In this paper we consider vibration control of tensegrity structures under stationary and nonstationary random excitations. These excitations may be representative of many physical loading conditions, such as earthquake, wind, aerodynamic and acoustic excitations. The optimal control theory based on H2 and controller with full state and limited state feedback is used for the control. The response of the tensegrity structure is represented by the zero lag covariance matrix and the same is obtained by solving the matrix Lyapunov equation. The force generated by the electro-mechanical coupling of the piezoelectric actuator is used in the formulation. A tensegrity structure of class-1 comprising of two modules, with 24 pretension cables and six struts with piezoelectric actuators, is considered.

https://iopscience.iop.org/article/10.1088/0964-1726/16/3/030/pdf

Active control of tensegrity structures under random excitation

The main objective of the present paper is to draw the attention of researchers towards the analyses of composite structures in non-deterministic environment. The various distinguishing features of the stochastic finite element methodologies for the analysis of composite structures have been discussed. A thorough literature review has been carried out while emphasizing on the bending, buckling, vibration analysis and failure analysis of composite structures by considering the uncertain behavior of material properties, mechanical loadings and others. This paper also presents an overview of various micromechanical models in the deterministic and stochastic domains, plate theories and impact of uncertainties on the processing techniques of various composite structures. The future research directions have been discussed which will be prolific to the material, design, civil, mechanical and aerospace engineers.

State of the art of composite structures in non-deterministic framework: A review

Orthotropic membrane structure is widely applied in construction buildings, mechanical engineering, electronic meters, space and aeronautics, etc. During their serving period, membrane structure is prone to vibrate stochastically and seriously under stochastic dynamic loads, which may lead to structural failure. For this purpose, this paper investigates the stochastic dynamic response and reliability analysis of membrane structure under impact load obeying Gaussian distribution. The equation of stochastic motion of membrane structure is established by Von Karman's large deformation theory. The results of stochastic dynamic response are obtained with perturbation method solving the equation. Then, reliability parameters of extreme value of dynamic response are calculated by Moment method based on first-passage probabilities of level crossing. Furthermore, the theoretical model proposed is validated by experimental study using Monte Carlo method. The effects of parameters including impact velocity, pretension force and radius on structural reliability are discussed in addition. The model proposed herein provides some theoretical basis for the stochastic vibration control and dynamic design of orthotropic membrane structure based on reliability theory.

Stochastic nonlinear vibration and reliability of orthotropic membrane structure under impact load

Parametric instability of a cantilever beam with magnetic field and periodic axial load

Stationary/Nonstationary Stochastic Response Analysis of Composite Laminated Plates with Aerodynamic and Thermal Loads

Vibration analysis of a magneto-elastic beam with general boundary conditions subjected to axial load and external force

A finite element analysis on random vibration of nonlinear shell structures

The statistical dynamic responses of geometrically nonlinear shell structures with stochastic Young's modulus of elasticity are investigated in this study. In general, large deformation of the shell structures must be considered when shell structures are under excessive loading, and then the governing equations of the shell structures become nonlinear since the stiffness matrix of the system is related to the deflection. In this paper, the stochastic finite element method along with the perturbation technique is used to deal with statistical responses of shell structures with structural randomness; in particular, the Newton–Raphson iteration procedure in conjunction with Newmark scheme is adopted to solve the nonlinearity of the dynamic governing equation of shell structures. Some results obtained by the perturbation technique and those from the Monte Carlo simulation approach show a good agreement. Finally, it should be emphasized that these statistically dynamic responses are very useful for estimating the reliability of structures.

M.-F. Liu

Papers

Vibration analysis of a magneto-elastic beam with general boundary conditions subjected to axial load and external force

A finite element analysis on random vibration of nonlinear shell structures

Finite element analysis of nonlinear shell structures with uncertain material property