Nonlinear harmonic vibrations of laminate plates with VE layers using refined zig-zag theory. Part 2 – Numerical solution

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

“…(i) Significant progress has been gained in the field of designing of rubber-like materials with high damping properties; some new materials have the maximum damping ratio of up to 30% (see [36]); (ii) Advanced rheological models (both classical and fractional) are now adopted to characterize dynamic properties of VE elements and sophisticated identification procedures are developed to determine the parameters of those models; (iii) The identification procedures are quite complicated and need further improvements in the future; a nonlinear model of dampers which takes into account the influence of vibration amplitude in dampers is very much desired; (iv) Currently, the influence of ambient temperature on parameters of VE elements and overall dynamic behavior of systems with these elements is taken into account only for the case of rheologically simple materials, usually adopting the frequencytemperature superposition principle and the shifting techniques; studies concerning the influence of ambient temperature on parameters of rheologically complex materials are required; (v) Non-linear dynamic analysis of beams and plates with VE layers became a highly popular research subject due to its practical importance; in particular, very recently, the refined zig-zag theory was successfully applied to the analysis of free and steady-state vibrations; see also the very recent papers [392,393]; (vi) Solution of an eigenvalue problem, in many cases a non-linear one, is required to determine dynamic characteristics of systems with VE elements; there are several methods available to solve this problem efficiently; (vii) Numerical integration methods for solving the equation of motion of systems with VE elements must take into account a complete history of the considered dynamic process, which significantly complicates the numerical procedure and for which further improvements aiming at the reduction in the total time of integration of equations of motion are very much desired; (viii) Recent achievements in sensitivity analysis and uncertainty quantification of design parameters involve the refinement of advanced methods to assess the influence of the parameter variability on the dynamic response of systems with VE elements; in the case of uncertain parameters, it is crucial to develop efficient methods because the recently proposed methods are computationally complex and involve multiple analyses to obtain reliable results; (ix) Heuristic methods are often used in optimization problems because of their reasonable physical relevance and simplicity, as dampers are added one by one with an even distribution or according to a certain pattern; however, their effectiveness is lower for asymmetrical structures or those featuring varying stiffness.…”