Microscopic control actions of LaSMP actuators on hemispherical shells

https://doi.org/10.1016/j.ymssp.2020.106744Get rights and content

Highlights

  • This work provides an analysis procedure on getting vibration control actions of Light activated shape memory polymer (LaSMP).

  • This work proves that the LaSMP can be used in vibration control for two dimensional spherical shell.

  • The microscopic actuation effects of actuator position, thickness and shell radius, LaSMP thickness are evaluated.

  • The parametric analyses confirm that the normalized control forces caused by membrane forces dominate the control effect and the best control position is near the boundary of hemispherical shell.

Abstract

Light activated shape memory polymer (LaSMP) is one of novel shape memory polymers with dynamic strain and Young’s modulus when exposed to UV lights. This study investigates distributed microscopic control actions of LaSMP patches on hemispherical shells with free boundary. Based on strain models established in the experiments, governing equations of the spherical shell are defined and control forces in the meridional, circumferential and transverse directions are derived respectively. In case studies of LaSMP patch laminated on the shell by covering specific wavelength at each mode in the circumferential direction, the meridional and circumferential forces turn to zero. Then, the dominant transverse control forces and its components resulting from the bending moments and membrane forces are compared at different modes. Parametric analyses are carried out to evaluate the microscopic actuation effects of actuator position, thickness and shell radius, LaSMP thickness, etc. LaSMP induced meridional and circumferential microscopic membrane/bending control actions on hemispherical shells are evaluated. The analyses indicate that the transverse control forces increase with increasing of LaSMP patch thickness and decreasing of hemispherical shell thickness and radius. Then, the normalized control forces are derived by dividing LaSMP patch size. The parametric analyses confirm that the normalized control forces caused by membrane forces dominate the control effect and the best control position is near the boundary of hemispherical shell. This work provides an analysis procedure on estimating LaSMP vibration control actions and gives theoretical predictions for idealized LaSMP vibration control of hemispherical shells.

Introduction

At present, shape memory materials as a kind of functional material are widely used in engineering, aerospace, electronics, bio-medical devices etc. [1], [2], [3]. For example, shape memory alloy (SMA) is served as a new type of foldable structure in the space-borne antenna [4] as well as artificial bone, heart stents and surgical suture in bionic structure [5], [6]. Different from SMAs activated by thermos elasticity, a variety of shape memory polymers (SMP) are compounded and applied in many fields. Recently, a new category of novel shape memory polymers is compounded which is activated by light, i.e. light activated shape memory polymer (LaSMP). Young’s modulus and strain of LaSMP can dynamically change when exposed to UV lights and realize non-contact actuation and control [7], [8], [9], [10]. By putting optical active substance Spiropyran into Ethylene vinyl acetate, Li, et al. in the StrucTronics and Control Laboratory has synthesized a kind of LaSMP [11]. The relation between Young’s modulus, strains and light intensities have been established and proved by the laboratory experiments [12]. With dynamic Young’s modulus and strain, this kind of shape memory polymers can be able to work as vibration actuator and controller [13].

Structures and components of hemispherical shells are very common in engineering systems, for example pressure vessels, storage tanks and signal receivers, etc. The vibration and natural frequency of hemispherical shells have been studied by theoretical methods and experiments over the years [14], [15], [16], [17]. The control effect of piezoelectric actuators on hemispherical shells was also investigated [18]. Based on dynamic strain model of LaSMP, the control effect of LaSMP/hemispherical shell systems on microscopic control actions are studied in this paper.

In this study, the LaSMP/shell governing equations are derived by using the classical bending approximation theory based on the LaSMP strain forward/backward reaction models proved in the laboratory experiments. By considering LaSMP patch on the hemispherical shell with free boundary, the control forces are derived as a function of LaSMP induced strains. In the case study of LaSMP patch laminated on the shell by covering specific wavelength at each mode in the circumferential direction, the components of the bending and membrane forces in the meridional and circumferential direction are compared at different modes, followed by discussion of actuator position, shell thickness and radius effect. LaSMP induced meridional and circumferential microscopic membrane/bending control actions on hemispherical shells are evaluated. The normalized control forces are analyzed by considering patch sizes and the results are evaluated.

Section snippets

Dynamic equations with LaSMP control forces

In this section, LaSMP constitutive behaviors are discussed first, followed by LaSMP control forces and moments defined for an arbitrary actuator patch. Dynamic control equations of a hemispherical shell coupled with LaSMP control forces/moments are then defined. Distributed LaSMP actuations are presented in the next section.

Microscopic LaSMP actuations

Dynamic control equations of the hemispherical shell coupled with LaSMP control forces/moments were defined above. Detailed distributed LaSMP microscopic actuations and their key contributing components are derived in this section.

Evaluation of distributed microscopic actuations

The in-plane vibrations in the meridional and circumferential directions are usually small, as compared with the out-of-plane transverse vibration of thin shells. Thus, the transverse LaSMP control force F̂k_transa is focused and its microscopic meridional and circumferential contributing components induced by LaSMP membrane forces and bending moments are compared. The geometric and material parameters used in case studies are listed in Table 1.

Again, the biaxial LaSMP actuation was

Conclusions

LaSMP induced meridional and circumferential microscopic membrane/bending control actions on hemispherical shells are evaluated in detail in this study. The shell governing equations with LaSMP control forces/moments are derived based on the bending approximation theory. The specific expressions of control forces of LaSMP patch on a hemisphere shell with free boundary are derived by using the Love control operators, followed by detailed analyses of modal control forces and their microscopic

CRediT authorship contribution statement

Dan Wang: Conceptualization, Investigation, Writing - original draft, Writing - review & editing, Funding acquisition, Resources. Mu Fan: Investigation, Funding acquisition, Resources. Zhu Su: Investigation, Supervision. Hornsen Tzou: Conceptualization, Writing - review & editing, Funding acquisition, Supervision.

Acknowledgements

This research is supported by Natural Science Foundation of China (Nos. 11872206, 11902151), Natural Science Foundation of Jiangsu Province (No. BK20180411, BK20180429, BK20170773), State Key Laboratory of Mechanics and Control of Mechanical Structures (MCMS-IZD1900201907).

References (19)

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