Input/output reduced model of a damped nonlinear beam based on Volterra series and modal decomposition with convergence results

This paper addresses the model reduction and simulation of a damped Euler–Bernoulli–von Kármán pinned beam excited by distributed force. nonlinear problem is formulated as PDE reformulated well-posed state-space system. The order are derived combining two approaches: Volterra series expansion truncation pseudo-modal defined from eigenbasis linearized problem. interest this approach lies in large class input waveshapes that can be considered simplicity structure. structure only involves cascades finite-dimensional decoupled linear systems multilinear functions. Closed-form bounds depending on coefficients orders provided for convergence domain approximation error. These theoretical results generalized to models, refinement also proposed sub-class. Numerical experiments confirm well approximated very first terms inside domain.