (Dirac de...

Lagrangian High-Order Staggered Conservative Gasdynamics Scheme on Unstructured Meshes

GE Quan-wen

2014, 35(1): 92-101. doi: 10.3879/j.issn.1000-0887.2014.01.010

Abstract(1590) PDF(1098)

Abstract:
A Lagrangian high-order staggered conservative gasdynamics scheme on unstructured meshes was presented.The high-order piecewise pressure on the cell arising from the present-moment subcell density and present-moment subcell acoustic speed was used to construct the high-order subcell force with the M...

A Dynamic Bayesian Network Model for Structural Time-Dependent Reliability Analysis of Resistance Deterioration

SUN Hong-bin, WU Zi-yan, LIU Shu-kui

2014, 35(1): 102-110. doi: 10.3879/j.issn.1000-0887.2014.01.011

Abstract(1667) PDF(1097)

Abstract:
A dynamic Bayesian network (DBN) model was proposed for timedependent reliability analysis of structures in deterioration. The structural resistance deterioration was modeled as a gamma process while the loads as random variables. The stochastic deterioration process was discretized in time domain ...