Mechanical & Materials Engineering, Department of


Date of this Version

Winter 12-3-2014


Xiaojian Yang, "Control of Responses of Smart Plate Structures Under Non-Stationary Random Excitations", University of Nebraska Lincoln, Dec. 2014


A THESIS Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Master of Science, Major: Mechanical Engineering and Applied Mechanics, Under the Supervision of Professor C. W. Solomon To. Lincoln, Nebraska: December, 2014

Copyright (c) 2014 Xiaojian Yang


This thesis is concerned with an investigation of the control of responses of plate structures with piezoelectric layers and under complicated excitations modeled as a non-stationary random process. The plate structures and piezoelectric layers are both discretized by the mixed formulation finite element method (FEM).

The investigation consists of three parts. The first part is a literature survey and theoretical development. The second part is the eigenvalue solution and computation of uncontrolled response statistics of laminated plate structures under nonstationary random excitations. The final part is the introduction and application of the stochastic central difference (SCD) method that was presented by To (1986, 2000) for the computation of response statistics. The responses computed by using the SCD method are compared with those obtained by the Runge-Kutta fourth order (RK4) numerical integration algorithm.

In the first part, publications specifically concerned with smart structures under various deterministic and stochastic excitations were reviewed. The theoretical development required for the present investigation are drawn from previous publications and introduced so as to provide a foundation for the response statistics computation subsequently. In this phase of the investigation, the three-node flat triangular piezoelectric shell finite element of To and Liu (2003), and To and Chen (2007) are applied. This mixed formulation based shell finite element has three nodes every one of which has seven degrees-of-freedom (dof). The latter include three translation, three rotation, and one electric dof. Without the electric dof the laminated composite shell finite element reduces to that developed by To and Wang (1998). The latter laminated composite shell finite element is able to provide correctly the six rigid-body modes.

The latter six rigid-body modes were confirmed in the eigenvalue solution during the second part of the investigation. A cantilever plate structure with and without the piezoelectric layers acting as sensor and actuator was studied. The differences in natural frequencies between the structure with and without the piezoelectric layers are of particular interest. Having verified the correctness of the eigenvalue solution, response statistics of mean squares of displacements are evaluated and compared with those in the literature.

In the third part of the investigation, two computer programs were developed based on the SCD method of To (1986, 2000), and the RK4 algorithm. Comparisons are made between responses with and without the applied voltage to the smart plate structures. The efficiency of computation of responses applying the SCD method and RK4 numerical integration scheme is examined.

Advisor: C. W. Solomon To