Static Deflection Research Articles

Experimental Study and Numerical Simulation Analysis on Vertical Vibration Performances of 12 m Span Wood Truss Joist Floors

Walking-induced vibration control in wood floors is a critical issue attracting the attention of many researchers and engineers. This paper presents an experimental study applying static deflection tests, modal tests, and pedestrian load tests to a series of full-scale 12 m span tooth plates connected to wood truss joist floors with strongbacks and partition walls. A comparison of the calculation error of vibration parameters between the theoretical formula and a numerical model was also conducted. The results show that strongbacks and partition walls effectively reduce both the vertical displacement and the root means acceleration at the center of the floor under pedestrian load but increases the natural frequency. The partition wall can achieve a better vibration-reduction effect than strongbacks. The error of the finite element model is higher than that of the theoretical formula. Using the theoretical formula in engineering wood floor design is recommended.

Sliding-boundary-constrained cantilever structure for vibration isolation via nonlinear stiffness modulation

In this paper, a novel sliding-boundary-constrained cantilever structure with nonlinear stiffness modulation (SCS-NSM) is proposed and systematically investigated for vibration isolation. The SCS-NSM is composed of a hemisphere-constrained cantilever structure (HCCS) and a pair of repulsive magnets. The nonlinear stiffness modulation mechanism for achieving quasi-zero stiffness (QZS), that is, using the hardening stiffness of the magnets to modulate the negative stiffness of HCCS, is fully revealed by static analysis. Furthermore, the QZS is adjustable to respond to different loads, and the modulation principle is clarified. Compared with conventional QZS isolators (paralleling negative and linear stiffness), the proposed SCS-NSM shows the advantages of wide load range and small static deflection. Static tests are performed to verify the effectiveness of the nonlinear stiffness modulation mechanism. Dynamic analysis shows that the SCS-NSM has a low resonant frequency and a wide vibration isolation frequency band due to its low stiffness. Periodic, sweep and random excitation tests are implemented to evaluate the vibration isolation performance of SCS-NSM. Experimental results validate the dynamic model and demonstrate that the vibration with a frequency higher than 4.6 Hz can be effectively attenuated. The proposed SCS-NSM provides a new perspective on low-frequency vibration isolation, and the nonlinear stiffness modulation mechanism has reference significance for designing QZS isolators with wide-bearing capacity and high compactness.

Non-linear Isolator for Vibration and Force Transmission Control of Unbalanced Rotating Machines

PurposeThe objective of this paper is to investigate with simulations how non-linear spring and non-linear damper components of isolators can be employed to effectively reduce both the oscillations and the force transmitted to ground in the whole spinning range of unbalanced rotating machines.MethodsThe principal goal of this paper is twofold. First, to present a concise and consistent formulation based on the harmonic balance approach for the vibration response of spinning machines mounted on linear/non-linear, softening/hardening, un-tensioned/pre-tensioned springs and linear/non-linear dampers. Second, to provide a comprehensive overview of the vibration and force transmission control with non-linear isolators specifically tailored to unbalanced machines.ResultsThe study has shown that, the best vibration isolation is provided by a pre-tensioned linear and cubic softening spring combined with a linear and negative quadratic damper. The pre-tensioned spring should be designed in such a way as it holds the weight of the machine and thus produces on the vibrating machine a symmetric elastic restoring force proportional to the linear and cubic powers of the displacement. The cubic softening stiffness should then be tuned to minimise the frequency, and thus the amplitude, of the resonant response of the fundamental mode of the machine and elastic suspension system, while preserving stability and a desired static deflection. In parallel, to reduce the force transmission to ground above the fundamental resonance frequency, the negative quadratic damping effect should be tailored to maximize the energy absorption at higher frequencies.ConclusionThe study has shown that non-linear spring and non-linear damper components can be effectively employed to control the vibration and force transmission in the whole spinning range of the machine. In particular, a pre-tensioned softening cubic non-linear spring can be used to mitigate the vibration and force transmission at low frequencies, close to the fundamental natural frequencies of the elastically suspended machine. Also, a negative quadratic non-linear damper can be used to tailor the energy dissipation of the isolator in such a way as to have high damping at low frequencies and low damping at higher frequencies, which enhances the vibration and force transmission control at low frequencies and, rather importantly, mitigates the force transmission at higher frequencies.

Effect of Carbon Nanotubes Volume Fraction on the Deflections and Stresses of Laminated Hybrid Composite Plates using First-Order Shear Deformation Theory

Carbon Nanotubes reinforced composite materials are widely used in aerospace engineering due to high strength-to-weight ratios, which can be tailored per requirements. The behaviour of the composite structures depends on various factors like, Lamination scheme, Ply orientation and loading conditions. In the present work, Static deflection and stresses analysis of a Carbon Nano Tube reinforced laminated hybrid composite plate extends the First Order Shear Deformation Theory with variable ply angles and volume fractions of CNT. A micromechanics model based on the Mori-Tanaka method is used to calculate the properties of CNT reinforced laminate. In this analysis, hybrid composite plates mainly consist of Graphite/epoxy, Kevlar/epoxy and CNT/ polystyrene sub-laminates. The lamination scheme and CNT volume fraction play a vital role in the non-dimensional deflections and stresses. The main intention of this work is to enhance the suitability of CNT reinforced Hybrid composite plates under static loading for structural applications.

Static and Dynamic Deflection Characteristics of Cracked Porous FG Panels

The deflection responses of the cracked porous graded structure under the variable loading conditions (static and dynamic) are investigated numerically with the help of a commercial tool (ABAQUS). The model includes the grading in two different directions (along the thickness and length by setting the relevant volume fraction exponents [Formula: see text] and [Formula: see text], i.e., of the functionally graded material (FGM) for the analysis purpose. Additionally, different material gradings, i.e., power-law (P-FGM), sigmoid (S-FGM), and exponential (E-FGM), are adopted to achieve the distribution patterns within the FG panel. Further, the porosity and the damage (crack) have been introduced in the graded structural panel. The python scripting language is used to model the FGM plate via the batch input technique, i.e., ABAQUS kernel, instead of the standard GUI interface. The accuracy has been confirmed by validating the results with the published available results, and the applicability is stated through a series of numerical examples by changing input parameters.

Investigating Static Deflection of Non-Prismatic Axially Functionally Graded Beam

In this study, the static deflection of non-prismatic axial function graded tapered beam (A-FGB) under distribution load has been analyzed using ANSYS workbench (17.2). According to a power-law model, the elastic modulus of the beam varies continuously in the axial direction of the beam. Also, the beam’s geometry, i.e., width, thickness, or both width and thickness of the beam, varies linearly in the axial direction with different values of non-uniformity parameter (1, 0.5,0, −0.5, and −0.75). The effects of martial distribution, i.e., power-law index, and non-uniformity parameter on the static deflection for A-FGB with different boundary conditions, in such free-clamped, clamped-free, and simply-supported, are studied. This research deals with functionally graded materials FGMs in more than one aspect in terms of using different boundary conditions; in addition, it studies the response of the non-prismatic beam non-uniformity parameter (α); therefore, this research studies comprehensively the deflection of the beam. The results show that the increase in power-law index causes decreasing in dimensionless deflection and its rate of change depends on the supporting types of the beam and non-uniformity parameters. The variation in both width and thickness for a free-clamped axial function–graded beam gives a significant decrease in dimensionless deflection at decreasing in non-uniformity parameter, whereas the variation in thickness for clamped-free axial function graded beam gives a significant decrease in dimensionless deflection at decreasing of non-uniformity parameter.

A study on porous nanocomposite graded plates using equivalent single layer and layerwise models

The static deflection of plates made from functionally graded materials integrating nanoparticles and porosities is analyzed. The models developed, consider equivalent single layer and layerwise approaches jointly with different shear deformation theories, and were implemented via finite element method. For the first-order shear deformation models, the shear correction factor is determined for each case. The models’ performances were verified and several case studies were considered to analyze the influence of parameters such as material properties, nanoparticles presence, and layers’ porosities distributions in the plates’ deflection. The results enable understanding the influence of design parameters as the models’ prediction trends.

Static analysis of porous core functionally graded piezoelectric (PCFGP) sandwich plate resting on the Winkler/Pasternak/Kerr foundation under thermo-electric effect

This paper analyzed static bending and deflection of the porous core functionally graded piezoelectric (PCFGP) sandwich plate resting on the Winkler/Pasternak/ Kerr foundations under thermomechanical and electromechanical loading with different conventional and unconventional boundary conditions. First-order shear deformation theory (FSDT) based displacement field and von Karman geometric nonlinear strain are used for problem formulation. The governing equations of the PCFGP sandwich plate are obtained using Hamilton’s principle. A higher-order finite element method has been employed with a modified iterative Newton-Raphson scheme for solving the governing equations. Convergence and comparison studies demonstrate that the validation of the current model has suitably correct. It has been observed that an increase in the porous exponent in the core part of the sandwich plate reduces the stiffness of the plate with an increase in stress, deflection, and electric potential. The maximum stress, deflection, and electric potential are obtained for porosity dispersion in the Uniform pore distribution (UD) type, while minimum in Un-symmetric pore distribution (USD) type dispersions. Hence, the different embedding porosity in the core part of the sandwich plate plays a significant role in reducing plate structural weight and offering good stability in plate structural bending stiffness.

A Novel Experimental Static Deflection Equation for Specific Cantilever beam Made of Ionic Polymer–Metal Composite

Background: Nowadays, ionic polymer–metal composites are widely used in various industries. They are in the group of electroactive polymers and smart materials with electromechanical properties. By applying a small amount of voltage, the nonlinear stress inside them will happen and their deformation can be seen. The energy transformation from electrical to mechanical is observable during the process of giving voltage to a specimen. The aim of this study is to investigate a novel experimental static deflection equation for specific cantilever beam made of ionic polymer–metal composite. Methods: In this paper, an ionic-polymer-metal composite is provided; the main core is based on an electroactive Fluoropolymer named Nafion, and the coated electrodes are made of Platinum. The length of the specimen is 27.131 mm and its width is 5.728mm. Voltage from 1.5 to 4.3V was applied to the specimen used in this study; the y-directional displacement of the IPMC at each step is measured and recorded; then, a finite element analysis was performed. Curve fitting of the data for the experimental analysis was also done. Moreover, the governing relations of IPMC according to the Nernst–Planck equation were investigated in this study. Results: The results have been validated in two forms of finite element method and experimental analysis. The results of finite element analysis showed that the ion flux in the polymer is calculated by the equation: [INSIDE:1]. In other words, this equation, which is called Nernst–Planck, is the basic equation of this type of material. This equation is the main governing equation to describe the transfer phenomena of IPMC materials. Furthermore, in order to calculate the deflection of IPMC membrane, 19 equations designed in this study were used. In the next step, the results of the experimental analysis showed that, based on the field emission scanning electron microscope images, the Nafion surface is completely sandblasted and its area is completely uniform. The right image taken by Dino-Lite shows the thesis effect on the electrode. Furthermore, the results showed that IPMC has high-quality coated electrodes. Conclusions: It is shown that a nonlinear equation governs the behavior of IPMCs' deflection versus voltage.

Analytical Determination of Static Deflection Shape of an Asymmetric Extradosed Cable-Stayed Bridge Using Ritz Method.

A practical method to analyze the mechanical behavior of the asymmetric extradosed cable-stayed (AECS) bridge is provided in this paper. The work includes the analysis of the equivalent membrane tension of the cables, the ratio of side-span cable force to middle-span cable force, and the deflection of the main girder subject to uniformly distributed load. The Ritz method is a simple and efficient way to solve composite structures, such as the AECS bridge, compared with the traditional force method, displacement method, or finite element method. The theoretical results obtained from the Ritz method are in good agreement with that from the finite element analysis, which shows the accuracy of this approach. Then, a parametric study of AECS bridges is carried out by using the proposed equations directly, instead of using the traditional finite element modeling process, which requires a lot of modeling work. As a result, reasonable values of very important parameters are suggested, which helps the readers reach a better understanding of the mechanical behavior of AECS bridges. More importantly, it helps the designers to enhance the efficiency in the stage of conceptual design.

Highly Linear and Wide Non-Resonant Two-Degree-of-Freedom Piezoelectric Laser Scanner.

Laser scanners with mechanically driven mirrors have exhibited increasing potential for various applications, such as displays and laser radar. Resonant scanners are the predominantly used scanners; however, non-resonant scanners are required for applications where point-to-point driving is desirable. Because a non-resonant drive cannot amplify the drive angle owing to the resonance phenomenon, high values are difficult to achieve for the main performance metrics of the scanners: mirror area, drive angle, and operating frequency. In this paper, we present a two-axis scanner with a piezoelectric actuator made of a piezoelectric single-crystal Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 as the actuation force source. The scanner contains a circular mirror with a diameter of 7 mm and achieves an average static mechanical deflection angle amplitude of 20.8° in two axes with a resonant frequency of 559 Hz. It is equipped with a transmission mechanism that can decouple each axis to achieve high linearity; in our study, the nonlinearity error was less than 1°.

Synergy in Flexure of High-Performance Fiber-Reinforced Concrete with Hybrid Steel Fibers

In this paper, the synergistic flexural behaviors of high-performance fiber-reinforced concrete (HPFRC) under static and cyclic loading were experimentally investigated. The HPFRCs were composed of an identical mortar matrix but different embedded fiber types and contents as follows: HPFRC0 (no fiber, 0.0% by volume), HPFRC1 (macro steel fiber, 1.5% by volume), HPFRC2 (micro steel fiber, 1.5% by volume), and HPFRC3 (hybrid fiber, 1.0% by volume macro steel fiber blended with 0.5% by volume micro steel fiber). All flexural specimens with the dimensions of 40×40×160 mm were tested under static and cyclic loading using a three-point bending fixture. The HPFRCs with embedded fibers demonstrated the clear enhancements in static flexural resistances of up to 3.54 times higher in flexural strength and 2.16 times higher in deflection capacity in comparison with the plain HPFRC. Under cyclic loading, the fatigue stress ratio, defined as the ratio of the fatigue stress amplitude to the static flexural strength, was changed to perform the fatigue behaviors of the HPFRCs. The endurance limits of the HPFRCs were observed more than 10,000 cycles at the fatigue stress ratio of 0.15, and exceeded 1,000 cycles at the fatigue stress ratio of 0.5. The order of the HPFRC series in terms of static flexural strength, static deflection capacity and fatigue life at the stress amplitudes more than 5 MPa were as follows: HPFRC3 > HPFRC2 > HPFRC1 > HPFRC0. A synergy behavior of the HPFRCs was observed for static flexural strength, static deflection capacity, and fatigue life with the stress amplitude more than 5 MPa. In addition, two models of the fatigue responses of the HPFRCs were built to predict the fatigue life of the HPFRCs according to applied cyclic load.

A Comprehensive Study of Bending and Stability Responses of 2D-FG Nanobeams Using a Microstructure-Surface Energy-Based Model under Various Boundary Conditions

The size-dependent bending and static stability characteristics of nanobeams made of bi-directional functionally graded materials (2D-FGMs) under different boundary conditions are comprehensively investigated. Based on the modified couple stress theory and surface elasticity theory, the size-dependent model is formulated for 2D-FG Euler-Bernoulli beam. The material properties of the beam smoothly change along both the axial and thickness directions according to power-law distribution. The continuous spatial variations of the single material length scale parameter and the three surface constants are incorporated to describe the effects of microstructure and surface energy, respectively. This model accounts for the axial and transverse displacements, the exact position of the physical neutral plane, and Poisson’s effect. To obtain the static response of the present model, Ritz method is employed by approximating the axial and transverse displacements in terms of polynomial forms. Different boundary conditions, i.e., Simply-simply (S-S), Clamped-clamped (C-C), Clamped-simply (C-S), and Clamped-free (C-F), are considered and satisfied by adding auxiliary functions to the displacement functions. Numerical results with various cases of boundary conditions are performed with an insight to explore the effects of gradient indices in thickness and length directions, surface energy, material length scale parameter, slenderness ratio, and thickness on the static deflection and buckling responses of 2D-FG nanobeams. Results disclose that, the material properties, the surface energy, and microstructure effects have a significant effect on the bending, and buckling responses of 2D-FG nanobeams. Hence, this study can be helpful in the design and optimization of 2D-FG nanobeams in bending and buckling responses.

Compound influence of surface and flexoelectric effects on static bending response of hybrid composite nanorod

Nanoscale beams and rods are extensively used in several nano-electro-mechanical systems (NEMS) and their applications such as sensors and actuators. The surface and flexoelectricity phenomena have an extensive effect on nanosized structures and are related to their scale-dependent characteristics. This article presents the effect of different surface parameters and flexoelectricity on the electrostatic response of graphene-reinforced hybrid composite (GRHC) nanorods (NRs) using the theory of linear piezoelectricity, Euler-Bernoulli (EB), and Galerkin residual method. Based on these theories, the theoretical and finite element (FE) model is produced to investigate the static bending deflection of GRHC NRs when subjected to point and uniformly distributed load (UDL) considering different boundary conditions: cantilever (FC), fixed-fixed (FF), and simply supported (SS). This proposed FE model provides a useful tool for analyzing and investigating the outcomes of analytical models, which are found to be in good agreement. Our results presented in this article reveal that the effect of surface and flexoelectricity on the static bending response of GRHC NRs is noteworthy. These effects diminish with increased thickness/diameter of NR, and hence, these effects can be neglected for large-sized structures. The results presented here would help to identify the desired electrostatic response of GRHC NRs in terms of static bending response for a range of NEMS using different loading and boundary conditions as well as graphene volume fraction. This current study offers pathways for developing new proficient novel GRHC materials with enhanced control authority and present models can be exploited for numerous other materials as well as line-type structural systems such as beams, wires, rods, column/piers, and piles to study their global response.

Thermomechanical loading and cut-out effect on static and dynamic responses of multilayered structure with TD properties

The influences of cut-out on the static and dynamic deflection of the multilayered composites under thermomechanical are predicted numerically. In this regard, a mathematical model is prepared using the third-order kinematics associated with the isoparametric finite element steps. Moreover, the solution accuracy of the derived model has been tested frequently by solving a series of examples (obtained from MATLAB code) similar to the published one. In addition, the model verification is extended further by comparing the numerical results with the in-house experimental data recorded under the static and dynamic loading conditions. The equivalent single-layer theoretical model (prepared for the cut-out abided laminated structure) exactness is maintained by considering the variation of in-plane displacement as cubic. In contrast, the state space variable along with the thickness is constant. Additionally, the experimental comparisons are made considering the influences of different cut-out geometry, temperature increment, and loading intensities. The effects of cut-out and the laminated structural geometrical parameters that affect the final design consideration due to the thermomechanical loading as well as the temperature-dependent properties are computed using the derived model, and the outcomes are discussed in detail.

Static High Voltage Actuation of Piezoelectric AlN and AlScN Based Scanning Micromirrors

Piezoelectric micromirrors with aluminum nitride (AlN) and aluminum scandium nitride (Al0.68Sc0.32N) are presented and compared regarding their static deflection. Two chip designs with 2 × 3 mm2 (Design 1) and 4 × 6 mm2 (Design 2) footprint with 600 nm AlN or 2000 nm Al0.68Sc0.32N as piezoelectric transducer material are investigated. The chip with Design 1 and Al0.68Sc0.32N has a resonance frequency of 1.8 kHz and a static scan angle of 38.4° at 400 V DC was measured. Design 2 has its resonance at 2.1 kHz. The maximum static scan angle is 55.6° at 220 V DC, which is the maximum deflection measurable with the experimental setup. The static deflection per electric field is increased by a factor of 10, due to the optimization of the design and the research and development of high-performance piezoelectric transducer materials with large piezoelectric coefficient and high electrical breakthrough voltage.

Optimization of a Radial Point Interpolation Meshless strategy for strain gradient nanoplates

A parameter optimization of the Radial Point Interpolation Meshless Method (RPIM) is presented in this work for solving the static bending analysis of Kirchhoff nanoplates which include the first order strain gradient theory. Optimization in meshless strategies is often required since shape parameters, of the Radial Basis Functions (RBFs) used, strongly influence the numerical results when different geometries, boundary conditions or various mechanical aspects are considered. Due to the introduction of a first order strain gradient theory within Kirchhoff plate framework, to approximate the bending degrees of freedom, a Hermite RPIM is used. The static deflection of thin plates with different aspect ratios and boundary conditions is analysed. The results of the static analysis are compared with the solutions available in the literature and good agreement among all presented results as well as convergence behaviour is shown.

Determination of the Fundamental Lateral Bending Mode Frequency of a Spacecraft from its Static Deflection

The primary structure of a spacecraft that involves the central cylinder is designed to meet a specific value of fundamental lateral mode frequency. Though this frequency can be theoretically estimated by using a finite element model, its experimental verification is only possible when the entire spacecraft is made ready. However, static load tests are done on the primary structure of the spacecraft as soon as the structure is realized. In this work, a methodology to determine the fundamental bending mode frequency of a spacecraft from the deflections measured when the structure alone is subjected to static load tests is developed. An expression relating the fundamental lateral bending mode frequency of a spacecraft, having several masses attached at different locations, and the deflection at its tip is derived. Two spacecraft, one of 3000kg class and the other of 6000kg class are taken as examples. The fundamental lateral frequencies are determined using this methodology. These frequencies are also obtained through resonance search tests. It is shown that the derived expression will be very useful in estimating the fundamental lateral mode frequency of a spacecraft with the help of the measured deflection.

Static deflection calculation for axially FG cantilever beam under uniformly distributed and transverse tip loads

The axially FG materials were used extensively in aerospace, automotive and defense industries because of the ability of design its properties. In this work, the static deflection of axially FG cantilever beam was computed using Rayleigh and Finite Element methods considering Beam Theory of Euler-Bernoulli. The material properties along the axial direction of axially FG beam were simulated using Power-Law Model. In Rayleigh method, the equivalent stiffness of two kinds of cantilever FG beams (Clamped – Free and Free –Clamped) were calculated for different power law index and then used to calculate the static deflection. The Finite Element model was built by ANSYS APDL version 17.2 using BEAM189 element. The effects of number of segment, power law index and type of applied load on the dimensionless deflection were studied. A very good accord between Rayleigh and ANSYS results was obtained for different load types, supporting types and power law index.

Online Deflection Compensation of a Flexible Hydraulic Loader Crane Using Neural Networks and Pressure Feedback

The deflection compensation of a hydraulically actuated loader crane is presented. Measurement data from the laboratory are used to design a neural network deflection estimator. Kinematic expressions are derived and used with the deflection estimator in a feedforward topology to compensate for the static deflection. A dynamic deflection compensator is implemented, using pressure feedback and an adaptive bandpass filter. Simulations are conducted to verify the performance of the control system. Experimental results showcase the effectiveness of both the static and dynamic deflection compensator while running closed-loop motion control, with a 90% decrease in static deflection.