Active traveling wave vibration control of elastic supported conical shells with smart micro fiber composites based on the differential quadrature method

• Published in: Applied mathematics and mechanics Vol. 46; no. 2; pp. 305 - 322
• Main Authors: Hao, Yuxin, Sun, Lei, Zhang, Wei, Li, Han
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2025; Springer Nature B.V
• Edition: English ed.
• Subjects: Actuators; Angular velocity; Applications of Mathematics; Classical Mechanics; Conical shells; Control systems; Deformation effects; Differential equations; Elastic deformation; Fiber composites; Fluid- and Aerodynamics; Impact loads; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Negative feedback; Ordinary differential equations; Partial Differential Equations; Piezoelectricity; Porous materials; Quadratures; Resonant frequencies; Shear deformation; Smart materials; Smart sensors; Springs (elastic); Traveling waves; Vibration control; elastic support; differential quadrature method; porous metal material; 74B05; rotating conical shell (CS); TB123; 74H60; active vibration control
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-025-3216-7

This paper investigates the active traveling wave vibration control of an elastic supported rotating porous aluminium conical shell (CS) under impact loading. Piezoelectric smart materials in the form of micro fiber composites (MFCs) are used as actuators and sensors. To this end, a metal pore truncated CS with MFCs attached to its surface is considered. Adding artificial virtual springs at two edges of the truncated CS achieves various elastic supported boundaries by changing the spring stiffness. Based on the first-order shear deformation theory (FSDT), minimum energy principle, and artificial virtual spring technology, the theoretical formulations considering the electromechanical coupling are derived. The comparison of the natural frequency of the present results with the natural frequencies reported in previous literature evaluates the accuracy of the present approach. To study the vibration control, the integral quadrature method in conjunction with the differential quadrature approximation in the length direction is used to discretize the partial differential dynamical system to form a set of ordinary differential equations. With the aid of the velocity negative feedback method, both the time history and the input control voltage on the actuator are demonstrated to present the effects of velocity feedback gain, pore distribution type, semi-vertex angle, impact loading, and rotational angular velocity on the traveling wave vibration control.