## 1 Introduction  
Structure-controlled studies of magnetostrictive composites were presented. In 2023, [PERSON] et al. [1] used the refined zigzag theory of structure modeling to study wave propagation of a functionally graded material (FGM) magnetostrictive porous nanocomposite. In 2023, [PERSON] et al. [2] reviewed some applications of magneto-optical sensor devices. In 2023, [PERSON] and [PERSON] [3] used higher-order shear-deformation theory (HSDT) and constant feedback control gain to provide a vibration control in magnetostrictive visco-Pasternak-medium FGM beams. In 2023, [PERSON] et al. [4] presented computational generalized differential quadrature (GDQ) with a third-order shear-deformation theory (TSDT) model to study a primary resonant of a magnetostrictive truncated-conical FGM micro shell. In 2022, [PERSON] et al. [5] reviewed the biomedical applications of magnetostrictive alloys. In 2022, [PERSON] et al. [6] studied and controlled high-frequency-excitation properties on the magnetostrictive layers of Terfenol-D, Fe-Ga, and Fe-Co materials under temperature effects. In 2022, [PERSON] et al. [7] studied the magnetic and elastic parameters under temperature effects for three types of giant magnetostrictive materials. In 2022, [PERSON] et al. [8] used large deformation, Villari effect of thin magnetostrictive film, and piston theory to study the FGM beam under an aerodynamic supersonic airflow and heat condition. In 2020, [PERSON] and [PERSON] [9] presented the nonlinear constitutive model for a magneto-strictive material under thermal environments. The following are some useful recent works from the affinity literature in terms of topic and theoretical approaches: In 2024, [PERSON] et al. [10] presented the GDQ results for the coupling hygrometric-thermal-magnetic-electric-mechanical properties of doubly curved shells. In 2024, [PERSON] et al. [11] presented the GDQ results for the coupling thermal-mechanical properties of doubly curved shells. To thoroughly discuss and review the existing literature for FGM plates, cylindrical shells, and beams with velocity feedback control law, more literature references are listed as follows: In 2016, [PERSON] and [PERSON] [12] presented the feedback control voltage from the sensor's inner-layer electric potential and control gain to control the vibration of an outer-layer piezoelectric actuator for a cylindrical FGM shell. In 2020, [PERSON] and [PERSON] [13] presented the two magnetostrictive outer layers of control law to control the vibration for the rotating cylindrical shell. In 2020, [PERSON] et al. [14] presented the feedback control voltage from the piezoelectric sensor inner layer to control the vibration of a piezoelectric actuator's outer layer for a cylindrical shell. In 2020, [PERSON] et al. [15] presented the feedback control voltage for the piezoelectric actuator's outer layer to control a cylindrical-FGM-shell-filling and -conveying fluid. In 2022, [PERSON] and [PERSON] [16] presented the magneto-electro-elastic layers of control law to control the vibration for a rotating FGM cylindrical shell. In 2011, [PERSON] et al. [17] presented the feedback control voltage from the piezoelectric sensor layer to control the vibration of a piezoelectric actuator layer for a plate. In 2010, [PERSON] and [PERSON] [18] presented the feedback control voltage from a piezoelectric sensor layer to control the vibration of a piezoelectric actuator layer for an FGM plate. In 2024, [PERSON] and [PERSON] [19] presented a magnetostrictive central layer of control law to control the vibration for an FGM nanobeam. Numerical GDQ computations in FGM compose the plate and shell by including the effect of applied heat. In 2022, [PERSON] [20] presented the thermal vibration of stress and displacement results for plate/cylindrical shell by including TSDT and advanced nonlinear shear. Some numerical GDQ solutions had been studied for the layer of magnetostrictive material by including first-order shear deformation theory (FSDT) model, with or without constant shear factor, respectively.