Dynamic Stability of Tensegrity Structures—Part I: The Time-Independent External Load

Obara, Paulina; Tomasik, Justyna

doi:10.3390/ma16020580

Cited by 7 publications

(24 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The most common methods were described in [35]. The methods often used include, e.g., the spectral analysis of linear stiffness matrix, the analytical solutions, the force density method, the dynamic relaxation, and the singular value decomposition (SVD) of the compatibility matrix B [29,30,34,36]. The SVD method is considered due to its ease of application and can be used both for simple and more complex structures.…”

Section: Qualitative Analysismentioning

confidence: 99%

“…It is the parametric analysis leading to the determination of the impact of the self-stress state (initial prestress) on the behavior of the structure under static load. To assess this behavior, a geometrically non-linear model (thirdorder theory) is used [29,31,37]:…”

Section: Quantitative Analysismentioning

confidence: 99%

“…where K L is linear stiffness matrix, K NL (q) is the non-linear displacement stiffness matrix. The explicit matrices forms can be found for example in [29,31].…”

Section: Quantitative Analysismentioning

confidence: 99%

“…In recent years, the form-finding of cable domes was investigated by many authors as well [22][23][24]. Popular areas of research on tensegrity domes include structure optimization [25,26] and the investigation of static and dynamic properties [27][28][29]. Nevertheless, there is a gap in the parametric analysis of tensegrity domes.…”

Section: Introductionmentioning

confidence: 99%

“…This analysis provides the determination of the static or dynamic parameters as the function of the prestress forces. It is a very important aspect due to the possibility of controlling the stiffness of tensegrity structures by modifying the level of self-stress state [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Qualitative and quantitative analysis of tensegrity domes

Obara,

Solovei,

Tomasik

2023

Bulletin of the Polish Academy of Sciences Technical Sciences

View full text Add to dashboard Cite

The paper concerns steel domes with regard to the special structures named tensegrity. Tensegrities are characterized by the occurrence of self-stress states. Some of them are also characterized by the presence of infinitesimal mechanisms. The aim of this paper is to prove that only tensegrity domes with mechanisms are sensitive to the change of the level of initial prestress. Two tensegrity domes are considered. In addition, a standard single-layer dome is taken into account for comparison. The analysis is carried out in two stages. Firstly, the presence of the characteristic tensegrity features is examined (qualitative analysis). Next, the behavior under static external loads is studied (quantitative analysis). In particular, the influence of the initial prestress level on displacements, effort, and stiffness of the structure is analyzed. To evaluate this behavior, a geometrically non-linear model is used. The model is implemented in an original program written in the Mathematica environment. The analysis demonstrates that for a dome with mechanisms, the adjustment of pre-stressing forces influences the static properties. It has been found that the stiffness depends not only on the geometry and properties of the material but also on the initial prestress level and external load. In the case of the non-existence of mechanisms, structures are insensitive to the initial prestress level.

show abstract

Section: Qualitative Analysismentioning

confidence: 99%

Section: Quantitative Analysismentioning

confidence: 99%

“…where K L is linear stiffness matrix, K NL (q) is the non-linear displacement stiffness matrix. The explicit matrices forms can be found for example in [29,31].…”

Section: Quantitative Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Qualitative and quantitative analysis of tensegrity domes

Obara,

Solovei,

Tomasik

2023

Bulletin of the Polish Academy of Sciences Technical Sciences

View full text Add to dashboard Cite

show abstract

Parametric dynamic analysis of tensegrity cable-strut domes

Obara,

Solovei,

Tomasik

2024

Journal of Theoretical and Applied Mechanics

View full text Add to dashboard Cite

The paper contains a parametric dynamic analysis of cable-strut domes. The special structures named tensegrity are considered. Two qualitative different tensegrity domes, i.e., the Geiger dome and the Levy dome are taken into account. The aim of the study is to compare the dynamic behaviour of such structures. The first stage of analysis involves the identification of initial prestress forces (system of internal forces, which holds structural components in stable equilibrium) and infinitesimal mechanisms. The second stage focuses on calculating natural frequencies, while in the last, the impact of time-independent external loads on vibrations is studied. The influence of initial prestress and external load on the dynamic response of the structures is considered. A geometrically non-linear model is used to analysis. Presented considerations are crucial for the next step in the analysis, i.e., dynamic stability analysis of the behaviour of tensegrity structures under periodic loads.

show abstract

The application of the immanent tensegrity properties to control the behavior of double-layered grids

2023

Archives of Civil Engineering

View full text Add to dashboard Cite

The paper focuses on the static behavior of double-layered tensegrity grids. Due to the specific characteristics, like the self-stress states and infinitesimal mechanisms, tensegrities can be used as deployable structures. For such structures, the possibility of the control of the behavior is very important. The main purpose of the work is to prove that the control of tensegrity structures with mechanisms is possible. The stiffness of such structures is found to depend not only on the geometry and material properties, but also on the initial prestress level and external load. In the case, when mechanisms do not exist, structures are insensitive to the initial prestress. It is possible to control the occurrence of mechanisms by changing the support conditions of the structure. Grids built with modified Simplex modules are considered. Two-stage analysis is performed. Firstly, the presence of the characteristic tensegrity features is examined and then, on that basis, the structures are classified into one of two classes. Next, the influence of the level of initial prestress on the behavior of structures under static load is analyzed. To evaluate this behavior, a geometrically non-linear model is used.

show abstract

Dynamic Stability of Tensegrity Structures—Part I: The Time-Independent External Load

Cited by 7 publications

References 33 publications

Qualitative and quantitative analysis of tensegrity domes

Qualitative and quantitative analysis of tensegrity domes

Parametric dynamic analysis of tensegrity cable-strut domes

The application of the immanent tensegrity properties to control the behavior of double-layered grids

Contact Info

Product

Resources

About