Nonlinear guided waves in the sandwich nanostructure coupled with piezoelectric actuator: Introducing machine learning approach to measure nonlinear phase velocities

Abstract

In today's rapidly changing corporate environment, business executives are turning to cutting-edge technology to solve complex problems efficiently. A machine learning approach allows for a more thorough understanding and quantification of decision-making outcomes, leading to increased confidence in business decisions. In this work for the first time, machine learning approach and mathematical simulation are used to model nonlinear guided waves in the sandwich nanostructure coupled with piezoelectric actuator. Using mathematical modeling, the current work studies the nonlinear phase velocity in a sandwich nanoshell composed of a bi-directional functionally graded (BD-FG) core and piezoelectric patch. The modeling uses first-order shear deformation theory with the fairly thick hypothesis to describe the displacement fields of piezoelectric layers. For core layer, a higher order shear deformation theory with terms of higher order in the Taylor series expansion is presented. The nanosystem is accurately modeled using nonlocal strain gradient theory, incorporating nonlocal and length scale characteristics. The solution approach section outlines the multiple scale method for the time domain and the harmonic solution methodology for the displacement domain to address nonlinear equations. To reduce the computational expenses, a machine-learning approach is introduced to address the nonlinear vibration issue in the current study. Validating the conclusions of the current study by comparing them with machine-learning solutions and another published paper can confirm their accuracy. The results section presents the impacts of factors like area of piezoelectric patch, length scale, applied voltage, nonlocality, geometry condition and FG power index on the nonlinear phase velocity of the BD-FG nanoshell coupled with piezoelectric patch.