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The paper contains a parametric analysis of tensegrity structures subjected to time-independent external loads. A complete dynamic stability analysis is a three-step process. The first stage involves the identification of self-stress states and infinitesimal mechanisms. The next stage concentrates on the static and dynamic behavior of tensegrities under time-independent external loads, whereas the third is under periodic loads. In this paper, the first two stages are carried out. The structures built with the most popular tensegrity modules, Simplex and Quartex, are considered. The effect of the initial prestress on the static parameters and frequency is analyzed. To assess this behavior, a geometrically non-linear model is used.

The concept of tensegrity is understood in many ways. This term is often improperly used for structures that have some, but not necessarily the key, tensegrity properties. The concept of tensegrity systems is misused in reference to both mathematical models and completed engineering structures. The aim of the study is to indicate which of the plane (2D) trusses presented in the literature are erroneously classified as tensegrities. Singular value decomposition of the compatibility matrix and spectral analysis of the stiffness matrix with the effect of self-equilibrated forces is used for the analysis. A new precise definition of tensegrity trusses is proposed and implemented.

The study includes a parametric analysis of a group of tensegrity plate-like structures built with modified Quartex modules. The quantitative assessment, including the calculation of the structure’s response to constant loads, was carried out. A static parametric analysis was performed, with particular emphasis on the influence of the initial prestress level on the displacements, the effort, and the stiffness of the structure. A geometrical non-linear model was used in the analysis. A reliable assessment required introducing a parameter for determining the influence of the initial prestress level on the overall stiffness of the structure at a given load. The stiffness of the structure was found to depend not only on the geometry and material properties, but also on the initial prestress level and external load. The results show that the effect of the initial prestress on the overall stiffness of the structure is greater with less load and that the effect of load is most significant with low pre-stressing forces. The analysis demonstrates that the control of static parameters is possible only when infinitesimal mechanisms occur in the structure.

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The vibration and stability analysis of uniform beams supported on two-parameter elastic foundation are performed. The second foundation parameter is a function of the total rotation of the beam. The effects of axial force, foundation stiffness parameters, transverse shear deformation and rotatory inertia are incorporated into the accurate vibration analysis. The work shows very important question of relationships between the parameters describing the beam vibration, the compressive force and the foundation parameters. For the free supported beam, the exact formulas for the natural vibration frequencies, the critical forces and the formula defi ning the relationship between the vibration frequency and the compressive forces are derived. For other conditions of the beam support conditional equations were received. These equations determine the dependence of the frequency of vibration of the compressive force for the assumed parameters of elastic foundation and the slenderness of the beam.

Abstract. The objective of this paper is to determine dynamic instability areas of moderately thick beams and frames. The effect of moderate thickness on resonance frequencies is considered, with transverse shear deformation and rotatory inertia taken into account. These relationships are investigated using the Timoshenko beam theory. Two methods, the harmonic balance method (HBM) and the perturbation method (PM) are used for analysis. This study also examines the influence of linear dumping on induced parametric vibration. Symbolic calculations are performed in the Mathematica programme environment. The majority of studies reported in the literature use numerical analysis for determining resonance areas. Only a few researchers have adopted an analytical approach.The purpose of this article is to propose two methods for determining parametric resonance areas for moderately thick beams and frames under various support conditions. These methods, never before used for this purpose, are the harmonic balance method (HBM) and the perturbation method (PM). The latter of these two methods represents a surprisingly simple tool for achieving the goal, as its results are very close to those obtained from the standard harmonic balance method which is far more troublesome in application.An analytical approach is used to analyze simply supported moderately thick beams, and a numerical technique, based on the finite element method with the use of physical shape functions [32] is applied to other beams and frames. The analysis covers the effect of moderate thickness on resonance frequencies and the influence of type of fixing used in the beams and frames on the instability areas. For this purpose, shear deformation and rotatory inertia are taken into account. The Timoshenko beam theory is applied to examine how these factors affect resonance frequency values. The results are compared with those obtained with the Bernoulli-Euler beam theory.In addition, the effect of linear dumping of induced parametric vibration is considered. Analysis of a simply supported beamThe following assumptions are adopted in physical and numerical modeling:• The beam is made of an isotropic homogenous linear elastic material with Young's modulus E, shear modulus G and Poisson's ratio v.

Abstract. Full-scale tensegrity skeleton of White Rhino is considered in this paper. The influence of self-stress state on structure behaviour is studied. Few models that consist of 15, 16, 17 or 18 elements are analysed. For the models self-stress states and infinitesimal mechanisms are considered. The impact of the level of self-stress state on displacement is investigated. Moreover a failure of White Rhino is considered. The influence of a damage of one, two or three cables on displacements is examined. Analyses are performed using the second order theory in the Mathematica environment and the third order theory using the Sofistic program.