DYNOR: dynamic analysis of structural systems

The dynamic analysis of a structural system with different material and geometric properties leads to linear eigenvalue problem such as generalized (or standard) eigenvalue problem. In general, the material and geometric properties are assumed to be in the form of crisp (or exact). However, due to several errors and insufficient or incomplete information of data, the uncertainties are assumed to be present in the material and geometric properties. These uncertain material and geometric properties may be modeled through convex normalized fuzzy sets. In standard fuzzy arithmetic, all the operands are assumed to be independent of each other. But when they are partially or completely dependent on each other, the standard fuzzy arithmetic results in a wider range. This situation is known as the “dependency problem” or “overestimation problem”. In this regard, a fuzzy-affine approach is developed to overcome the dependency problem. This proposed approach may improve the outer enclosures and give tighter bounds to the fuzzy solution set. This chapter deals with the dynamic analysis of various structural systems viz. multi degrees-of-freedom spring-mass structural system, multi-storey frame structural system, etc. by adopting the proposed approach. Several numerical examples related to the dynamic analysis of these structural systems have been worked out to illustrate the reliability and efficiency of the present approach.KeywordsAffine arithmeticFuzzy-affine arithmeticDynamic analysis of structural systemFuzzy generalized eigenvalue problemFuzzy standard eigenvalue problem

A modal superposition pseudo‐force method for the dynamic analysis of structural systems with non‐proportional damping is presented. The method combines the advantages of the classical modal superposition method and the pseudo‐force method. When the system damping is non‐proportional, the dynamic equilibrium equations in generalized coordinates are coupled through the damping terms. In the present method, these coupled equations are solved by an iterative process in which the coupling terms are treated as pseudo‐forces. A proof of the convergence of the iterative process is given. Numerical examples show the good convergence characteristics of the process and the good accuracy of the obtained results.

This paper presents a homogenised finite element formulation for the transient dynamic analysis of asymmetric and symmetric unconstrained layer damping beams in which the viscoelastic material is characterised by a five-parameter fractional derivative model. This formulation is based on the weighted residual method (Galerkin’s approach) providing a fractional matrix equation of motion. The application of Grunwald-Letnikov’s definition of the fractional derivatives allows to solve numerically the fractional equation by means of two different implicit formulations. Numerical examples for a cantilever beam with viscoelastic treatment are presented comparing the response provided by the proposed homogenised formulation with that of Padovan, based on the principle of virtual work. Different damping levels and load cases are analysed, as well as the influence of the truncation and time-step. From the numerical applications it can be concluded that the presented formulation allows to reduce significantly the degrees of freedom and consequently the computational time and storage needs for the transient dynamic analysis of structural systems in which damping treatments have been applied by means of viscoelastic materials characterised by fractional derivative models.

Hysteresis is a non-linear phenomenon exhibited by the mechanical systems. Beyond elastic limit the loading and unloading path of most of the system will differ and that nonlinear path is indicated by hysteresis. The reason for shape of hysteretic cure may due to either changes in material properties beyond the elastic range or due to the changes in structural geometry because of subjected load. This response is a function of both immediate deformation and the previous residual deformation acted on it since it represents the dissipated energy of structure. The hysteretic characteristics or degrading characteristics includes pinching, stiffness degradation, load deterioration, and sliding. A study of four commonly available hysteresis models, which are Bouc Wen Model, Mostaghel Model, Menegotto Pinto Model and Preisach Model were briefly reviewed and discussed in this section and the outcome of this study is the best fitted model for the nonlinear analysis. The scope of the work is to simulate nonlinear response of the building frame subjected to earthquake excitation in a most effective way.

An iterated improved reduced system (IIRS) procedure combined with sub-structuring scheme for nonclassically damped structural systems is presented. For dynamic analysis of such systems, complex eigenproperties are required to incorporate properly the nonclassical damping effect. In complex structural systems, the equations of motion are written in the state space from. Thus, the number of degrees of freedom of the new equations of motion and the size of the associated eigenvalue problem required to obtain the complex eigenvalues and eigenvectors are doubled. Iterated IRS method is an efficient reduction technique because the eigenproperties obtained in each iteration step improve the condensation matrix in the next iteration step. However, although this reduction technique reduces the size of problem drastically, it is not efficient to apply this technique to a single domain finite element model with degrees of freedom over several thousands. Therefore, for a practical application of the reduction method, accompanying sub-structuring scheme is necessary. In the present study, iterated IRS method combined with sub-structuring scheme for nonclssically damped structures is developed. Numerical examples demonstrate the convergence and the efficiency of a newly developed scheme.

Geometric nonlinear static analysis of structural systems with cable elements is carried out using point based iterative procedure. In all sub systems as cable systems, constituted for each node having at least one degree of freedom that is idealized by finite elements, successive calculations are performed. In the analysis part, based on finite element displacement method, to the maximum number of unknown displacements required for each sub-system calculation is limited with three. Tangent stiffness matrix, including pre-stressed internal forces as well as varying geometries with respect to different external force applications, is utilized. The convergence procedure is adapted into the method to prevent excessive displacements through the calculations. In the present study, a computer program has been developed to present a very effective calculation method. Different numerical applications have been considered and the results were compared with the literature results. Key words: Cable systems, nonlinear analysis, point based iterative procedure, convergence procedure.

An equivalent stiffness approach for modelling the behaviour of compression members according to Eurocode 3

The [formula omitted]-compound of a difference–algebraic system

In this paper, a new way of computing the constraint transfer matrix for the inverse dynamic and joint force analysis of multibody systems is developed. The method is based on the Newton–Euler method and the screw theory notations. This method is first developed in (Taghvaeipour et al. in Multibody Syst. Dyn. 29(2):139–168, 2013), however, in this study, it is efficiently modified by incorporating a unified constraint transfer matrix for all types of joints. This change makes both the derivation of the equations and the computations less time consuming. Moreover, in the foregoing procedure, the constraint wrenches of a system are obtained in one reference frame, namely, the global reference frame. As a case study, the proposed method is carried out on the agile wrist which is a three-legged spherical parallel robot with three degrees of freedom. At the end, the results obtained by the modified method are verified with the ones calculated by the original procedure and a software package.

Model reduction for friction-induced vibration of multi-degree-of-freedom systems and experimental validation

The finite element method (FEM) is widely accepted for the steady-state dynamic response analysis of acoustic systems. It exhibits almost no restrictions with respect to the geometrical features of these systems. However, it is limited to the low-frequency range due to the rapidly growing model size for increasing frequencies. An alternative method is the wave based method (WBM), which is based on the indirect Trefftz approach. It exhibits better convergence properties than the FEM and therefore allows accurate predictions at higher frequencies. However, the applicability is limited, since the high computational efficiency only appears for systems of moderate geometrical complexity. In order to benefit from the advantageous features of both methods, i.e. the wide application range of the FEM and the high convergence rate of the WBM, the coupling between both methods is proposed. Only the parts of the problem domain with a complex geometry are modeled using the FEM, while the remaining parts are described with a wave based model. The resulting hybrid model contains less degrees of freedom, which allows a further model refinement. The proposed coupled approach has the potential to cover the mid-frequency range, where it is still difficult to obtain satisfactory prediction results with currently existing deterministic techniques.

A nonlinear modal analysis procedure is presented for the forced response of nonlinear structural systems. It utilizes the notion of invariant manifolds in the phase space, which was recently used to define nonlinear normal modes and the corresponding nonlinear modal analysis for unforced vibratory systems. For harmonic forcing, a similar procedure could be formulated, simply by augmenting the size of the free vibration problem. However, in order to accommodate general, nonharmonic external excitations, the invariant manifolds associated with the unforced system are used herein for the forced response analysis. The procedure allows one to generate reduced-order models for the forced analysis of structural systems. Although strictly speaking the invariance property is violated, good results are obtained for the case study considered. In particular, it is found that fewer nonlinear modes than linear modes are needed to perform a forced modal analysis with the same accuracy. For systems with small and/or diagonal damping, approximate invariant manifolds are determined, which are shown to yield good results for both the unforced and forced responses. (Author)

One of the advanced structural systems that have been applied in tall buildings to improve the building strength during quake loads is the outrigger system. Most of the previous researches interested to study the behavior of steel outrigger truss system, although the hard connection between the concrete and steel members may give us the inaccurate output. For that, This research aims to find the best structural concrete outrigger system by performing a comparison between two structural outrigger systems, the wall beam outrigger system, and the vierendeel outrigger system which makes the building facing strong actual earthquakes. All the models were analyzed in the advanced Midas-Gen software program and the building response was studied under El-Centro time history earthquake load. And also, finding the best outrigger position through the building height when the outrigger is applied in one and two stories. This comparison is built on different parameters as storey drift, storey drift ratio, and the base storey overturning moment. The results showed that a one-storey wall beam structural system is better than two stories vierendeel structural system when these systems are applied as an outrigger system. The best position for one storey outrigger is about 0.45 of the total building height and for the two stories outrigger, the 0.20 and 0.45 of the total building height are the best positions. Overall, the concrete outrigger systems are an effective structural system to make the tall buildings facing the earthquake loads.

In the system identification using finite element method (FEM), system responses of overall degree of freedoms (DOFs) are necessary. Because of the limitation of sensor and other experiment equipment, the responses of unspecified DOFs have to be contained in the design variables. This increase of the design variable makes difficult to solve the inverse problem. It is one of the solutions about the problem of limited responses that the responses of unspecified DOFs are represented by the responses of specified DOFs, using the condensation method. In the previous study, we applied iterative inverse perturbation method (IIPM) to enhance the efficiency and the solution convergence of the structural system identification problems using the condensation method. So we efficiently identify structural system through solving the optimization problem with design variables which have the same number of elements. However, if the size of problem developed to analyze practical model is increased, the number of design variables which had to be considered in solving process is extremely increased. To identify large structural system, optimization strategy to efficiently change design variables during the iteration of optimization is required. In this study, we suggest two optimization strategies which are adaptive sub-domain method and genetic concept method. Numerical examples are presented to verify the efficiency of the proposed methods and to compare with those methods.

The selection of representative ground motions (GMs) for dynamic analysis of soil and structural systems considering soil–structure interaction (SSI) is critical for accurately predicting their performance under seismic loads. Site-specific GMs are typically generated first by selecting a set of seed time histories and then modifying them by matching to the target spectrum using either Time-Domain (TD) or Frequency-Domain (FD) techniques. While previous studies have recommended TD over FD techniques based on 1D site response analysis and engineering judgment, their effects on predicting soil and structural performance, considering SSI, are poorly understood in a 3D nonlinear domain. In this study, a set of seed ground motions corresponding to 3% and 50% in 75 years hazard conditions specific to Charleston, SC, was selected and modified using TD and FD techniques. Then, sixteen dynamic nonlinear 3D finite element simulations of a bridge bent supported by a 2 × 2 pile group were performed using the general-purpose finite element software ABAQUS by applying the motions generated using the FD and TD techniques. The geotechnical properties specific to Charleston were obtained from published documents, and the stress–strain behavior of the soil was represented by the Drucker-Prager model. The soil domain was spatially discretized with 3D brick elements. The structural components were represented by linear elastic beam elements. Results indicate that FD matching tends to distort nonstationary waveform components, particularly in displacement time histories. In contrast, TD matching preserves waveform features, including phase and frequency content, more effectively. Despite this, these distortions in FD-matched motions did not lead to substantial differences in structural response in most cases. However, noticeable response variations were observed in the 1 to 2.5-s period range. Overall, TD matching exhibited greater consistency and reliability in preserving input motion characteristics and is recommended for use in nonlinear SSI analyses.