Generalized Beam Theory for Thin-Walled Beams with Curvilinear Open Cross-Sections

Latalski, Jarosław; Zulli, Daniele

doi:10.3390/app10217802

Cited by 9 publications

(2 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Te shear force caused cross-sectional deformation, and therefore applying Bredt's formulas was needed for necessity. Latalski and Zulli [35] applied the generalized beam theory on a thinwalled beam whose out-of-plane components were derived from the proposition of Vlasov's internal constraint of shear in-deformable middle surface. Tey provided the crucial contribution in case of a change in cross section that happened at equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Multiple Time-Scales Analysis to Predict the Quasiperiodic Oscillatory Response of a Thin-Walled Beam Subjected to $1 : 1 : 1$ Simultaneous Resonance

Kandil,

Hamed,

Awrejcewicz

et al. 2023

Shock and Vibration

View full text Add to dashboard Cite

This paper introduces a study on the horizontal and vertical deflections of the cross section of a thin-walled rotating beam. These deflections are governed by a system of two ordinary differential equations in order to describe their Cartesian directions. Based on multiple time-scales analysis, truncated asymptotic expansions are assumed to be approximate solutions to the given problem. Furthermore, an extracted autonomous system of differential equations governs the change rate of the amplitudes and phases of the beam deflections. The beam’s rotation speed is adjusted to be in the neighborhood of both of the natural frequencies of the deflections such that the beam is subjected to 1 : 1 : 1 simultaneous resonance. A stability test is conducted according to the first method of Lyapunov in order to determine whether the equilibrium point is asymptotically stable or not. The beam’s deflections turn unstable once its speed is in the neighborhood of its modal natural frequencies. There exists a multistable solution at some values of the beam’s speed depending on the hysteresis manner of the model according to forward or backward sweeping of this speed. Furthermore, a range of centrifugal forces of the rotating hub can make the beam’s deflections exhibit quasiperiodic responses which are confirmed by time response, orbital map, and amplitude spectrum. Eventually, some remarks are recommended for the external excitation frequency in order that the beam stays in the periodic behavior.

show abstract

Section: Introductionmentioning

confidence: 99%

Multiple Time-Scales Analysis to Predict the Quasiperiodic Oscillatory Response of a Thin-Walled Beam Subjected to $1 : 1 : 1$ Simultaneous Resonance

Kandil,

Hamed,

Awrejcewicz

et al. 2023

Shock and Vibration

View full text Add to dashboard Cite

show abstract

“…It represents a compelling instrument where, still dealing with one-dimensional continua, the local effects are apriori determined and described by assumed functions, amplified by parameters which are evaluated through equilibrium conditions. In this context, the choice of the assumed functions, as an outcome of the cross-section analysis, denotes a main step, as discussed in [10][11][12], where the use of free-dynamical modes of equivalent frames is proposed, and in case of curvilinear cross-sections [13].…”

Section: Introductionmentioning

confidence: 99%

Static Response of Double-Layered Pipes via a Perturbation Approach

2021

Self Cite

View full text Add to dashboard Cite

A double-layered pipe under the effect of static transverse loads is considered here. The mechanical model, taken from the literature and constituted by a nonlinear beam-like structure, is constituted by an underlying Timoshenko beam, enriched with further kinematic descriptors which account for local effects, namely, ovalization of the cross-section, warping and possible relative sliding of the layers under bending. The nonlinear equilibrium equations are addressed via a perturbation method, with the aim of obtaining a closed-form solution. The perturbation scheme, tailored for the specific load conditions, requires different scaling of the variables and proceeds up to the fourth order. For two load cases, namely, distributed and tip forces, the solution is compared to that obtained via a pure numeric approach and the finite element method.

show abstract

Nonlinear dynamics of a tubular beam considering distortion of the cross sections and internal resonances

2023

View full text Add to dashboard Cite

The nonlinear dynamics of a thin tube under the action of a harmonic external load is addressed in the paper. Use is made of a beam-like model which extends the Timoshenko beam model with further kinematic descriptors, related to the change in shape of the cross section. The external load is applied in half cap of the pipe, directly triggering both the bending of the axis-line and the flattening of the cross sections. The equations of motion are projected on a reduced basis constituted by the first three linear modes, and then the solutions are sought via the multiple scale method, for two different external resonance conditions. Internal resonances among the modes are considered as well. The outcomes, compared with pure numerical solutions, highlight the possible energy exchange between local modes, i.e., those describing flattening and warping of the cross sections, and global modes, i.e., those related to bending of the axis-line and rotation of the cross section of the pipe.

show abstract

Generalized Beam Theory for Thin-Walled Beams with Curvilinear Open Cross-Sections

Cited by 9 publications

References 30 publications

Multiple Time-Scales Analysis to Predict the Quasiperiodic Oscillatory Response of a Thin-Walled Beam Subjected to $1 : 1 : 1$ Simultaneous Resonance

Multiple Time-Scales Analysis to Predict the Quasiperiodic Oscillatory Response of a Thin-Walled Beam Subjected to $1 : 1 : 1$ Simultaneous Resonance

Static Response of Double-Layered Pipes via a Perturbation Approach

Nonlinear dynamics of a tubular beam considering distortion of the cross sections and internal resonances

Contact Info

Product

Resources

About

Generalized Beam Theory for Thin-Walled Beams with Curvilinear Open Cross-Sections

Cited by 9 publications

References 30 publications

Multiple Time-Scales Analysis to Predict the Quasiperiodic Oscillatory Response of a Thin-Walled Beam Subjected to 1 : 1 : 1 Simultaneous Resonance

Multiple Time-Scales Analysis to Predict the Quasiperiodic Oscillatory Response of a Thin-Walled Beam Subjected to 1 : 1 : 1 Simultaneous Resonance

Static Response of Double-Layered Pipes via a Perturbation Approach

Nonlinear dynamics of a tubular beam considering distortion of the cross sections and internal resonances

Contact Info

Product

Resources

About

Multiple Time-Scales Analysis to Predict the Quasiperiodic Oscillatory Response of a Thin-Walled Beam Subjected to $1 : 1 : 1$ Simultaneous Resonance

Multiple Time-Scales Analysis to Predict the Quasiperiodic Oscillatory Response of a Thin-Walled Beam Subjected to $1 : 1 : 1$ Simultaneous Resonance