Free-free Boundary Conditions Research Articles

Stress analysis of rotating functionally graded polar orthotropic disk under thermomechanical loading

In this paper, thermo-elastic stress analysis of rotating variable thickness annular disk made of polar orthotropic functionally graded material (FGM) is presented. Elasticity modulus, density and thick-ness of the disk are assumed to vary radially according to a power law function. The material of the disk is assumed to be temperature dependent and different temperature distributions are assumed for variation of the temperature in radial direction. Radial stress and radial deformation of the disk with Clamped- Free (C-F) and Free-Free (F-F) boundary conditions are obtained using the numerical finite difference (FD) method. It is concluded that, by increasing the temperature variation, the radial stress and displacement increase. It is also observed that the radial stress in the rotating FG disk is more than the radial stress in rotating homogeneous disk and by increasing the FG index, the location of maximum stress in the disk shifts toward the outer surface. Also, the effects of temperature variation along the radius and orthotropy of the material on the radial stress and deformation are evaluated and concluded that their effect are significant. The results are compared with the available results in the literature and the good agreement between the present results and results in the literature shows the accuracy of FD method in thermo-elastic analysis of rotating FG orthotropic disk of variable thickness.

Study of Vibration Behaviour of Stiffened Polymer Composite Shells for Underwater Structural Applications

This paper presents vibration behavior of ring stiffened polymer composite thick shells used for underwater structures. Filament wound shells stiffened with internal and external rings and with hemispherical ends were tested for vibration in air and water in free-free boundary condition using roving hammer and fixed response method. Modal testing of the shells was performed under hydrostatic loading in a custom designed buckling tester for determining natural frequency at higher sea depths. Accelerometer was mounted on the inner surface of the shell. It was excited using a plumbob, rope and pulley arrangement. Experimental results were validated by modal analysis using Hyperworks and ANSYS. Vibration behavior in water was simulated by Fluid structure interaction approach. Experimental first natural frequency in water was lesser than that in air. With increase in hydrostatic pressure, the shell showed moderate variation in natural frequency. The experimental and numerical results of natural frequency and mode shapes were in good agreement with each other. Natural frequencies were lower in long and thick shells.

Study on static and dynamic behavior of jute/sisal fiber reinforced epoxy composites

In this work, the mechanical characteristics and free vibration behavior of Jute, Sisal and hybrid Sisal/Jute epoxy composites were investigated. A free Vibration test was conducted using the Impulse Frequency response test under a free-free boundary condition. Plain weave Jute and Sisal fabric were used in the ratio of 60:40. The hand fabrication method was used for fabrication, followed up with compression under the compression molding method. Alkaline treatment was carried out before fabrication to improve the interfacial strength between the matrix and fiber. Mechanical properties like Tensile strength and flexural strength are found to be higher for Hybrid Sisal/Jute than the Jute and Sisal polymer composites. Reduced resonant amplitude in the FRF shows Hybrid laminate has a good damping tendency than other considered composites.

The Application of Non-deterministic Model Updating method of a Complex Jointed Structure using Central Composite Design based meta-model

Finite element (FE) model of a structure is highly depended on idealising and simplification of model, however, the model may not truly represent the physical structure. The application of FE model updating is advocated to modify FE model of structure in order to acquired better correlation between the predicted and measured structure response. Nevertheless, for complex jointed structure, a FE model is containing a very large degree of freedoms that may contribute to high computational time. Therefore, this paper presents the application of response surface method in non-deterministic model updating using central composite design (CCD) sampling for improving the efficiency of a finite element model of a laser stitch welded structure. In this study, FE model of the structure is developed using CQUAD4 shell elements and ACM2 element connectors been used to representing the laser stitch weld joints. For the measured data, experimental modal analysis was performed using LMS SCADAS and conducted under free-free boundary conditions. In the model updating, the minimisation of uncertainties parameters in the FE model is based on the objective function that is formed from the residuals between the FE and experimental natural frequencies. The results show that the response surface method using CCD sampling is efficient to be used in FE model updating because it is capable of improving the accuracy of the initial FE model.

On a method for finding position and orientation of accelerometers from their signals

In many experimental structural dynamics applications where accelerometers are used, it is important to know their position and orientation. The typical approaches to determine this are time-consuming and can require additional costly equipment. The study presents a method that can retrieve this information directly from the accelerometers’ readings, under the assumption that the object under test can move as a rigid body. To some degree, this assumption is satisfied in some practical applications, such as experimental modal analysis, where free-free boundary conditions are often assumed, and the test object can move as a rigid body within a constrained range. However, the presented method is not applicable for test objects with fixed supports, and cannot be used in, for example, many civil engineering applications.The paper introduces the method, discusses its applicability and constraints, demonstrates the method on a case study and provides the estimations of the method’s precision. The study also compares the method with the analogous accelerometer arrays self-calibration method, which was developed for different application areas.

Modeling and design of a class of hybrid bistable symmetric laminates with cantilever boundary configuration

Multistable laminates have been widely analyzed in the recent past for their potential in morphing applications. However, all the analytical models developed up until now have taken into account only the free-free boundary condition. In this work two objectives are met: (a) an analytical model is developed, which extends the previously available models in literature to account for the cantilever boundary condition for a special class of hybrid bistable symmetric laminates (HBSL); (b) the previously proposed HBSL is modified by replacing the aluminum layers with bi-direction glass-epoxy prepregs in the layup. It is observed that the modified layup has a curvature similar to the previously proposed HBSL while maintaining bistability. The analytical model developed here successfully captures the equilibrium shapes and the snap-through behavior for this special class of laminates which is validated against the results obtained using ABAQUS® and experiments. The developed model is then subsequently used to study the design space and bistability characteristics of the HBSL and the proposed modified layup (m-HBSL) in the cantilever boundary condition.

Theoretical and experimental modal analysis of circular cross-section shaft

Experimental Modal Analysis (EMA) is very helpful in engineering design and manufacturing of machine components. In this paper, modal parameters which are natural frequencies, mode shapes and damping ratios are extracted for free-free boundary conditions circular shaft, using EMA, then two disks are added to this shaft as second case study. EMA has been verified as effective and accurate tool, despite of increasing geometrical complexity and nonlinear behaviour of the structure. The two well-known excitation techniques (i.e. impact hammer and shaker) are used for this purpose. For validation, natural frequencies and mode shapes are determined analytically and numerically by Finite Element Modelling (FEM) ANSYS 15 workbench software, and then compared with results obtained experimentally. Noticeable remarks about these approaches are listed. Coherence plots are compared between impact and shaker tests. Digital Signal Processing (DSP) settings like windows type and sample (record) time are compared. The recommended DSP settings mentioned in this work can be used as a general guidance for researchers and people who are working in modal analysis.

Operational Modal Analysis of Damage Gear

As natural frequencies and mode shapes are often a key to understanding dynamic characteristics of structural elements, modal analysis provides a viable means to determine these properties. This paper investigates the dynamic characteristics of a healthy and unhealthy condition of a commercially used helical gear using the Frequency Domain Decomposition (FDD) identification algorithm in Operational Modal Analysis (OMA). For the unhealthy condition, a refined range of percentage of defects are introduced to the helical gear starting from one (1) tooth being defected (1/60 teeth) to six (6) teeth being defected (6/60 teeth). The specimen is tested under a free-free boundary condition for its simplicity and direct investigation purpose. Comparison of the results of these varying conditions of the structure will be shown to justify the validity of the method used. Acceptable modal data are obtained by considering and accentuating on the technical aspects in processing the experimental data which are critical aspects to be addressed. The natural frequencies and mode shapes are obtained through automatic and manual peak-picking process from Singular Value Decomposition (SVD) plot using Frequency Domain Decomposition (FDD) technique and the results are validated using the established Modal Assurance Criterion (MAC) indicator. The results indicate that OMA using FDD algorithm is a good method in identifying the dynamic characteristics and hence, is effective in detection of defects in this rotating element.

An Integrated Approach for Instability Analysis of Lattice Brake System Using Contact Pressure Sensitivity

This paper presents an attempt to evaluate the sensitivity of lattice parameters on the contact pressure instability of newly lattice brake disc. The instability characteristics are investigated through theoretical representation, modal analysis experiments, and nonlinear finite element thermo-mechanical analysis. Lattice properties are defined concerning the lattice truss angle geometry in the unit cell and periodicity of the lattice cell on the lattice plate. Motion dynamics of lattice plate concern the principal coordinates on the rotating disc are presented to use in the braking system. The modal behaviour of vanned and lattice brake disc/pad systems are defined through experimental modal analysis at free-free boundary conditions, and results are used as inputs of nonlinear finite element models as it goes through a partial simulation of the SAE J2521 drag braking noise test. Subsequently, the dynamic instability analysis of the brake disc is detailed by using the complex eigenvalue extraction technique concerning the contact pressure and lattice parameters effect. The sensitivity analysis of the brake instability respected to the mass fraction factor and relative density of the lattice structure is presented by using the average standard deviations of the contact pressure force. The likelihood of instability occurrence is quantified by definition of a single indicator derived from the system eigenvalues. The analysis indicates that the higher relative density with lower mass fraction factor of lattice structure is led to a higher temperature at the disc and pad surface. Mutually, the higher mass fraction factor with lower relative density is led to the lower temperature. The maximum contact pressure is observed in the model with less mass fraction factor and more uniform pressure distributions are observed at higher values of the mass fraction factor. The instability analysis points out that high instability frequencies are predicted at lower mass fraction factor and higher relative density.

Transfer matrix formulations and single variable shear deformation theory for crack detection in beam-like structures

This study aims to estimate crack location and crack length in damaged beam structures using transfer matrix formulations, which are based on analytical solutions of governing equations of motion. A single variable shear deformation theory (SVSDT) that considers parabolic shear stress distribution along beam cross-section is used, as well as, Timoshenko beam theory (TBT). The cracks are modelled using massless rotational springs that divide beams into segments. In the forward problem, natural frequencies of intact and cracked beam models are calculated for different crack length and location combinations. In the inverse approach, which is the main concern of this paper, the natural frequency values obtained from experimental studies, finite element simulations and analytical solutions are used for crack identification via plots of rotational spring flexibilities against crack location. The estimated crack length and crack location values are tabulated with actual data. Three different beam models that have free-free, fixed-free and simple-simple boundary conditions are considered in the numerical analyses.

Stress and deformation analysis of functionally graded varying thickness profile orthotropic rotating disk

The present study deals with a finite element based formulation to determine the deformation and stresses of rotating disks made of functionally graded polar orthotropic material with mechanical properties varying in radial direction. The analysis is carried out using element based gradation of material properties over the discretized domain. The element-wise grading is implemented using an in-house source code in APDL and is implemented as UDF subroutine in ANSYS. Deformation and stresses of functionally graded rotating disk with varying thickness profile and material grading along the radial and tangential directions are investigated and effects of the grading parameter and other parameters, governing the orthotropic nature of the material are studied for free-free boundary condition. The proposed method is first validated with benchmark results, it can be seen that there is a significant reduction of stresses in variable thickness disks as compared to uniform disks. Further the effects of grading parameter and other governing parameters representing degree of orthotropic are also investigated and presented.

The effect of laser stitch welding residual stress on the dynamic behaviour of thin steel structure

Laser stitch welding is one of the most reliable and efficient permanent metal joining processes in the automotive industry, particularly in the manufacturing of a car body-in-white (BIW). It is widely known that this welding process induces the generation of residual stresses that can influence the dynamic behaviours of welded structures. In order to accurately predict the dynamic behaviours of these welded structures, it is important to experimentally understand the influence of residual stress. Therefore, this study addresses the finite element modelling method of thin steel welded structures with and without the influences of residual stress in order to identify its effect towards dynamic behaviours. The finite element models of thin steel welded structures are developed by employing the area contact model (ACM2) format element connector. The accuracy of the finite element models is then compared in terms of natural frequencies and mode shapes with the experimental counterparts. The dynamic behaviours of the measured structure are obtained using an impact hammer with free-free boundary conditions. The results demonstrate the importance of considering the influence of laser stitch welding residual stress in predicting the dynamic behaviours of thin steel welded structure.
 

Miscellaneous Modeling Approaches and Testing of a Satellite Honeycomb Sandwich Plate

The honeycomb sandwich structures are commonly and efficiently adopted in the development of light mass satellite structures as a result of their inherent high stiffness and strength properties. Through a comprehensive study, the equivalent finite element modeling of honeycomb sandwich structures utilizing miscellaneous modeling approaches is introduced. For the sake of validating results, both theoretical analysis and experimental modal testing are implemented upon a honeycomb sandwich plate utilizing free-free boundary conditions. Based on the results, the sandwich theory and its related shell-volume-shell approach introduce a good match with the experimental results. The aforementioned approach is utilized extensively during the process of satellite structural design and modeling. In addition, a parametric study is executed so as to relate the geometric and material variations to the resonant modal frequencies. The study results indicate a crucial influence of both honeycomb core and facing sheets thicknesses on the modal frequency values.

Determination of Natural Frequency and Mode Shape for Hollow Thin Plates

The determination of natural frequency and the mode shape of structures are important in characterizing the properties or behavior of the structures. The existing hollow in solid thin plate will change the vibration behavior in term of resonance frequency and mode behavior. A lot of structure consists of hollow space such as inner panel of car hood and bonnet. However, simplifying the model from hollow structure with solid thin plates only will resulting some difference in their vibration performance. This study begins with conducting modal analysis experiment using solid thin plate under free-free boundary condition. Next, the finite element methods were performing to compare with the experimental results. The average error of 3.96% was obtain when compared which provide a good confident level with the simulation result. Next, the study continued by finding the natural frequency and the mode shape for the thin plate under various position of hole, number of holes and shape of hole by using FEM software. Finally, finite element was also being carried out on the simplified design model of the inner panel car hood based from the real product and compared the resonance frequency from the model with some vibration reference sources. Through this study, it is found that the diversity of the hole position, the increasing number of holes and the change of the hole shape play a role in changing the natural frequencies of a thin plate. Since there is a lot of hollow thin plates in the car part, designing every parts are important to make sure the NVH quality is improve and not opposite of it.

Nondeterministic Model Updating of Laser Spot Welded Structure via Response Surface Methodology

This paper presents the application of response surface method in finite element model updating, as an approach for improving the accuracy and efficiency of the finite element model of a laser spot welded structure, to reflect the physical responses of the structure. The procedures of implementation for response surface in model updating such as sampling method, selecting the significant updating parameters and constructing a quadratic polynomial response surface are discussed. Initially, the finite element model of the structure was developed using CQUAD4 shell element alongside CWELD element connectors to represent laser spot weld joints. Then, NASTRAN SOL 103 was used to calculate the dynamic behaviour of the model (natural frequencies and mode shapes). The experimental modal analysis was then conducted under free-free boundary conditions via LMS SCADAS to obtain experimental data. The minimisation of the discrepancies of the finite element model was based on objective function that was formed by the residuals between finite element and experimental natural frequencies. Results show that response surface method was efficient to be used in finite element model updating since it is capable to improve the accuracy of the finite element model.

Joining Strategy Analysis of Structural Dynamic in Top Hat Plate of Dissimilar Materials

Structural dynamic can be described as a study regarding analysis of model under exertion of dynamic loading. Joining in structure such as riveting, welding and soldering were strongly effects the structural dynamic properties. The aim of this paper is to conduct various joining strategy analysis in finite element software by using top hat plate structure in car as a model and result is compared with experimental data. Normal mode analysis with free-free boundary condition is applied. Resistance spot welding (RSW) technique is selected to weld flange part in top hat plate between dissimilar materials which is mild steel 1010 and stainless steel 304 with specified parameters applied. Modal testing via impact hammer test is carried out at the welded top hat plate for experimental analysis purpose. Correlation in between FEA and EMA results need to be conducted. By selecting identified parameters to execute model updating on the structure using sensitivity analysis method, the discrepancies in natural frequencies were reduced between FEA and EMA. CWELD element was chosen to represent weld model for spot weld joints due to its accurate prediction of frequencies and mode shapes compare to other weld modelling. As a closure, connection in structure parts play significant role in structural dynamics and model updating is one of successful method to lessen the discrepancies between FEA and EMA.

Experimental Modal Analysis Procedure for a Laser Spot Welded Hat-Plate Structure

Measuring the dynamic behaviour of a structure made from light thin steel sheets becomes arduous as a result of the double impact, local modes and mass loading issues which lead to inaccurate results. In addition, the attachments of accelerometers, selection of suspension types and methods of excitation adopted to the measurement greatly affect the quality of the experimental results. The aim of this paper is to present detailed procedure for the experimental setup of a welded structure made from thin steel sheets. A hat shaped plate and flat plate connected together by several laser spot welds were used for the demonstration of the experimental modal analysis. The laser spot welded hat-plate structure was tested under free-free boundary conditions using impact testing with roving accelerometers and an LMS Test Lab. This work revealed that the proper procedures used for the experimental setup would help dynamicists enhance and improve the quality of the measured results of frequency response function and the results could be confidently used for the validation purposes and updating analytical models.

Finite element modeling and updating of the composite plate structure

Composite plate structure is broadly used in engineering structures for automotive and aerospace applications. Furthermore, the problem in vibrational is one of the industries main challenges. Composite materials are frequently used in industry for weight and cost reduction to enhance mechanical properties in structural components. This research aims to execute a composite plate structure model updating procedure. Through finite element analysis (FEA) and experimental modal analysis (EMA), modal parameters such as natural frequencies, mode shapes, and damping ratios are collected. Composite plate structure is set to be free-free boundary condition and node equivalence is done in the surface plate area. Correlation is executed between these two data sets. The discrepancies in natural frequencies between FEA and EMA were reduced with the selected parameters identified to perform structure updating model using sensitivity analysis.

Direct Determination of Dynamic Elastic Modulus and Poisson’s Ratio of Rectangular Timoshenko Prisms

AbstractIn this paper, the exact solution of the Timoshenko beam vibration frequency equation under free-free boundary conditions is determined with an accurate shear shape factor. The exact soluti...

Finite Element Modelling of Laser Stitch Welding Joints for Structural Dynamic Predictions

Laser stitch welding is a joining technique that has been increasingly popular in automotive industries, such as in the manufacturing and assembling of the car’s body-in-white (BiW) due to its advantages over the resistance spot weld, such as low heat application and high strength weld. The dynamic behaviour of a laser stitch welded structure is relatively difficult to predict accurately due to local parameters being induced during the laser welding process, such as heat affected zone (HAZ) and residual stress in the welded structure. This paper presents the idea of modelling the laser stitch weld by investigating different types of element connectors that can be used to represent laser stitch weld, such as rigid body element (RBE2), shell element (CQUAD4), bar element (CBAR) and area contact model (ACM2) format of element connectors. The accuracy of finite element models of laser stitch welded joints is compared in terms of natural frequencies and mode shapes with the experiment counterparts. The dynamic behaviour of the measured structure is obtained by using an impact hammer with free-free boundary conditions. It is found that the accuracy of the finite element models of the laser stitch welded structure highly depends on the involvement of residual stress and the heat affected zones that are generated from the welding process.