# Mechanical Engineering

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Item A Simulation-Based Fatigue Life Estimation Method for Nonlinear Systems under Non-Gaussian Loads(2023-01-01) Mande, Onkar K; Mourelatos, Zissimos P.; Gu, Randy J; Monroe, Ryan; Drignei, DorinShow more In the fields of durability and stochastic structural dynamics, it is customary to focus on linear structures subjected to Gaussian excitations. However, real-world engineering systems often exhibit nonlinear behavior and are exposed to non-Gaussian loads. Calculating fatigue life for such nonlinear systems under non-Gaussian loading presents many challenges such as complex nonlinear dynamics, multifaceted statistical characteristics, and time-dependent effects resulting in a very high computational effort. To overcome these hurdles, this research uses non-Gaussian Karhunen-Loeve expansion (NG-KLE) to not only predict the expected fatigue life but also obtain the Probability Density Function (PDF) of fatigue life. It integrates a sub-domain-based technique to significantly reduce the computational demands while preserving accuracy, by efficiently obtaining long time trajectories of random processes. This development is very useful for excitation signals that far exceed the process correlation length. The NG-KLE method serves as the main tool for characterizing the excitation process by estimating its non-Gaussian marginal distribution and autocorrelation function. A Karhunen-Loeve (KL) expansion is executed only for the first subdomain, and then extended to subsequent subdomains by establishing correlations between the KL expansion coefficients of adjacent subdomains. This innovative approach is adapted to non-Gaussian (NG) excitation, allowing for efficient characterization of both the input and output random processes using NG-KLE, enabling the generation of very long synthetic output random stress process samples. The fatigue life corresponding to each output stress trajectory contributes to the estimation of the PDF of fatigue life. The proposed generalized fatigue life estimation approach accommodates both Gaussian and non-Gaussian processes for both narrow and wide band signals. To demonstrate its effectiveness, we use a duffing oscillator system and a practical example involving a truck assembly modeled by the Finite Element Method (FEM).Show more Item Amplitude Method to Detect Debonding for Stack Bond Adhesive(2024-01-01) Huang, Xiabao; Barber, Gary; Gu, Randy; Wang, Xia; Latcha, Michael; Qu, Hongwei; Zhou, JunShow more Adhesively bonded joints have been applied in the automotive industry for the past few decades due to their advantages such as higher fatigue resistance, light weight, capability of joining dissimilar materials, good energy absorption and high torsional stiffness for overall body structure. They also provide an effective seal against noise and vibration at a low cost. There exists the challenge of defining the fatigue characteristics of adhesive joints under cyclic loading conditions and conventional methods have limitations in detecting the crack initiation of a bonded joint. This study introduces a method of detecting crack initiation by using the frequency method. It is found that stiffness change in the system is highly correlated to change in natural frequencies. By monitoring the change in natural frequencies, the crack initiation can be detected.Show more Item Molecular Dynamics Simulation of the Effect of Particle Hardness on Tribological Properties of Nanofluids(2022-01-01) Xu, Cang; Barber, Gary; Schall, James; Yang, Ankun; QAu, Hongwei; Zhao, PengShow more The determination of physical properties of nanofluids is mature, but the knowledge of tribological properties of nanofluids is limited. In this paper, the effects of surface roughness, fluid thickness, nanoparticle hardness, and number of nanoparticles on friction are explored systematical using a 2D Lennard-Jones molecular dynamics model. LJ parameters were chosen such that the ratio of stiffness of the nanoparticles to the opposing surfaces was approximately equal to ratio of stiffness of either aluminum oxide or zinc oxide to steel. A total of two hundred and twenty configurations were investigated. The results show that the benefits or drawbacks of nanofluid lubricants are sensitive to the friction regime (boundary, mixed, or hydrodynamic). When nanoparticles are present in lubricant-starved boundary conditions (fluid thickness less than the surface roughness amplitude), nanoparticles offer support that keeps the opposing surfaces separated. This separation results in reduced contact between the opposing surfaces and provides surface smoothing, which in turn lowers friction relative to the base fluid. At intermediate levels of fluid thickness where the fluid thickness and roughness are approximately equal, the presence of nanoparticles has a detrimental effect on friction. Nanoparticles jam and lock surfaces together and increase friction relative to the base fluid. As fluid thickness increases, the friction of the nanofluid generally remains higher than the base fluid likely due to the increased viscosity of fluid due to the presence of the nanoparticles. This work suggests nanofluids may offer limited benefits under specific lubrication conditions, but are detrimental under most conditions.Show more Item Virtual Methodology for Active Force Cancellation in Automotive Application Using Mass Imbalance and Centrifugal Force Generation (CFG) Principle(2024-01-01) Paul, Abhishek; Latcha, Michael A; Mourelatos, Zissimos P; Cooley, Christopher; Haider, Syed; Schmidt, DarrellShow more Structures under the influence of an external force are excited to resonance when the frequency of the external force and the natural frequency of the structure align with each other. Resonance leads to large deformation, which may cause damage to the integrity of the structure. There have been numerous applications of external devices that dampen the effects of excitation to the structure, such as tuned mass dampers, semi-active and active dampers, which have been implemented in buildings, bridges, and other large structures. One of the methods used for active cancellation uses the principle of centrifugal forces generated by the rotation of an imbalanced mass. These forces help counter the external excitation force applied to the structure. This research focuses on the working principle of active force cancellation using centrifugal forces due to mass imbalance and provides a virtual solution to simulate and predict the forces required to cancel the external excitation to an automotive structural system. This research addresses the challenges to miniaturize the CFG used for a Body on Frame truck and effectively reduce the amplitudes of the response due to a forcing function. The virtual tool presented in this thesis will help predict the maximum amplitude cancellation at resonance for given imbalance mass and frequency of forced excitation.Show more Item Using Salt Gradient Energy and Thermal Energy to Enhance Reverse Osmosis Desalination(2024-01-01) Yagnambhatt, Sanjana; Maisonneuve, Jonathan; Guessous, Laila; Wang, Xia; Yang, Ziming; Ladner, DavidShow more Improving desalination energy efficiency is crucial for meeting rising global water demands. Reverse osmosis (RO) is a common desalination process that uses an applied pressure to overcome the natural osmotic potential of seawater to drive nearly pure water permeate through a semipermeable membrane. However, it has high specific energy consumption ranging from 4-5 kWh/m3 and environmental issues associated with discharging the highly concentrated brine that is left over after separation. This work investigates two methods of improving the energy efficiency of RO desalination: (1) Recovering salt gradient energy from desalination brine, and (2) Using thermal energy to pre-heat RO feed water and reduce mechanical pump work.Show more Item Process Optimization of Autoclave Bonded Light-Weight Material Joints(2022-01-01) Jagatap, Shraddha Ratnakar; Nassar, Sayed; Shillor, Meir; Yang, LianXiang; Wu, ZhijunShow more This dissertation research fills a gap in the existing open literature regarding the significance of autoclave cure process variables and their interactions on the static strength of lightweight material single lap joints under tensile-shear loading. Specifically, the research investigates the dependence between the degree of cure of the epoxy adhesive and the mechanical performance of the single lap joint boded with same epoxy adhesive. Lightweight material system includes polycarbonate, Aluminum 6061 and glass reinforced plastics (GFRP) extren 500. A commercially available polyurethane film adhesive PE399 was selected to bond Polycarbonate single lap joints (SLJ) while epoxy film adhesive AF163-2K was selected to bond aluminum and GFRP joints. Studied variables include cure temperature, cure pressure and their respective rates as well as the duration of cure time. Dynamic Mechanical Analysis (DMA) is used to quantify glass transition temperature of AF163-2K cured with different combinations of autoclave process variables. The relative significance of variables and variable combinations are investigated for their effect on the bond strength. Experimental test data shows interaction between autoclave variable cure temperature in combination with cure time, temp ramp rate and pressure ramp rate have significant effect on glass transition temperature, bond strength and failure mode. Changes in joint static load transfer capacity (LTC) was investigated after cyclic temperature profile fluctuates between 20 C and 85 C at a constant relative humidity (RH) level of 85 .Show more Item Novel Membrane Systems for Energy Harvesting and Water Recovery(2023-01-01) Moussaddy, Sarah; Maisonneuve, Jonathan JMShow more Improving energy efficiency is an important part of the transition for mitigating greenhouse gas emissions. This dissertation introduces two novel membrane processes that can improve the energy efficiency of key sectors: (1) energy recovery from exhaust gases for improved power plant efficiencies, and (2) fertilizer-based liquid desiccant systems for improved dehumidification of indoor plant farms.Regarding the first, large amounts of energy are currently wasted from gradients of gas mixtures that are released from power plant exhaust. The energy is estimated to be 1-2 of the plant’s overall power capacity. To recover this energy, this work introduces a membrane process that uses ambient air as a sweep gas to draw concentrated gases from an exhaust source to do mechanical work in the form of compressed permeate gas flow. The concept and the developed numerical model are experimentally validated with a polydimethylsiloxane membrane using a binary gas mixture of nitrogen (N2) and water vapor in a first study, where power density of 57 mW/m2 is observed under relatively conservative test conditions. In a second study, N2 and carbon dioxide (CO2) was used and power of up to 6.35 W/m2 is experimentally observed when pure CO2 is supplied as feed, and up to 0.37 W/m2 when 20 CO2 feed is supplied. Regarding the second application of membranes, the focus is on a solution to improve the efficiency of energy, water, and fertilizer used in agriculture. This work introduces the novel concept of using fertilizer as a liquid desiccant for energy efficient dehumidification of indoor plant environments. The first-ever experimental demonstration of the concept is done using a polydimethylsiloxane membrane and a water vapor flux of up 1.90 g/m2/h is obtained. Dehumidification is confirmed across a range of standard greenhouse conditions and operating parameters. A theoretical modelling analysis is also performed to investigate the effects of operating conditions on the specific energy. As a result, a specific energy as low as 0.15 kWh/ kg is obtained under certain conditions with optimized desiccant temperatures and air flow rates.Show more Item Molecular Dynamics Simulation Of The Effect Of Particle Hardness On Tribological Properties Of Nanofluids(2022-07-20) Xu, Cang; Barber, Gary; Schall, James; Yang, Ankun; Qau, Hongwei; Zhao, PengShow more The determination of physical properties of nanofluids is mature, but the knowledge of tribological properties of nanofluids is limited. In this paper, the effects of surface roughness, fluid thickness, nanoparticle hardness, and number of nanoparticles on friction are explored systematical using a 2D Lennard-Jones molecular dynamics model. LJ parameters were chosen such that the ratio of stiffness of the nanoparticles to the opposing surfaces was approximately equal to ratio of stiffness of either aluminum oxide or zinc oxide to steel. A total of two hundred and twenty configurations were investigated. The results show that the benefits or drawbacks of nanofluid lubricants are sensitive to the friction regime (boundary, mixed, or hydrodynamic). When nanoparticles are present in lubricant-starved boundary conditions (fluid thickness less than the surface roughness amplitude), nanoparticles offer support that keeps the opposing surfaces separated. This separation results in reduced contact between the opposing surfaces and provides surface smoothing, which in turn lowers friction relative to the base fluid. At intermediate levels of fluid thickness where the fluid thickness and roughness are approximately equal, the presence of nanoparticles has a detrimental effect on friction. Nanoparticles jam and lock surfaces together and increase friction relative to the base fluid. As fluid thickness increases, the friction of the nanofluid generally remains higher than the base fluid likely due to the increased viscosity of fluid due to the presence of the nanoparticles. This work suggests nanofluids may offer limited benefits under specific lubrication conditions, but are detrimental under most conditions.Show more Item Development of Digital Shearography for Complex Defects Inspection(2021-11-09) Zhang, Boyang; Yang, Lianxiang; Barber, Gary; Qu, Hongwei; Narainen, RoderigueShow more Digital shearography measures the first derivative of the object surface deformation, which has the advantages of high sensitivity, full field, non-contact, realtime and anti-disturbance. It is widely used in materials inspection in industry. The information acquisition methods of the first derivative distribution are mainly divided into the intensity method and the phase shift method. The intensity method is to directly obtain the first derivative phase distribution by subtracting the light intensity map. The phase shift method to obtain phase information can be divided into temporal phase shift and spatial phase shift. Most digital shearography systems are single camera based and can only capture one image every shoot. However, unpredictable defects like the narrow crack and minor flaws could induce incomplete detection due to some limitations. There are two major issues on the measurement, one is the defect with the irregular shape which is not sensitive to the digital shearography, another is the deformation made of defects that is much smaller than the resolution of cameras. Digital Shearography measures the first derivative of deformation on the object surface because the shearing direction determines the derivative direction being measured, tests using multiple shearing directions are sometimes required to detect all kinds of defects. When the deformation is long and narrow as a crack while the shearing direction is perpendicular to the crack growing direction, digital shearography has the best sensitivity. In opposite, if the crack growing direction is parallel to the shearing direction, digital shearography is not able to find it out. Irregular shape defects detection is a tough challenge for digital shearography. Another challenge is the defects that are too small for the field of view. The limited pixels can miss the defects due to the low signal to noise ratio. To increase the sensitivity of detecting minor defects, a small field of view measurement is needed but it is time consuming in a large surface area inspection. The new development can be divided into three categories: 1) Modified Michelson interferometer based dual shearing digital shearography. 2) Spatial light modulator based dual shearing direction shearography. 3) Polarized digital shearography for simultaneous dual sensitive measurement. The basic theory, optical path analysis, preliminary studies, results analysis and research plan are shown in detail in this dissertation.Show more Item Load Distributions in Bolted Single Lap Joints Under Non-Central Tensile Shear Loading(2021-11-16) Sinthusiri, Chaiwat; Nassar, Sayed; Shillor, Meir; Yang, Xianjie; Wu, ZhijunShow more This study uses a numerically calibrated beam theory-based model to investigate the bolt load distributions in a preloaded two-bolt single lap joint under non-central tensile shear loading. The linear spring-based modeling is used for the two preloaded bolts and substrates. The bolt stiffnesses were derived from the bolt flexibilities influence by the bending deformation, the shear deformation, the bolt, and plate contact deformations. Due to the non-uniform load distribution along the bolt shank, the 3D finite element analysis was used to determine the correlation factors of each influence factors. Non central loading may be due to geometric tolerances that would cause additional moment loading on the joint. Thus, the load would not be equally distributed among all bolts in the joint. The effect of various joint parameters, bolt preload and off-center location of the tensile shear loading is investigated and discussed.Show more Item Self-Crack Healing of Engineering Ceramics(2022-03-21) Hammood, Israa Arif; Barber, Gary; Adams, Robert; Schall, J Dave; Debnath, Debatosh; Yang, Ankun; Zaidan, ShihabShow more The purpose in its simplicity is to heal the damage in a sample composed of ceramic particles through the heat treatment or through applying another source to heal the damage might be through using a laser source at room temperature to reduce the cost of wasting efforts and materials. The system can be designed to include a sensor to sense the damage in the component and a healing agent like loose particles or a specific source that provides an immediate treatment through the heating in order to create or generate the glassy phase. Self-crack-healing materials are able to sense the crack and heal it. The notion of not giving up on things can be considered as the motive for such type of research. Most ceramics are brittle and hence they are sensitive to flaws and cracks. Ceramics are subjected to thermal and mechanical stresses during service. Residual stresses may eventually cause microcracks (internal and surface cracks) and the failure of the component in use. This limits their use as structural engineering materials, and thus applying or inducing a self-crack healing ability would be a solution to overcome this problem. Great benefits can be expected from the components in use while applying the self-healing ability, such as reducing maintenance, inspection, and the cost of machining and polishing as well, which enhances the reliability of the component in use, and hence achieving a higher structural integrity*. Developing new materials with increasing resistance to wear and corrosion is the goal for many researchers and manufacturers as well. Consequently, an attempt to imitate the mechanisms employed by nature through the biological systems have been made to design self-healing materials and coatings for corrosion protection which can result in complete recovery*. Ceramics can be used in many applications including aeroengine turbine blades, gas turbine blades, high performance bearings and many other applications that require high temperature service *. However, these ceramics have low fracture toughness, which means that they are brittle and sensitive to flaws such as micro and macro cracks, which limit their applications as structural components. The present research is focused on the self-crack healing ability of Spinel nanocomposites and SiC bonded Kaolinite. The self-crack healing behavior was investigated as a function of the healing conditions (time, temperature, and chemical composition) as well as the mechanism responsible for healing the cracks.Show more Item Experimental Implementation of a New Durability / Accelerated Life Testing Time Reduction Method(2021-11-13) Baseski, Igor; Mourelatos, Zissimos P.; Latcha, Michael; Drignei, Dorin; Wang, XiaShow more Fatigue can be defined as a cyclic degradation process resulting in a failure at lower stress levels than the ultimate load. Fatigue reliability is defined as the probability that a structure will perform its intended function throughout its lifetime without any fatigue failure. Durability testing aims to predict fatigue damage in order to estimate the remaining useful life (RUL) based on fatigue. The latter is a useful metric in design for life-cycle cost. The objective of this research is to develop a new durability time reduction method to experimentally estimate the fatigue life of a vehicle component or system with accuracy using a short duration test. We assume that the loading random process (e.g. terrain configuration) is stationary and ergodic so that a single time trajectory can quantify the loading statistics. For the single time trajectory of the load process, we measure the corresponding output stress trajectory at a specified location on the structure. The latter is cycle counted using the 4-point rainflow counting algorithm. The cycle counting identifies all signal (stress) peaks and valleys using a peak picking algorithm and uses them to identify the range of all individual fatigue damage cycles and the time they occur based on a chosen fatigue damage model. Using this information (range of each cycle and the time it occurs), we build a synthetic signal exhibiting the same fatigue damage cycles in the sequence they occur in the actual stress signal. The sequence can be important in order to properly account for the cumulative damage accumulation. Finally, based on the fact that the cycle damage is independent of the time it occurs, we compress the synthetic signal so that its Power Spectral Density (PSD) does not exceed an upper limit dictated by the durability equipment. This proposed durability approach achieves therefore, the same cumulative damage with the original signal in a much shorter testing time. We demonstrate the new durability approach with two examples, and validate it experimentally using a commonly used Belgian block terrain excitation on the suspension coil spring of a military HMMWV (High Mobility Multi-purpose Wheeled Vehicle).Show more Item Generation of Internal Combustion Engine Maps and Spark Timing Profiles Using Metamodels(2022-03-14) Tafreshi, Ali; Mourelatos, Zissimos; Sangeorzan, Brian; Drignei, Dorin; Maisonneuve, JonathanShow more With the growth of computing technologies, many leading automotive companies tend to use simulation tools to reduce the number of actual engine testing for evaluating the performance of Internal Combustion (IC) engines. However, a high-fidelity engine model which is very complex and computationally demanding, is needed. In this dissertation, we present efficient and accurate metamodels to predict an engine fuel map and to also obtain the spark timing profile to generate a specified torque curve. Time-dependent Kriging metamodels using Singular Value Decomposition (SVD) and Nonlinear Autoregressive metamodels with Exogenous inputs (NARX) in conjunction with Neural Networks (NN) are developed and used. A sequential process was first developed to generate steady-state engine fuel maps using Kriging accounting for different engine characteristics at different operating conditions. The generated map predicts engine output parameters such as Brake Mean Effective Pressure (BMEP) and fuel flow rate. The Kriging metamodels are created sequentially to ensure acceptable accuracy with a small number of expensive engine simulations. Two optimization problems are solved for full load and part load conditions, respectively. We demonstrate that the estimated fuel map is of high accuracy compared to the actual map. The internal combustion engine is a source of unwanted vehicle vibration produced by engine mount forces which depend on the engine torque profile during a transient tip-in or tip-out maneuver. A methodology was also developed to obtain the desired engine torque profile to minimize the unwanted vibration by controlling a set of engine calibration parameters. A set of design coefficients defining a spark timing profile and the corresponding engine torque profiles are used to construct time-dependent metamodels using SVD and Kriging. The accuracy of the approach is demonstrated using GT-Power engine simulations. In addition, we developed a time-dependent NARX-NN metamodel to predict engine spark timing and cylinder pressure profiles corresponding to a desired torque profile. The NARX-NN metamodel predicts the spark timing accurately using a very small number of engine simulations.Show more Item 2-D Modeling of Moisture and Heat Diffusion in Adhesively Bonded Joints(2021-11-15) Gerini Romagnoli, Marco; Nassar, Sayed A.; Yang, Lianxiang; Gu, Randy; Dembinski, RomanShow more In this dissertation research, a novel two-dimensional model is proposed for adhesively-bonded Single Lap Joints (SLJ) under combined mechanical loads and moisture/heat diffusion. Governing partial differential equations of the constitutive stress-diffusion model are formulated and solved numerically. Various scenarios for individual and combined diffusion of moisture and heat through the joint substrates and directly into the adhesive layer are analyzed. The resulting location-dependent material model is fed into the governing partial differential equations. Shear and peel stresses in the adhesive layer are investigated. Results are presented, with a focus on the improvements brought by the capability of the proposed model to predict the effects of diffusive patterns that are perpendicular to the axial tensile-shear load.Moisture diffusion across the joint width is found to have a significant effect on the shear stress distribution for structural epoxy adhesives with high elastic modulus. Numerical comparison with a linear Finite Elements Analysis is provided. Material properties are derived from experimental testing of commercially available two-component epoxy and polyurethane adhesives. This document is organized as follows: Chapter One "Introduction and Literature Review" includes a description of the analytical, numerical, and experimental work that serves as foundation for this dissertation. A previous one-dimensional analytical model is revised, and the motivations driving this research effort are illustrated. Chapter Two "Modeling of Heat and Moisture Diffusion" lays the groundwork for the analysis of diffusive patterns in the joint substrates and in the adhesive layer. Multiple scenarios of moisture and heat diffusion are explored, and their effect on the elastic properties of the adhesive is investigated. Governing partial differential equations are derived, and solution strategies are discussed. Chapter Three "Elastic Model" includes the formulation of coupled stress-diffusion partial differential equations for the shear and peel stresses in the adhesive layer, resulting from the application of an external tensile-shear load on the two adherends. Equilibrium considerations, stress-strain, and strain-displacement relationships are used to generate the constitutive equations, with adequate assumptions and simplifications. Chapter Four "Elastic Modulus of Structural Adhesives: Relationship to Bulk Material Temperature" contains the experimental procedure and results for the bulk adhesive tests. The elastic moduli of two-component epoxy and polyurethane adhesives are measured using a DMA Q800, and a linear law relating temperature to material properties is inferred. Chapters Five, Six, and Seven present the results of the shear and peel stress models for adhesive joints subjected to two-dimensional moisture-only, heat-only, and combined moisture/heat diffusion, respectively. A convergence study is performed on the two-dimensional solution to the heat equation governing moisture and heat diffusion in the adhesive layer. Stress gradients along the length and width of the bondline are analyzed, and the results are compared to the previous one-dimensional coupled stress-diffusion model. The results of the two-dimensional model are compared with a Finite Elements Analysis in Chapter Eight "FEA Comparison". Chapter Nine "Conclusions and Future Work" summarizes the major findings of this dissertation research, and outlines the potential for future work.Show more Item Process Optimization of Autoclave Bonded Light-Weight Material Joints(2022-04-01) Jagatap, Shraddha Ratnakar; Nassar, Sayed; Shillor, Meir; Yang, LianXiang; Wu, ZhijunShow more This dissertation research fills a gap in the existing open literature regarding the significance of autoclave cure process variables and their interactions on the static strength of lightweight material single lap joints under tensile-shear loading. Specifically, the research investigates the dependence between the degree of cure of the epoxy adhesive and the mechanical performance of the single lap joint boded with same epoxy adhesive. Lightweight material system includes polycarbonate, Aluminum 6061 and glass reinforced plastics (GFRP) extren 500. A commercially available polyurethane film adhesive PE399 was selected to bond Polycarbonate single lap joints (SLJ) while epoxy film adhesive AF163-2K was selected to bond aluminum and GFRP joints. Studied variables include cure temperature, cure pressure and their respective rates as well as the duration of cure time. Dynamic Mechanical Analysis (DMA) is used to quantify glass transition temperature of AF163-2K cured with different combinations of autoclave process variables. The relative significance of variables and variable combinations are investigated for their effect on the bond strength. Experimental test data shows interaction between autoclave variable cure temperature in combination with cure time, temp ramp rate and pressure ramp rate have significant effect on glass transition temperature, bond strength and failure mode. Changes in joint static load transfer capacity (LTC) was investigated after cyclic temperature profile fluctuates between 20° C and 85° C at a constant relative humidity (RH) level of 85 %.Show more Item Solution Methodology for Constrained Eigenvalue Problems and Its Applications with Experimental Validation in Structural Characteristics Identification(2021-11-15) Chen, Longhan; Gu, Randy; Yang, Lianxiang; Mourelatos, Zissimos P.; Spagnuolo, AnnaShow more A numerical reverse algorithm was developed in this dissertation to find some unknown parameters of an object. For example, if the natural frequency of an object is known, find the mass of the particle placed at a specific place in the object. There is nos such direct formula or algorithm that can solve this kind of problem, we can use the reverse algorithm to solve it. Since the objective function can be built after the structure's stiffness matrix and mass matrix were obtained using the finite element method, and the structure's natural frequencies are known, this kind of problem becomes a constrained eigenvalue problem. The constrained eigenvalue problem can be solved by minimizing the objective function and executed using numerical methods. In this dissertation, we developed Newton's iteration to solve it and also developed the Genetic Algorithm as an alternative algorithm when Newton's iteration cannot find unknown parameters. Several numerical examples, such as beam, plane frame, three-dimensional frame, and plate structure, were chosen to test the proposed algorithm's feasibility, accuracy, and solving time. Furthermore, some groups of experimental validation were also provided to testify to it.Show more