Dynamic model of a rotating flexible arm-flexible root mechanism driven by a shaft flexible in torsion

Abstract. This paper presents a dynamic model of a rotating flexible beam carrying a payload at its tip. The model accounts for the driving shaft and the arm root flexibilities. The finite element method and the Lagrangian dynamics are used in deriving the equations of motion with the small deformation theory assumptions and the Euler-Bernoulli beam theory. The obtained model is a nonlinear-coupled system of differential equations. The model is simulated for different combinations of shaft and root flexibilities and arm properties. The simulation results showed that the root flexibility is an important factor that should be considered in association with the arm and shaft flexibilities, as its dynamics influence the motor motion. Moreover, the effect of system non-linearity on the dynamic behavior is investigated by simulating the equivalent linearized system and it was found to be an important factor that should be considered, particularly when designing a control strategy for practical implementation

Cascades of subharmonic stationary states in strongly non-linear driven planar systems

The dynamics of a one-degree of freedom oscillator with arbitrary polynomial non-linearity subjected to an external periodic excitation is studied. The sequences (cascades) of harmonic and subharmonic stationary solutions to the equation of motion are obtained by using the harmonic balance approximation adapted for arbitrary truncation numbers, powers of non-linearity, and orders of subharmonics. A scheme for investigating the stability of the harmonic balance stationary solutions of such a general form is developed on the basis of the Floquet theorem. Besides establishing the stable/unstable nature of a stationary solution, its stability analysis allows obtaining the regions of parameters, where symmetry-breaking and period-doubling bifurcations occur. Thus, for period-doubling cascades, each unstable stationary solution is used as a base solution for finding a subsequent stationary state in a cascade. The procedure is repeated until this stationary state becomes stable provided that a stable solution can finally be achieved. The proposed technique is applied to calculate the sequences of subharmonic stationary states in driven hardening Duffing's oscillator. The existence of stable subharmonic motions found is confirmed by solving the differential equation of motion numerically by means of a time-difference method, with initial conditions being supplied by the harmonic balance approximation.Comment: 37 pages, 11 figures, revised material on chaotic motio

Identificazione di danni strutturali mediante analisi delle vibrazioni

Dottorato di ricerca in meccanica applicata. 9. ciclo. Coordinatore V. Parenti Castelli. Tutore U. MeneghettiConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

Dynamic Model of a Rotating Flexible Arm-Flexible Root Mechanism Driven by a Shaft Flexible in Torsion

This paper presents a dynamic model of a rotating flexible beam carrying a payload at its tip. The model accounts for the driving shaft and the arm root flexibilities. The finite element method and the Lagrangian dynamics are used in deriving the equations of motion with the small deformation theory assumptions and the Euler-Bernoulli beam theory. The obtained model is a nonlinear-coupled system of differential equations. The model is simulated for different combinations of shaft and root flexibilities and arm properties. The simulation results showed that the root flexibility is an important factor that should be considered in association with the arm and shaft flexibilities, as its dynamics influence the motor motion. Moreover, the effect of system non-linearity on the dynamic behavior is investigated by simulating the equivalent linearized system and it was found to be an important factor that should be considered, particularly when designing a control strategy for practical implementation

On the Steady State Response of a Cantilever Beam Partially Immersed in a Fluid and Carrying an Intermediate Mass

This paper presents a study on the nonlinear steady state response of a slender beam partially immersed in a fluid and carrying an intermediate mass. The model is developed based on the large deformation theory with the constraint of inextensible beam, which is valid for most engineering structures. The Lagrangian dynamics in conjunction with the assumed mode method is utilized in deriving the non-linear unimodal temporal equation of motion. The distributed and concentrated sinusoidal loads are accounted for in a consistent manner using the assumed mode method. The non-linear equation of motion is, analytically, solved using the single term harmonic balance (SHB) and the two terms harmonic balance (2HB) methods. The stability of the system, under various loading conditions, is investigated. The results are presented, discussed and some conclusions on the partially immersed beam nonlinear dynamics are extracted

On the steady state response of a cantilever beam partially immersed in a fluid and carrying an intermediate mass

This paper presents a study on the nonlinear steady state response of a slender beam partially immersed in a fluid and carrying an intermediate mass. The model is developed based on the large deformation theory with the constraint of inextensible beam, which is valid for most engineering structures. The Lagrangian dynamics in conjunction with the assumed mode method is utilized in deriving the non-linear unimodal temporal equation of motion. The distributed and concentrated sinusoidal loads are accounted for in a consistent manner using the assumed mode method. The non-linear equation of motion is, analytically, solved using the single term harmonic balance (SHB) and the two terms harmonic balance (2HB) methods. The stability of the system, under various loading conditions, is investigated. The results are presented, discussed and some conclusions on the partially immersed beam nonlinear dynamics are extracted

Influence of Temperature on Shear Behavior of Lightweight Reinforced Concrete Beams Using Pozzolana Aggregate and Expanded Polystyrene Beads

The innovation inherent to employing expanded polystyrene (EPS) beads lies in its transformative impact on traditional concrete practices. Through the incorporation of EPS beads in concrete mixtures, a novel approach emerges that significantly alters the material’s characteristics, and opens up new avenues for construction and design. Studying the shear behavior of RC beams made with EPS beads is essential for advancing knowledge, improving design practices, ensuring structural integrity, and promoting the effective and responsible use of innovative materials in construction. This research experimentally investigated the effect of using EPS beads and pozzolana aggregate (PA) on the shear behavior of the RC beams. A total of 27 simply supported rectangular beams were cast, using three novel distinct mix designs, and were subjected to two-point load testing until failure. These three mixes were categorized as follows: a control mix, a mix with only EPS, and a mix with EPS, along with an additive. The ultimate failure load was experimentally recorded for all specimens, and the influence of the temperature (300 °C and 600 °C) on the RC beams made with EPS was examined. The findings revealed a reduction in the concrete compressive strength and density in the beams containing EPS and EPS with superplasticizers of (21.7%, 24.9%) and (11.3%, 16.2%), respectively. Additionally, EPS played a significant role in diminishing the ultimate shear capacity of the beams, compared to the control beams, by about 19.4%. However, the addition of a superplasticizer along with the EPS helped to maintain the beam capacity, to some extent. Conversely, the beams exposed to a temperature of 300 °C exhibited an almost similar capacity to that of the control beams without heating. Nevertheless, at 600 °C, the beams displayed a noticeable decrease in the ultimate load capacity, compared to the unheated control beams