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The sandwich plate (SP) with supported mass can model structural systems such as platform or floor with installed vibration-sensitive apparatus under random loading. The stochastic optimal control (in time domain) of periodic (in space) viscoelastomer (VE) SP with supported mass subjected to random excitation is an important research subject, which can fully use VE controllability, but it is a challenging problem on optimal bounded parametric control (OBPC). In this paper, a stochastic OBPC for periodic VESP with supported mass subjected to random base loading is proposed according to the stochastic dynamical programming (SDP) principle. Response-reduction capability using the proposed OBPC is studied to demonstrate further control effectiveness of periodic SP via SDP. Controllable VE core modulus of SP is distributed periodically in space. Differential equations for coupling vibration of periodic SP with supported mass are derived and transformed into multi-dimensional system equations with parameters as nonlinear functions of bounded control. The OBPC problem is established by the system equations and performance index with bound constraint. Then, an SDP equation is derived according to the SDP principle. The OBPC law is obtained from the SDP equation under bound constraint. Optimally controlled responses are calculated and compared with passively controlled responses to evaluate control effectiveness. Numerical results on responses and statistics of SP via the proposed OBPC show further remarkable control effectiveness. [ABSTRACT FROM AUTHOR]

Systems whose specifications change abruptly and statistically, referred to as Markovianjump systems, are considered in this paper. An approximate method is presented to assess the stationary response of multidegree, nonlinear, Markovian-jump, quasi-nonintegrable Hamiltonian systems subjected to stochastic excitation. Using stochastic averaging, the quasi-nonintegrable Hamiltonian equations are first reduced to a one-dimensional Itô equation governing the energy envelope. The associated Fokker-Planck-Kolmogorov equation is then set up, from which approximate stationary probabilities of the original system are obtained for different jump rules. The validity of this technique is demonstrated by using a nonlinear two-degree oscillator that is stochastically driven and capable of Markovian jumps.

An analytical method was used to express the substructural displacements as functions of linear combinations of the lower fixed-interfacial modes and the lower free-interfacial. The procedure resulted in the formulation of a modal synthesis method utilizing mixed modes. The truncated frequency of the substructural free-interface modes and the truncation frequency of the substructural fixed-interface modes were established as the main criteria for the truncation frequency of the system synthesis modes.

A multimode perturbation method for frequency response analysis of nonlinearly vibrational beams with periodic distribution parameters is proposed. The partial differential equation with spatial varying parameters for nonlinear vibration of beams with periodic parameters under harmonic excitations is derived. The procedure of the multimode perturbation method includes three main steps: first, the nonlinear partial differential equation is transformed into linear partial differential equations with varying parameters by applying perturbation method; second, the linear partial differential equations are transformed into ordinary differential equations with multimode coupling by applying Galerkin method, where multiple vibration modes of the beams are used and the equations are suitable to nonlinear vibration of periodic structures with high parameter-varying wave in wide frequency band; third, the ordinary differential equations are solved by applying harmonic balance method to obtain vibration response of the nonlinear periodic beam, which is used for characteristics analysis of frequency response and spatial mode. Furthermore, the stability problem of nonlinear harmonic vibration as multidegree-of-freedom system with periodic time-varying parameters is solved by applying direct eigenvalue analysis approach. The proposed method can incorporate multiple vibration modes into response analysis of nonlinear periodic structures and consider mode-coupling effects due to structural nonlinearity and parametric periodicity. Finally, a nonlinear beam with periodic supports under harmonic excitations is studied. Numerical results on frequency response of the beam are given to illustrate an application of the proposed method, new frequency response characteristics, and influences of periodic parameters on structural response. The results have potential application to nonlinear structural vibration control and support damage detection of nonlinear structures with periodic supports. [ABSTRACT FROM AUTHOR]

The dynamic characteristics of the infinite-length and finite-length rods with periodic distribution parameters are studied. The differential equation of longitudinal motion of the period-parametric rod is given. The algebraic matrix equation for the wave motion characteristics of the infinite-length periodic rod is derived based on the Bloch theorem and Fourier series. The characteristic frequencies are determined by the matrix eigenvalues which depend on the characteristic wave number and parametric wave number. Then the algebraic matrix equation for the dynamic characteristics of the finite-length periodic rod is derived based on the Galerkin method. The natural frequencies are determined by the matrix eigenvalues which depend on only the parametric wave number. An improving approach algorithm for solving the eigenvalue problem of high degree-of-freedom systems is developed based on the Rayleigh quotient. Finally, the circular cross-section rod with period-varying diameter is considered and numerical results on the dynamic characteristics are given. Large characteristic wave number and parametric wave number are considered for the infinite-length and finite-length periodic rods. The characteristic frequencies varying with the characteristic wave number and parametric wave number are shown, and the band gaps vanishing are revealed for increasing characteristic wave number. The finite-length periodic rod has the dynamic characteristics different from the infinite-length periodic rod. The effect of the term number of the displacement expansion on the natural frequencies and the natural frequencies varying with the parametric wave number and wave amplitude are shown for the finite-length periodic rod. The local resonance and periodical short descent of the natural frequencies with the increase of the parametric wave number and the different changes of the natural frequencies with the parametric wave amplitude are revealed. The above new dynamic characteristics of the infinite-length and finite-length rods with periodic distribution parameters have a potential application to period-structural design and optimization. [ABSTRACT FROM AUTHOR]

A nonlinear stochastic optimal bounded control strategy for quasi-Hamiltonian systems with actuator saturation is proposed based on the stochastic averaging method and stochastic maximum principle. First, the averaged Itô stochastic differential equations are derived by using the stochastic averaging method for quasi-Hamiltonian systems. Then, the stochastic Hamiltonian system for optimal control with a given performance index is established based on the stochastic maximum principle. The bounded optimal control consisting of unbounded optimal control and bounded bang–bang control is determined by solving the forward-backward stochastic differential equations with control constraint. Finally, three examples of quasi-Hamiltonian systems with controls are given to illustrate the application of the proposed strategy. Numerical results show that the proposed control strategy significantly improves the control efficiency and chattering attenuation of the corresponding bang–bang control. [ABSTRACT FROM PUBLISHER]

An optimal control method for peak response reduction and its application to a tall building structure for reducing peak earthquake responses are presented in this paper. A critical value is used for magnifying large responses and performance index. A structural control system is transformed, and the dynamical programming principle is applied to form a dynamical programming equation. For a certain higher-order power function in the index, a nonlinear optimal control law with the corresponding Riccati equation is obtained for minimizing structural large responses or peak responses. The asymptotic stability of the autonomous controlled system is proved by using the Lyapunov method. Then the proposed control method is applied to a single degree-of-freedom system and a 51-storey building structure with active mass damper on the top floor under earthquake excitation. Numerical results on peak displacements, interstorey drifts, accelerations and controls are given to illustrate the high control effectiveness of the proposed control method for peak response reduction. The proposed control method has a simple and convenient procedure for multi-degree-of-freedom structures. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A minimax stochastic optimal semi-active control strategy for stochastically excited quasi-integrable Hamiltonian systems with parametric uncertainty by using magneto-rheological (MR) dampers is proposed. Firstly, the control problem is formulated as an n-degree-of-freedom (DOF) controlled, uncertain quasi-integrable Hamiltonian system and the control forces produced by MR dampers are split into the passive part and the semi-active part. Then the passive part is incorporated into the uncontrolled system. After that, the stochastic optimal semi-active control problem is solved by applying the minimax stochastic optimal control strategy based on the stochastic averaging method and stochastic differential game. The worst-case disturbances and the optimal controls are obtained by the minimax dynamical programming equation with the constraints of disturbance bounds and MR damper dynamics. Finally, the system response and the control performance are evaluated by using Monte Carlo simulation. An example of a two-DOF system with coupling damping and parametric uncertainty under Gaussian white noise excitations is worked out in detail to illustrate the procedure and effectiveness of the proposed control strategy, which is also compared with the clipped linear-quadratic-Gaussian control strategy to show the advantages. [ABSTRACT FROM PUBLISHER]

A strategy of feedback control optimization of stochastic dynamic systems via stationary response is proposed. First, the control system subjected to wide-band random excitations is formulated based on the stochastic averaging method for quasi-integrable Hamiltonian systems and then transformed into Ito stochastic differential equation. Second, the averaged Ito stochastic differential equation for the system is derived and the stationary solution of the Fokker-Plank-Kolmogorov equation associated with the averaged Ito equation is obtained. Third, the mean square value of the control force and the Hamiltonian function are combined handily as the performance index of the system and the optimal control force is obtained. Finally, two examples are worked out in detail to illustrate the application and the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

Piezoelectric structures as a smart sensor system have potential application in engineering. The stochastic vibration of piezoelectric structures is a significant research subject. In the present paper, an approach to solving the stochastic response of piezoelectric axisymmetric cylinder shells is proposed and the analytical expressions for solution are obtained. Firstly, the basic equations of a piezoelectric cylinder shell subjected to boundary stochastic excitations are given. Then, the excitations are incorporated in the differential equations of motion by using the transformations of displacements and electric potentials. And the displacement of the shell is expanded as a series of the Legendre polynomial in space. The partial differential equation of motion is converted into ordinary differential equations by using the Galerkin method. Finally, the expressions of mean-square displacement and acceleration of the shell are derived according to the theory of random vibration. The effects of stochastic excitations on mean-square response, electric potential, and the electrical and mechanical coupling characteristics can be analyzed. It is pointed out that there exists the asymmetry of generalized stiffness matrix due to the electrical and mechanical coupling relationship. [ABSTRACT FROM AUTHOR]

Objective: To study the bone state with ultimate stress by examining biomechanical distribution of upper femur in Chinese, in order to accumulate more experiences for clinical work., Methods: Totally 60 Chinese femurs from fresh cadavers were randomly divided into two groups. All the femurs were cleaned, and the body age ranged from 36 to 72 years old, averaged 56.4 years, including 41 from males, and 19 from females. These two groups underwent mechanical stress and bending stress tests. Special mechanical laboratory and machines were used to get the information. Results about the loading value at each testing point under stress were collected., Results: The four faces of the upper femur suffered different stress under external forces. The bone on upper femur can tolerate more mechanical stress than bending stress. Medial and lateral region of the femur neck and the rear side of the small tuberosity section were themain position enduring the vertical stress. The rear position of the base femur neck and the small tuberosity section were the main regions enduring the bending stress. Those main positions had strong cancellous bones. The intertrochanteric fracture fixation and artificial femoral stems were designed depending on this biomechanical basis., Conclusion: According to our experiment result, doctors need to chose more effective fixations for upper femur fracture, and femoral stems for the patients. More information should be collected by further researches.