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Vibration control of composite structures with distributed masses under random loadings is a significant issue. Adjustability of dynamic characteristics including response spectrum peaks and valleys is important for structural vibration control. The vibration control design in space contains structure and conformation designs which combination results in periodic composite structures. In the present paper, spatial periodicity control design is proposed. Stochastic response adjustable performance of a visco-elastomer sandwich plate with harmonic distribution of geometrical and physical parameters and distributed supported masses under random base motion loading is studied. Both facial layer thickness and core layer modulus of the sandwich plate are considered as harmonic distribution in length and width directions as well as periodically distributed masses. Partial differential equations of coupling motions of the sandwich plate system are derived and converted into ordinary differential equations for multi-mode coupling vibration. Generalized stiffness, damping, and mass coefficients are functions of the harmonic distribution parameters. An analysis solution with frequency response function and response spectral density expressions of the sandwich plate system is obtained. Numerical results are given to show the response adjustable performance through the harmonic geometrical and physical parameters and distributed masses. The results have a potential application to stochastic vibration control or dynamic optimization design of smart composite structure systems. [ABSTRACT FROM AUTHOR]

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]

Introduces a modal synthesis technique for structural dynamics using mixed modes. Importance of the technique in determining the truncation frequency of system synthesis modes; Manner of expressing the exact residual modes; Derivation of nonlinear synthesis formulas based only on lower modes involved in the synthesis process.