Nonlinear Dyn https://doi.org/10.1007/s11071-019-05074-7 ORIGINAL PAPER Nonlinear multi-element interactions in an elastically coupled microcantilever array subject to electrodynamic excitation P. N. Kambali · F. Torres · N. Barniol · O. Gottlieb Received: 13 December 2018 / Accepted: 14 June 2019 © Springer Nature B.V. 2019 Abstract In this work, we formulate and investigate a nonlinear initial boundary-value problem for an array of N elastically coupled hybrid microcantilever beams that are subject to electrodynamic excitation. The equa- tions of motion for the individual viscoelastic element consist of two fields: the base component which is common to all cantilevers and the unrestrained com- ponent which is excited electrodynamically. The cou- pling of the elements is obtained via an equivalent lin- ear stiffness that is estimated from experimental mea- surements of a 5-element array. We employ a Galerkin ansatz to obtain a modal dynamical system that con- sistently incorporates a quintic nonlinearity due to the combined effects of cubic viscoelasticity and quadratic electrodynamics. We validate the periodic response of a 5-element array with moderate damping and con- struct numerically a comprehensive bifurcation struc- ture for a 25-element array. The analysis reveals an intricate structure for small damping that includes both quasiperiodic and nonstationary chaotic-like energy transfer between the elements of the array. It is note- worthy that an array with a larger coupling stiffness, corresponding to a smaller distance between adjacent P. N. Kambali · O. Gottlieb (B ) Department of Mechanical Engineering, Technion - Israel Institute of Technology, Haifa, Israel e-mail: oded@technion.ac.il F. Torres · N. Barniol Department of Electrical Engineering, Autonomous University of Barcelona, Bellaterra, Spain elements, yields a chaotic bifurcation structure for a larger value of viscoelastic damping. Keywords Microcantilever array · Common base elastic coupling · Electrodynamic excitation · Nonlinear bifurcation structure · Quasiperiodic energy transfer · Nonstationary dynamics 1 Introduction The study of nonlinear dynamics of micro- and nano- electromechanical system (MEMS/NEMS)-based arrays has gained increased interest in recent years for their potential applications such as multi-functional mass sensors [1, 7, 34, 36, 38], biosensors [2], multian- alyte detection and identification [4], multi-element atomic force microscopy (AFM) [8, 17, 19, 25, 26]. There are many experimental and theoretical stud- ies showing advantages of arrays over a single ele- ment. Buks and Roukes [3] employed an optical diffrac- tion method to study the collective modes and the response of an array consisting 67 clamped paramet- rically excited microbeams. Baguet et al. [1] studied two- and three-beam arrays using asymptotic methods to increase the mass sensing capability. In Ref. [6], a large array of elastically coupled microcantilevers of variable length was studied experimentally and numer- ically which facilitated the separation of the resonant peaks corresponding to individual beams when oper- ating in vacuum at third harmonic. Endo et al. [7] 123