Cantilever Square Research Articles

Testing of wood shear modulus based on cantilevered square plate torsional vibration method

ABSTRACT The application of the energy method has proposed a dynamic testing method for the shear modulus in two mutually perpendicular directions on the principal surface of wood using a cantilevered square plate torsional vibration method. In the study, this method was applied to measure the shear modulus of larch wood in the LT and TL directions, as well as the longitudinal and transverse shear modulus of Laminated Veneer Lumber (LVL) sheets. The validity of the results was confirmed through experimental verification using the asymmetric four-point bending beam method, the free plate torsional vibration method, and the free square plate torsional mode method. Simulation calculations of the principal shear modulus for six species of trees with width-to-thickness ratios ranging from 10 to 25 were also conducted using this method. The conclusions drawn suggest that a width-to-thickness ratio of 15 for the cantilevered square plate provides sufficient accuracy for testing the principal shear modulus of wood. Furthermore, the difference in shear modulus between two mutually perpendicular directions on the principal surface of wood is dependent on the width-to-thickness ratio of the cantilevered square plate, indicating that this method outperforms other dynamic methods for testing wood shear modulus.

Benefits of FIR-based spectral proper orthogonal decomposition in separation of flow dynamics in the wake of a cantilevered square cylinder

A comparative analysis is presented to illustrate the benefits of finite impulse response (FIR)-based spectral proper orthogonal decomposition (SPOD) over traditional proper orthogonal decomposition (POD) in separating coherent contributions within narrow spectral bandwidth. The wake of a cantilevered square cylinder of height-to-width ratio h/d=4 protruding a thin laminar boundary layer (δ/d=0.21) is investigated at a Reynolds number (Re) of 10600 using time-resolved stereoscopic particle image velocimetry. In the vicinity of the obstacle-plate junction region (z<0.5d), spectral analysis of the temporal modes obtained with both POD and FIR-based SPOD show fluctuation energy concentration centered on the vortex shedding frequency (fs), as well as weaker contributions at 0.1, 0.4, 0.9, 0.95, 1.05, 1.1, and 2fs. Broad-band spectral energy concentrations around 0.4fs are mainly observed close to the ground plane, while the energy contents at (1±0.05)fs and (1±0.1)fs increase at higher planes. With POD, the frequencies are not separated in the modes and it is very difficult to associate each to specific phenomena within the wake region. However, with tuning of the filter bandwidth, FIR-based SPOD represents each of the identified frequencies in a separate mode pair, which permits a better interpretation of the related dynamics. Notably, the improved modal separation assists in associating the 0.4fs spectral contribution with the interactions between the extensions of horseshoe vortex system and Kármán vortices in the wall-body junction region and the (1±0.05)fs and (1±0.1)fs frequencies to perturbation of the shedding cycle resulting from interactions with the lower frequency dynamics.

Effect of boundary layer state on the wake of a cantilevered square cylinder of aspect ratio 4

We examine the effect of an incoming boundary layer state (laminar vs. turbulent) on the near wake of a surface-mounted square cylinder with a height-to-width aspect ratio of 4 at a Reynolds number ~${10}^{4}$. The mean wake structure for both cases is a dipole structure consisting of a counter-rotating pair of streamwise vortices extending from the recirculation region. For the laminar boundary layer case, the wake contains an additional vortex pair. We use oil-film flow visualizations over the base plate, reconstructed 3D phase-averaged velocity fields, and energy transfer between coherent and incoherent fields, to elucidate the influence of the boundary layer state.

Experimental investigation on cantilever square CFST columns under lateral continuous impact loads

Concrete-filled steel tube (CFST) columns can be used in passive flexible protective engineering to improve the bearing capacity of the overall protective system. This paper conducted the lateral continuous impact resistance of cantilever square weathering concrete-filled steel tube (WCFST) columns and compared it with that of the normal CFST. Considering the effect of steel tube wall thickness and prestress on the lateral impact resistance of such components, a total of 10 specimens were subjected to impact tests. The damage form and failure mode of each member were studied in detail, and the effects of the different impact mass and the height of the impact point were considered. The dynamic strain, displacement, and acceleration of each member under different impact loads were analyzed and compared. It was found that tested members show local damage at the impact point, bent failure through whole members, and bulged or fractured at the root. Slippage occurs between the internal concrete and the steel pipe wall of the member without prestressing, and this phenomenon always occurred at the second impact. Results show that when the height of the impact point of members is 0.30 h, the position of the peak displacement point is 0.76 h, where h stands for column height. The application of prestressing can significantly reduce the dynamic strain, displacement, and acceleration of members. Under the same circumstances, applying to the prestress of cantilever members can control the final deformation of it more than increasing the wall thickness. Moreover, the smaller the wall thickness of the component, the better the effect of applying to prestress to control the plastic displacement. The final cumulative plastic displacement of the member is positively correlated with its stiffness degradation after each impact.

Seismic Behaviors and Resilience of Concrete-encased Concrete-Filled Steel Tubular Columns with Debonded High-Strength Rebars: Experiment and Assessment

ABSTRACT A total of six cantilever square concrete-encased CFST columns were fabricated for testing under both lateral load and constant compressive load. The debonded high-strength PSB 930 steel rebars were used as the longitudinal rebar to provide resilience for specimen columns. Experimental results indicated that the specimens with debonded PSB longitudinal rebars had smaller residual deformation and smaller yield sectional stiffness compared with the specimen with normal steel rebars because the yielding progress of the longitudinal rebar was delayed. Based on the parametric analytical results, some models are proposed to assess the yield and post-yield sectional stiffness and the residual drift.

Shape Optimization of Rectangular Plates for Vibration-Based Fatigue Testing

Abstract In vibration-based high cycle fatigue testing, a base-excited plate is driven at a high frequency resonant mode until failure. In one vibration-based method involving a cantilevered square plate, a mode often referred to as the “two-stripe” mode is sometimes used because it exists at high frequencies and produces large uniaxial bending stresses along the free edge that are suitable for fatigue testing. The purpose of this work is to precisely investigate how the dimensions of a more generally rectangular plate influence performance when driven at the two-stripe mode. Included are the results of many thousands of modal analysis simulations. From these simulations, general trends with respect to resonant frequencies, frequency isolation, and stress fields in the plate are examined. Results of select geometries were then experimentally validated using a 1000 lb shaker. It is generally shown that, compared with square plates, rectangular plates with 1.37 length-to-width ratio exhibit more favorable stress distributions and frequency isolation. Recommendations are also given for how to quickly select preferable plate dimensions when planning a test based around the operating frequencies of the test setup.

Nonlinear structural performance and seismic fragility of corroded reinforced concrete structures: modelling guidelines

The current paper provides modelling guidelines for nonlinear analysis and fragility assessment of corrosion-damaged reinforced concrete (RC) structures. A systematic guideline is proposed to model the adverse impact of corrosion on mechanical properties of steel and concrete materials including the negative impact of corrosion on inelastic buckling and low-cycle fatigue (LCF) degradation of reinforcing bars. The proposed fibre-based modelling technique is capable of simulating the spatial variability of localised corrosion and the influence of corrosion on damage states (DS). Corrosion-dependent pushover and cyclic analyses, incremental dynamic analyses (IDAs) and fragility analyses are carried out on three different case studies: (i) a cantilever square RC column, (ii) a cantilever circular RC column and (iii) a RC frame. The analyses results indicate that corrosion significantly affects the DS, sequence of failure mode, flexural capacity and energy dissipation capacity of RC structures. Moreover, alongside the corrosion, the geometry of RC components also affects their failure sequence, cyclic behaviour and energy dissipation capacity. It is shown that increasing degree of corrosion penetration results in the concentration of damage mainly in confined concrete.

Control of the VIV of a cantilevered square cylinder with free-end suction

A steady slot suction near the free-end leading edge of a finite-length square cylinder was used to control its aerodynamic forces and vortex-induced vibration (VIV). The freestream oncoming flow velocity (U) was from 3.8 m/s to 12.8 m/s. The width of the tested cylinder d = 40 mm and aspect ratio H/d = 5, where H was the height of the cylinder. The corresponding Reynolds number was from 10,400 to 35,000. The tested suction ratio Q, defined as the ratio of suction velocity (Us) at the slot over the oncoming flow velocity at which the strongest VIV occurs (Uv), ranged from 0 to 3. It was found that the free-end slot suction can effectively attenuate the VIV of a cantilevered square cylinder. In the experiments, the RMS value of the VIV amplitude reduced quickly with Q increasing from 0 to 1, then kept approximately constant for Q > 1. The maximum reduction of the VIV occurs at Q = 1, with the vibration amplitude reduced by 92% , relative to the uncontrolled case. Moreover, the overall fluctuation lift of the finite-length square cylinder was also suppressed with the maximum reduction of 87%, which occurred at Q = 1. It was interesting to discover that the free-end shear flow was sensitive to the slot suction near the leading edge. The turbulent kinetic energy (TKE) of the flow over the free end was the highest at Q = 1, which may result in the strongest mixing between the high momentum free-end shear flow and the near wake.

Influence of various setting angles on vibration behavior of rotating graphene sheet: continuum modeling and molecular dynamics simulation.

The Eringen's nonlocal elasticity theory is employed to examine the free vibration of a rotating cantilever single-layer graphene sheet (SLGS) under low and high temperature conditions. The governing equations of motion and the related boundary conditions are obtained through Hamilton's principle based on the first-order shear deformation theory (FSDT) of nanoplates. The generalized differential quadrature method (GDQM) is utilized to solve the nondimensional equations of motion. The molecular dynamics (MD) simulation is conducted, and fundamental frequencies of the rotating cantilever square SLGS are computed using the fast Fourier transform (FFT). The comparison of MD and GDQM results leads to finding the appropriate value of the nonlocal parameter for the first time. As an interesting result, this value of the nonlocal parameter is independent of the angular velocity. Results indicate that increases in various parameters, such as the angular velocity, hub radius, nonlocal parameter, and temperature changes in low temperature conditions, leads the first and the second frequencies to increase. In addition, it can be seen that the influence of the hub radius or nonlocal parameters on frequencies cannot be ignored in high angular velocities. Moreover, it is not possible to neglect the angular velocity or nonlocal parameter in high hub radius. The results show that the influence of parameters such as setting angle or nonlocal parameter on the first and the second frequencies increases when some parameters increase, such as the angular velocity, hub radius or temperature change. Graphical abstract (a) A schematic of a rotating cantilever nanoplate. (b) A schematic of cantilever armchair SLGS simulated by MD.

Low-frequency dynamics in the turbulent wake of cantilevered square and circular cylinders protruding a thin laminar boundary layer

Low-frequency dynamics in the turbulent wake of cantilevered square and circular cylinders protruding a thin laminar boundary layer

Free-End Suction Control of the Aerodynamic Forces of a Cantilevered Square Cylinder

Steady slot suction is applied near the leading edge of the free end of a cantilevered square cylinder to investigate its effects on the aerodynamic forces. The slot suction significantly changes the flow separation on the free end and also the aerodynamic forces on the entire cylinder span. The best control result appears at the suction coefficient Q = 1 (Q = Us/U∞, where Us is the suction velocity at the slot, and U∞ is the oncoming flow velocity), with the fluctuation drag and lift reduced by 17.8% and 45.5%, respectively. At Q = 1, the shear flow at the leading edge is weakened and reattaches on the cylinder free end, which results in stronger momentum transport between the free-end shear flow and the wake, thus suppressing the vortex shedding and aerodynamic forces efficiently.

Effects of oncoming flow conditions on the aerodynamic forces on a cantilevered square cylinder

The aerodynamic forces on a cantilevered square cylinder with a height-to-width ratio (H/d) of 5 in a crossflow were experimentally investigated in a closed-loop low-speed wind tunnel. The freestream oncoming flow velocity (U∞) ranged from 5 to 45 m/s, corresponding to Reynolds numbers, based on U∞ and d, of 0.68 × 105 to 6.12 × 105. Two different oncoming flow conditions were tested. In case 1, the majority of the cylinder span was in the uniform flow, except the lower 1d which was immersed in a thin turbulent boundary layer; in case 2, the tested cylinder was completely immersed in a turbulent boundary layer. In both cases, the Reynolds number had a negligible effect on the aerodynamic forces of the cylinder. The predominant vortex shedding frequency was constant along the cylinder span, regardless of the thickness and nature of the boundary layer. In case 1, the lift fluctuated periodically with a large amplitude or did not exhibit obvious periodicity, which correspond to the anti-symmetric and symmetric vortex shedding modes, respectively. Proper orthogonal decomposition (POD) analysis showed that, in case 2, anti-symmetric vortex shedding tends to occur, instead of the symmetric mode, thus resulting in a larger fluctuating lift than that observed case 1.

Experiments on vibration suppression for a piezoelectric flexible cantilever plate using nonlinear controllers

This paper reports an investigation of the active vibration control of a piezoelectric flexible cantilever plate. The bending and torsional vibration of the flexible plate can be measured and actuated by distributed bonded piezoelectric sensors and actuators, after conducting optimal placement. To suppress the vibration, a kind of composite nonlinear controller is proposed and implemented. The control gain of the developed nonlinear control algorithm can be adjusted according to the measured vibration amplitude and the corresponding parameters. The advantage of the nonlinear controller is the ability to regulate the control value online to suppress both the larger and the smaller amplitude vibrations effectively, without allowing excessive saturation or insufficient phenomenon of the control effect. An experimental setup characterizing a thin, cantilever square plate bonded with piezoelectric patches was developed to verify the proposed controller. Experimental comparison studies were carried out for suppressing both the bending and torsional vibrations, and the control performance of the nonlinear controller is analyzed and discussed. The experimental results demonstrate that significant vibration suppression can be achieved by using the presented control schemes.

황동 개재물이 있는 Al 외팔형 정사각판의 자유진동해석

The free vibration characteristics of Al cantilever square plates with a brass inclusion were analyzed experimentally and numerically The experimentally obtained natural frequencies and mode shapes were compared with the FEM analysis results. The impulse exciting method was used for experiment and ANSYS software package was used for FEM analysis. The natural frequencies obtained iron experiment and numerical analysis matched within . It was found that the natural frequencies of the Al cantilever square plates with a brass inclusion decrease as the size of inclusion increases. For the third mode shape, comparing the nodal line of the Al plate and the Al plate with a inclusion, the mode shape showed the reversed quadratic curve. The natural frequencies of inclusion plate were decreased as the location of inclusion moves from the clamped edge to the tree edge.

Finite Element Modeling of MFC/AFC Actuators and Performance of MFC

The anisoparametric three-node MIN6 shallow shell element is extended for modeling Macro-Fiber Composite/Active Fiber Composites (MFCTM/AFC) actuators for active vibration and acoustic control of curved and flat panels. The recently developed MFCTM/AFC actuators exhibit enhanced performance, they are anisotropic and highly conformable as compared to the traditional monolithic isotropic piezoceramic actuators. The extended MIN6 shell element includes embedded or surface bonded MFCTM/AFC laminae. The fully coupled electrical-structural formulation is general and it is able to handle arbitrary doubly curved laminated composite and isotropic shell structures. A square and a triangular cantilever isotropic plates are modeled using the MIN6 elements to demonstrate the anisotropic actuation of a surface bonded MFCTM actuator for coupled bending and twisting plate motions. Steady state modal bending and twisting amplitudes of the cantilever square and triangular plates with MFCTM actuator are compared with the plate’s steady state modal amplitudes with traditional PZT 5A actuator for different angle orientations. Frequency Response Functions (FRF) for the square plate with MFCTM and PZT 5A actuators are also obtained and their actuation performance is compared. The actuation performance of the MFCTM at different locations is also investigated.

Experimental and numerical analysis of vibrating cracked plates at resonant frequencies

Owing to the advantages of noncontact and fullfield measurement, an optical system called the amplitude fluctuation electronic speckle pattern interferometry (AFESPI) method with an out-of-plane setup is employed to investigate the vibration of a cantilever square plate with a crack emanating from one edge. Based on the fact that clear fringe patterns will be shown by the AFESPI method only at resonant frequencies, both the resonant frequencies and the vibration mode shapes can be obtained experimentally at the same time. Three different crack locations will be discussed in detail in this study. One is parallel to the clamped edge, and the other two are perpendicular to the clamped edge. The numerical finite element calculations are compared with the experimental results, and good agreement is obtained for resonant frequencies and mode shapes. The influences of crack locations and lengths on the vibration behavior of the clamped cantilever plate are studied in terms of the dimensionless frequency parameter (λ 2) versus crack length ratio (a/L). The authors find that if the crack face displacements are out of phase, a large value of stress intensity factor may be induced, and the cracked plate will be dangerous from the fracture mechanics point of view. However, there are some resonant frequencies for which the crack face displacements are completely in phase, causing a zero stress intensity factor, and the cracked plate will be safe.

Dynamic stress analysis of a tapered cantilever square plate under impact load

In this paper the effects of different types of variations in profile and thickness on the amplitude of vibration and the dynamic bending stresses of a square cantilever plate subjected to a point impact load have been investigated. A four-noded plate bending element was used for the analysis. In each case the results obtained for different thickness variations are compared with those obtained for the uniform thickness plate. It is observed that considerable reductions in amplitude and/or bending stresses can be achieved by proper selection of thickness variation.

Studies on dynamic behaviour of a cantilever square plate with varying thickness

The effects of different types of variations in profile and thickness on the amplitude and the dynamic bending stresses of a square cantilever plate excited by a point harmonic load resonance has been investigated. A four-noded plate bending element has been used for the analysis. The response has been determined for the first three modes of vibration. In each case the results obtained for different thickness variations are compared with those of the uniform thickness plate. It is observed that considerable reductions in amplitude and/or bending stresses can be achieved by the proper selection of thickness variation.

Optimal vibration support of continuous systems. (3rd Report, Maximization of difference between adjacent frequencies).

Using the support position as the design variable, the optimal designs of vibtrating beams and plates are determined to maximize the defference between two adjacent natural frequencies. A previously developed gradient technique is used for optimization. Numerical examples include continuous nouniform veams and cantilever square plates. The transfer matrix and Ritz-Langrange multiplier methods are used to yield freqency equations. The iterative solution process for the optimal support is illustrated on frequency maps.

Interactions between a partially or totally immersed vibrating cantilever plate and the surrounding fluid

The dry and wet dynamic characteristics of a vertical and a horizontal cantilever square plate [1] immersed in fluid are discussed from the viewpoint of a linear hydroelasticity theory [2–5]. The surface piercing vertical plate is partially immersed in the fluid and the influence of submerged plate length on the resonance frequencies investigated. For the horizontal plate the influence of submerged depth below the free surface on the resonance frequencies is examined. Incorporated into the theoretical model is a free surface boundary condition allowing wave disturbances to be present. The interaction existing between the vibrating cantilever plate and the free surface is clearly exhibited in the calculated curves describing the generalized hydrodynamic coefficients. A limited comparison between predictions and experimental data [1] is also included.