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The parametrically excited instability of the spatially periodic visco-elastomer sandwich plate with supported masses under quadrilateral longitudinal temporal harmonic excitations is studied. The improvability of the parametrically excited instability by periodic distribution parameters is explored. The direct eigenvalue analysis approach for solving the parametrically excited stability problem of the periodic sandwich plate system under longitudinal harmonic excitations is proposed. The spatial periodic distribution of facial layer thickness and core layer modulus of the sandwich plate is considered. The non-linear partial differential equations of longitudinal and transverse coupling motions of the periodic visco-elastomer sandwich plate with supported masses under biaxial longitudinal boundary excitations are derived. The longitudinal displacements of the sandwich plate are separated into two parts and the longitudinal boundary excitations relevant to symmetric part are incorporated into the sandwich plate system. Then the partial differential equations with boundary excitations are converted into parametrically excited system equations and further converted into ordinary differential equations with time-varying parameters, which describe the parametrically excited vibration with multi-mode coupling of the periodic sandwich plate system. The fundamental perturbation solution to the equations is expressed as the product of periodic and exponential parts based on the Floquet theorem. The ordinary differential equations with harmonic parameters are converted into a set of algebraic equations using the harmonic balance method. Then the parametrically excited instability of the periodic sandwich plate system is determined directly by matrix eigenvalues. The overall instability characteristics of parametrically excited vibration with multi-mode coupling of the system under longitudinal harmonic excitations are illustrated by numerical results on unstable regions. The parametrically excited instability can be improved by the spatially periodic distribution of geometrical and physical parameters. The proposed approach is applicable to general sandwich structures with spatial distribution parameters in multi-mode-coupling parametrically excited vibrations for overall instability analysis on continuous frequency band. [ABSTRACT FROM AUTHOR]

This paper presents train-induced dynamic response and fatigue damage analyses for the hangers of a tied-arch railway bridge. A train–bridge interaction analysis is carried out using the vector form intrinsic finite element method, through which the inertial force effect of the moving train can be effectively analyzed. The responses of the bridge deck and its hangers are investigated at resonant train speeds. Significantly larger stresses are observed on the shorter hangers near the arch anchorages, which is primarily caused by the first two anti-symmetrical vibration modes. The fatigue damage to the hangers is estimated using the Palmgren-Miner model (PMM) for linear fatigue damage accumulation and the continuum damage mechanics (CDM) method for nonlinear accumulation. The mean stress effect is considered in the S–N curve primarily by Smith–Watson–Topper equation in terms of the effective stress range with a zero-mean stress. Two probability distributions for train speed are considered for the current and future operating conditions with mean speeds of 220 and 300 km/h, respectively. This study found that the fatigue lives estimated by the nonlinear CDM are significantly shorter than those estimated by the linear PMM. It also found that the shortest hanger reflects the shortest fatigue life at the current operating speed, whereas the longer hanger near the third point of the bridge deck may have the shortest fatigue life at an increased speed in the future. [ABSTRACT FROM AUTHOR]

A direct eigenvalue analysis approach for solving the stability problem of periodically supported beams with multi-mode coupling vibration under general harmonic excitations is developed based on the Floquet theorem, Fourier series and matrix eigenvalue analysis. The transverse periodic supports are considered for improving the parametrically excited stability of beams under longitudinal periodic excitations. The dynamic stability of parametrically excited vibration of the beam with transverse spaced supports under longitudinal harmonic excitations is studied. The partial differential equation of motion of the beam with spaced supports under harmonic excitations is given and converted into ordinary differential equations with time-varying periodic parameters using the Galerkin method, which describe the parametrically excited vibration of the beam with coupled multiple modes. The fundamental solution to the equations is expressed as the product of periodic and exponential components based on the Floquet theorem. The periodic component and periodic parameters are expanded into Fourier series, and the matrix eigenvalue equation is obtained which is used for directly determining the parametrically excited stability. The dynamic stability of parametrically excited vibration of the beam with spaced supports under harmonic excitations is illustrated by numerical results on unstable regions. The influence of the periodic supports and excitation parameters on the parametrically excited stability is explored. The parametrically excited stability of the beam with multi-mode coupling vibration can be improved by the periodic supports. The developed analysis method is applicable to more general period-parametric beams with multi-mode coupling vibration under various harmonic excitations. [ABSTRACT FROM AUTHOR]

This paper demonstrates that a sandwich beam with the continuous harmonic distribution of geometrical and physical parameters can be adjusted to yield the desired response. The facial layer thickness and core layer modulus of the sandwich beam are considered as the harmonic distribution. The frequency responses and response spectral densities of the finite harmonic sandwich beam with supported mass under stochastic support motion excitations are studied for improving the performance. The partial differential equations for the horizontal and vertical coupling motions of the harmonic sandwich beam are derived and converted into the ordinary differential equations for the multi-mode coupling vibration. The modal stiffness, mass and excitation coefficients are functions of the harmonic distribution parameters (HDPs). The vibration responses including resonances and anti-resonances can be adjusted by the harmonic parameter wave numbers and amplitudes. The frequency responses and response spectral densities of the harmonic sandwich beam are obtained. The single and two-mode vibrations are analyzed to demonstrate that the response resonance and anti-resonance can be adjusted via the HDPs of the beam. The substantially improved vibration response characteristics and the influence of the HDPs on the response spectral densities are illustrated with numerical results. [ABSTRACT FROM AUTHOR]

The Tsing Ma Bridge is a cable suspension bridge carrying both highway and railway. A bridge health monitoring system called wind and structural health monitoring system (WASHMS) has been installed in the Tsing Ma Bridge and operated since 1997 to monitor the structural performance and its associated loads and environments. However, there exists a possibility that the worst structural conditions may not be directly monitored due to the limited number of sensors and the complexity of structure and loading conditions. Therefore, it is an essential task to establish structural performance relationships between the critical locations/components of the bridge and those instrumented by the WASHMS. Meanwhile, to develop and validate practical and effective structural damage detection techniques and safety evaluation strategies, the conventional modeling for cable-supported bridges by approximating the bridge deck as continuous beams or grids is not applicable for simulation of real damage scenarios. To fulfil these tasks, a detailed full three-dimensional (3D) finite element model of the Tsing Ma Bridge is currently established for direct computation of the stress/strain states for all important bridge components. This paper presents the details of establishing this full 3D finite element model and its calibration. The major structural components are modeled in detail and the connections and boundary conditions are modeled properly, which results in about half million elements for the complete bridge model. The calibration of vibration modes and stresses/strains due to passing trains is carried out, and a good agreement is found between the computed and measured results. [ABSTRACT FROM AUTHOR]

A symplectic numerical approach to the stability analysis of nonlinear parametric excited systems with multi-degree-of-freedom is developed and the stability of a nonlinear vibration system depends on the dynamic behavior of its perturbation. The nonlinear parameter-varying differential equations for the perturbation motion are expressed in the form of Hamiltonian equations with time-varying Hamiltonian, and are converted further into the classical Hamiltonian equations with extended time-invariant Hamiltonian by augmenting the state variables. The solution to the augmented Hamiltonian equations has the symplectic structure in terms of the symplectic transformation. Then the difference equations of the symplectic Runge-Kutta algorithm with a sufficient condition are constructed, which is proved to preserve the intrinsic symplectic structure of the original solution. In particular, the symplectic Gauss-Runge-Kutta algorithm with stage 2 and order 4 is proposed and applied to the stability analysis of a nonlinear system. Unstable regions based on the nonlinear periodic-parameter perturbation equation are obtained by using the symplectic Gauss-Runge-Kutta algorithm, analytical solution method and non-symplectic conventional Runge-Kutta algorithm to verify the higher accuracy of the proposed algorithm. Unstable regions based on the nonlinear perturbation are given to illustrate the improvement over those based on the linear perturbation. The developed symplectic approach to the stability analysis can preserve the symplectic structure of the original system and is applicable to nonlinear parametric excited systems with multi-degree-of-freedom. [ABSTRACT FROM AUTHOR]

A direct numerical approach for solving the instability problem of multi-degree-of-freedom dynamic systems with general period-parameter excitation is developed based on the Floquet theory, Fourier series and generalized eigenvalue analysis. The developed direct numerical approach to the instability is applied to an inclined stay cable with sag under periodic two-support-motion excitation. The partially differential equation for the parametrically excited vibration of the cable is derived by using the transformation of displacements and converted into ordinary differential equations according to the Galerkin method. The unstable regions for parametrically excited vibration of the damped cable system with multi-degree-of-freedom are obtained to illustrate its overall instability. The effects of each mode vibration and parameters of the cable on the unstable regions are analyzed. The developed direct numerical approach to the parametrically excited instability is applicable to more general periodic parameter-excited systems. [ABSTRACT FROM AUTHOR]