Wave Mode Control of Cantilever Slab Structure of T-Beam Bridge with Large Aspect Ratio

The cantilever plate structure in a T-beam bridge with a large aspect ratio will cause vibration under the influence of environmental disturbance and self-stress, resulting in fatigue damage of the plate structure. Wave control based on elastic wave theory is an effective method to suppress the vibration of the cantilever plate structure in a beam bridge. Based on the classical thin plate theory and the wave control method, the active vibration control of the T-shaped cantilever plate with a large aspect ratio in the beam bridge is studied in this paper. The wave mode control strategy of structural vibration is analyzed and studied, the controller is designed, the vibration mode function of the cantilever plate is established, and the control force/sensor feedback wave control is implemented for the structure. The dynamic response of the cantilever plate before and after applying wave control force is analyzed through numerical examples. The results show that the response of the structure is intense before control, but after wave control, the structure increases damping, absorbs the energy carried by the elastic wave in the structure, weakens the sharp response, and changes the natural frequency of the structure to a certain extent.

Analysis and Study on Bending Vibration Frequency of New Corrugated Steel Web Composite Box Girder

In order to accurately analyze the bending vibration frequency of the new composite box girder, the effects of web folding effect, shear lag, and shear deformation are comprehensively considered in this paper, and the elastic control differential equation and natural boundary conditions of the composite box girder are established by using the Hamilton principle. A one-span composite box girder with corrugated steel webs is used as a numerical example. The effects of height span ratio, width span ratio, web thickness, cantilever plate length, and fold effect on the vertical vibration frequency of the new composite box girder are analyzed. The results show that the analytical solution is in good agreement with the finite element solution. When considering the shear lag and fold effect, the vibration frequency of composite box girder decreases. With the increase in order, the influence of shear lag and fold effect on its frequency becomes stronger. The changes of height span ratio and web thickness of composite box girder have a great influence on its folding effect, while the changes of width span ratio and cantilever plate length have little influence on it. The conclusion can provide a reference for the design of medium section new composite bridge in practical engineering.

Effect of crack on free vibration of a pre-stressed curved plate

In this study, the effect of crack on free vibration of a large deflected cantilever plate, which forms the case of a pre-stressed curved plate, is investigated. A distributed load is applied at the free edge of a thin cantilever plate. Then, the loading edge of the deflected plate is fixed to obtain a pre-stressed curved plate. The large deflection equation provides the non - linear deflection curve of the large deflected flexible plate. The thin curved plate is modeled by using the finite element method with a four-node quadrilateral element. Three different aspect ratios are used to examine the effect of crack. The effect of crack and its location on the natural frequency parameter is given in tables and graphs. Also, the natural frequency parameters of the present model are compared with the finite element software results to verify the reliability and validity of the present model. This study shows that the different mode shapes are occurred due to the change of load parameter, and these different mode shapes cause a change in the effect of crack.

Load monitoring of a cantilever plate by a novel multimodal fibre optic sensing configuration

Optical fibre sensors and in particular fibre Bragg gratings (FBG) have received a lot of interest for Structural Health Monitoring in different application fields, such as aerospace, pipeline and civil engineering. FBGs are conventionally used to monitor strain and sometimes temperature. In this paper, we propose a new method for load monitoring of a cantilever plate subjected to point loading. The bending of plate is complex due to the interaction between the axial and transverse bending stiffnesses of the material. We use a novel algorithm for interrogating fibre Bragg grating sensors based on both hybrid interferometry and FBG spectral sensing. The method is demonstrated in this paper using a single-mode optical fibre containing four FBG sensors to estimate both the point loading position and the loading magnitude at an arbitrary location on a 1 m$$^{2}$$ 2 cantilever plate. The algorithm first utilizes point strain information through spectral sensing as well as strain from interferometric sensing over a long path. The gratings are interrogated using Wavelength Division Multiplexing (WDM). We calibrated the system using an experimental model. This model was then verified by using single point static loading tests and comparing the calculated sensing position with the actual position. The method achieved a good estimation of loading position achieving a measurement error of about 9% in a 2D plane. The analysis discusses the possible sources of inaccuracies. This study forms the basis of our future work involving morphing smart-wing sections for the purpose of load monitoring. Article highlights A new optical sensing configuration is demonstrated for load and structural health monitoring of cantilever structures. The algorithm successfully estimates the position of an arbitrary load on a cantilever plate, with an error of 9%. This methodology will be extended to monitor more complex structures, in- cluding morphing aircraft wing sections.

Nonlinear Vibrations of Rotating Pretwisted Composite Blade Reinforced by Functionally Graded Graphene Platelets Under Combined Aerodynamic Load and Air Flow in Tip Clearance

The primary resonance and nonlinear vibrations of the functionally graded graphene platelet (FGGP) reinforced rotating pretwisted composite blade under combined the external and multiple parametric excitations are investigated with three different distribution patterns. The FGGP reinforced rotating pretwisted composite blade is simplified to the rotating pretwisted composite cantilever plate reinforced by the functionally graded graphene platelet. It is novel to simplify the leakage of the air flow in the tip clearance to the non-uniform axial excitation. The rotating speed of the steady-state adding a small periodic perturbation is considered. The aerodynamic load subjecting to the surface of the plate is simulated as the transverse excitation. Utilizing the first-order shear deformation theory, von-Karman nonlinear geometric relationship, Lagrange equation and mode functions satisfying the boundary conditions, three-degree-of-freedom nonlinear ordinary differential equations of motion are derived for the FGGP reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations. The primary resonance and nonlinear dynamic behaviors of the FGGP reinforced rotating pretwisted composite cantilever plate are analyzed by Runge-Kutta method. The amplitude-frequency response curves，force-frequency response curves, bifurcation diagrams, maximum Lyapunov exponent, phase portraits, waveforms and Poincare map are obtained to investigate the nonlinear dynamic responses of the FGGP reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations.

BENDING OF ORTHOTROPIC RECTANGULAR CANTILEVER PLATE

An iterative method of superposition of correcting functions is proposed. The partial solution of the main differential bending equation is represented by a fourth-degree polynomial (the beam function), which gives a residual only with respect to the bending moment on parallel free faces. This discrepancy and the subsequent ones are mutually compensated by two types of correcting functions-hyperbolic-trigonometric series with indeterminate coefficients. Each function satisfies only a part of the boundary conditions. The solution of the problem is achieved by an infinite superposition of correcting functions. For the process to converge, all residuals must tend to zero. When the specified accuracy is reached, the process stops. Numerical results of the calculation of a square ribbed plate are presented.

Stability of rectangular cantilever plates with high elasticity

The problem of cantilever plate stability has been little studied due to the difficulty of solving the corresponding boundary problem. The known approximate solutions mainly concern only the first critical load. In this paper, stability of an elastic rectangular cantilever plate under the action of uniform pressure applied to its edge opposite to the clamped edge is investigated. Under such conditions, thin canopies of buildings made of new materials can be found at sharp gusts of wind in longitudinal direction. At present, cantilever nanoplates are widely used as key components of sensors to create nanoscale transistors where they are exposed to magnetic fields in the plate plane. The aim of the study is to obtain the critical force spectrum and corresponding forms of supercritical equilibrium. The deflection function is selected as a sum of two hyperbolic trigonometric series with adding special compensating summands to the main symmetric solution for the free terms of the decomposition of the functions in the Fourier series by cosines. The fulfillment of all conditions of the boundary problem leads to an infinite homogeneous system of linear algebraic equations with regard to unknown series coefficients. The task of the study is to create a numerical algorithm that allows finding eigenvalues of the resolving system with high accuracy. The search for critical loads (eigenvalues) giving a nontrivial solution of this system is carried out by brute force search of compressive load value in combination with the method of sequential approximations. For the plates with different side ratios, the spectrum of the first three critical loads is obtained, at which new forms of equilibrium emerge. An antisymmetric solution is obtained and studied. 3D images of the corresponding forms are presented.