Nonlinear Geometric Thermoelastic Response of Structures with Uncertain Thermal and Structural Properties

Uncertainty Analysis of Piezoelectric Vibration Energy Harvesters Using a Finite Element Level-Based Maximum Entropy Approach

“…Different from the mass matrix, the randomization of the stiffness and the coupling matrices needs to be carried out together as a multiple-physics one due to the electromechanical coupling, similar to the heated structure case [40,42]. To this end, construct the matrix…”

“…EE denotes a n H -by-n H matrix relating to the strain energy induced by the electromechanical coupling, see Ref. [40] for discussion in the thermal case, and which will be discussed later in this section. The randomization of the elemental stiffness and the elemental electromechanical coupling matrices is carried out with the mean K…”

“…Such an uncertainty modeling is proposed here based on the very recent work in Refs. [40][41][42], where the developed nonparametric approach is nonintrusive to the finite element software, requiring only the capability to output finite element mass, stiffness, electromechanical coupling, and piezoelectric capacitance matrices for the mean harvester design. The approach in Refs.…”

“…The approach in Refs. [40][41][42] follows the original work of Soize in Ref. [43], in which the maximum entropy principle is applied and the uncertainty is modeled directly at the level of a reduced-order model of the structure, not within the finite element formulation as is done with the stochastic finite element approach.…”

“…The specific formulation in Refs. [40][41][42], also used in this study, is a modification of the original methodology of Soize, in which the elemental mass and stiffness matrices are recognized as reduced order model matrices of the structure within each of the finite elements with the interpolation functions serving as basis functions inside the elements. Once the mean model elemental matrices have been obtained, uncertainty is introduced element per element for each sample of the uncertain harvester, the structural-piezoelectric matrices are reassembled and the simulation, e.g., output power determination, can be carried out.…”