The dynamic similitude design of a thin-walled cylindrical shell by considering the strength requirement

Abstract

In designing the test model of thin-walled cylindrical shells, geometrically distorted models are widely used. This study investigates a method of designing a distorted cylindrical shell model by considering the strength requirement, which means the test model should reflect the strength situation or even failures of the prototype. The significance of this study is that it provides an acceptable process which guides the design of test models. First, governing equations are employed to derive the scaling law of the natural frequency. The harmonic response is calculated in order to obtain the scaling law of the vibration response amplitude. As the study is based on governing equations of elastic cylindrical shells, only elastic behavior is discussed. Then considering the different materials’ ultimate stress, an excitation force ratio is defined. An applicable size interval is investigated and the range of the excitation force is obtained. Finally, an aluminium alloy cylindrical shell is used as a prototype and a NO. 45 steel scaled down cylindrical shell is used as a distorted test model. The accuracy of the prediction is verified by using simulation data.

Keywords

Cylindrical shell ultimate stress distorted model scaling laws applicable size intervals

Get full access to this article

View all access options for this article.

References

Luo

Sun

Wang

. Study of vibration characteristics of the short thin cylindrical shells and its experiment. J Vibroeng 2013; 15: 1270–1283.

Suzuki

. Dynamic behaviour of thin cylindrical shell rotating with high-speed. Ingenieur-Archiv 1977; 46: 75–84.

Alves

Oshiro

. Scaling impacted structures when the prototype and the model are made of different materials. Int J Solid Struct 2006; 43: 2744–2760.

Rezaeepazhand

Simitses

Starnes

. Scale models for laminated cylindrical shells subjected to axial compression. Compos Struct 1996; 34: 371–379.

Rezaeepazhand

Simitses

Starnes

. Design of scaled down models for predicting shell vibration response. J Sound Vibrat 1996; 195: 301–311.

Ungbhakorn

Singhatanadgid

. Similitude and physical modeling for buckling and vibration of symmetric cross-ply laminated circular cylindrical shells. J Compos Mater 2003; 37: 1697–1712.

Ungbhakorn

Wattanasakulpong

. Structural similitude and scaling laws of anti-symmetric cross-ply laminated cylindrical shells for buckling and vibration experiments. Int J Struct Stabil Dynam 2007; 7: 609–627.

Rezaeepazhand

Simitses

. Structural similitude for vibration response of laminated cylindrical shells with double curvature. Compos Part B-Eng 1997; 28: 195–200.

Yazdi

. Prediction flutter boundaries of laminated cylindrical shells using scaling laws. J Aerosp Eng 2012; 27: 86–92.

10.

Chouchaoui

Parks

Ochoa

. Similitude study for a laminated cylindrical tube under tension, torsion, bending, internal and external pressure – Part II: Scale models. Compos Struct 1999; 44: 231–236.

11.

Chouchaoui

Ochoa

. Similitude study for a laminated cylindrical tube under tension, torsion, bending, internal and external pressure – Part I: Governing equations. Compos Struct 1999; 44: 221–229.

12.

Oshiro

Alves

. Predicting the behaviour of structures under impact loads using geometrically distorted scaled models. J Mech Phys Solid 2012; 60: 1330–1349.

13.

Oshiro

Alves

. Scaling of structures subject to impact loads when using a power law constitutive equation. Int J Solid Struct 2009; 46: 3412–3421.

14.

Oshiro

Alves

. Scaling of cylindrical shells under axial impact. Int J Impact Eng 2007; 34: 89–103.

15.

Luo

Zhao

Zhu

. Determination method of the structure size interval of dynamic similar models for predicting vibration characteristics of the isotropic sandwich plates. J Vibroeng 2014; 16: 608–622.

16.

Zhu

Luo

Zhao

. Determination method of the structure size interval of dynamically similar models for predicting vibration characteristics of the coated thin plates. Proc IMechE, Part C: J Mechanical Engineering Science 2014; 299: 59–68.

17.

Qatu

. Vibration of laminated shells and plates, London: Academic Press, 2004.

18.

Luo

Zhu

Zhao

. Determination method of dynamic distorted scaling laws and applicable structure size intervals of a rotating thin-walled short cylindrical shell. Proc IMechE, Part C: J Mechanical Engineering Science 2014; 229: 806–817.

19.

Qin

Yan

Chu

. Influence of clamp band joint on dynamic behavior of launching system in ascent flight. Proc IMechE, Part G: J Aerospace Engineering 2014; 228: 97–114.