The undergraduate course, Design of Machine Elements has been offered by the University of Connecticut’s Mechanical Engineering Department for many years. It has been one of the most difficult courses for students to follow and understand, and also for the faculty to teach. A strong basic knowledge of mathematics, theoretical mechanics and the mechanics of materials is required for students to take this mandatory course and to fully follow its contents. To understand entirely the concepts of Design of Machine Elements, students should be acquainted with the history of the strength of materials. Being aware of the importance of such a course the ME faculty has worked to establish outstanding structural engineering teaching and research methods, and to create a departmental nucleus of intensive development of engineering mechanics research and development. The efforts described in this paper have facilitated the teaching and learning of the mechanics of materials and consequently the Design of Machine Elements as well. To accomplish these in both teaching and practical problem solving the instructor must use the unconventional approaches and students must put a great deal of effort into learning the material. It is important for students to have a general knowledge of mathematics and theoretical mechanics, but as this is a foundation of the course, the instructor should review and clarify the specific assumptions of engineering mechanics and strength of materials. One of the pedagogical challenges to be overcome, which is faced by both instructors and students, has always been to connecting the basic theorems and application procedures of engineering mechanics to their practical use in designing machine elements and in calculating static and dynamic stresses and deformations. The concept of avoiding stress concentrations by properly designing the shapes of machine frames and parts should also be emphasized. Transforming plane stresses and deformations into three-dimensional representations and calculations should also be considered. Since machine elements are usually in motion, a dynamic approach to stress and deflection analysis is important as well. After introducing the analysis of dynamic stresses and deformations, the instructor should cover the concept of fatigue, which is the next crucial step. The instructors’ approaches and the unconventional methods they use to familiarize students with such complicated concepts are discussed in this paper. An analysis of representations of stresses and deformations and fatigue analyses of different machine elements are also considered. This paper connects to some approaches previously presented in earlier papers as well as in courses, books and discussions by outstanding engineering mechanics theoreticians, including UConn faculty, especially Dr. Roman Solecki. The paper concludes by recommending effective teaching approaches to complicated machine design concepts and summarizing the lessons learned. This paper is a companion piece to the IMECE 2015 50776 [1].

Thin films of titanium-silicon carbonitride (TiSiCN) with titanium adhesion layers were deposited at approximately 280°C on horizontally and vertically-mounted strips of 301-stainless steel by reactive magnetron sputtering. Considerable differences in the mid-deflections and radii of curvature between the vertical and horizontal samples were observed. Cross-sectional characterizations done on a TEM revealed a columnar growth and uniform microstructure. A finite-element model of the tri-layer sandwich structure using Mesh-Tie constraints was developed to estimate the intrinsic stress levels in the overcoat as probable functions of substrate location and orientation. The computational model in the absence of intrinsic stress was validated by analytical expressions for multilayer films. The initial stress state parameter was varied in Abaqus until consistency in curvature-values was achieved with the physical measurement obtained from an optical setup specially-constructed for this purpose. The difference in the S11/S22 principal stresses provided the intrinsic stress estimate. The calculated values of intrinsic stress were then applied to an FEA test model with fixed constraints to computationally determine the stress reduction for individual samples.

The current trend in the wind power market is to develop large diameter rotors in order to maximize the power extraction from the wind. Those rotors exhibit issues related to blade deflection and structural integrity that can be mitigated implementing design variations that were present on the early wind turbine designs, such as rotors with less than three blades located behind the tower in downwind configuration. This work assesses the aerodynamic performance of a downwind two-bladed wind turbine based on CFD simulations coupled with the Actuator Line Model (ALM). This design is compared with the MEXICO project upwind three-bladed wind turbine, for which experimental data is available. The simulations showed good agreement with measurements especially upstream the rotor and for higher inlet velocities. Furthermore, the downwind configuration was successfully modeled using ALM and the performance prediction of the turbines was physically accurate since realistic variations were obtained between the evaluated wind turbines and none of their performance coefficients exceeded Betz theoretical limit.

In our group, we are developing flexure hinge based manipulators made of nitinol for minimally invasive surgery. On the one hand, sufficient flexibility is required from flexure hinges to be able to cover the surgical workspace. On the other hand, the bending amount of the flexure hinges has to be limited below the yielding point to ensure a safe operation. As a result of these considerations, it has to be questioned how much bending angle a nitinol flexure hinge with given geometric dimensions can provide without being subject to plastic deformation. Due to the nonlinearities resulting from large deflections and the material itself, the applicability of the suggested approaches in the literature regarding compliance modeling of flexure hinges is doubtful. Therefore, a series of experiments was conducted in order to characterize the rectangular cross section nitinol flexure hinges regarding the flexibility-strength trade-off. The nitinol flexure hinge samples were fabricated by wire electrical discharge machining in varying thicknesses while keeping the length constant and in varying lengths while keeping the thickness constant. The samples were loaded and unloaded incrementally until deflections beyond visible plastic deformation occured. Each pose in loaded and unloaded states was recorded by means of a digital microscope. The deflection angles yielding to permanent set values corresponding to 0.1% strain were measured and considered as elastic limit. A quasilinear correlation between maximum elastic deflection angle and length-to-thickness ratio was identified. Based on this correlation, a minimal model was determined to be a limit for a secure design. The proposed guideline was verified by additional measurements with additional samples of random dimensions and finite element analysis.

The Hybrid-III Rail Safety (H3-RS) anthropomorphic test device (ATD), also known as a crash test dummy, was developed by the Rail Safety and Standards Board (RSSB), DeltaRail (now Resonate Group Ltd.), and the Transport Research Laboratory (TRL) in the United Kingdom between 2002 and 2005 for passenger rail safety applications [1]. The H3-RS is a modification of the standard Hybrid-III 50th percentile male (H3-50M) ATD with additional features in the chest and abdomen to increase its biofidelity and eight sensors to measure deflection. The H3-RS features bilateral (left and right) deflection sensors in the upper and lower chest and in the upper and lower abdomen; whereas, the standard H3-50M only features a single unilateral (center) deflection sensor in the chest with no deflection sensors located in the abdomen. Additional H3-RS research was performed by the Volpe National Transportation Systems Center (Volpe Center) under the direction of the U.S. Department of Transportation, Federal Railroad Administration (FRA) Office of Research, Development, and Technology. The Volpe Center contracted with TRL to conduct a series of dynamic pendulum impact tests [2]. The goal of testing the abdomen response of the H3-RS ATD was to develop data to refine an abdomen design that produces biofidelic and repeatable results under various impact conditions with respect to impactor geometry, vertical impact height, and velocity. In this study, the abdominal response of the H3-RS finite element (FE) model that TRL developed is validated using the results from pendulum impact tests [2]. Results from the pendulum impact tests and corresponding H3-RS FE simulations are compared using the longitudinal relative deflection measurements from the internal sensors in the chest and abdomen as well as the longitudinal accelerometer readings from the impactor. The abdominal response of the H3-RS FE model correlated well with the physical ATD as the impactor geometry, vertical impact height, and velocity were changed. There were limitations with lumbar positioning of the H3-RS FE model as well as the material definition for the relaxation rate of the foam in the abdomen that can be improved in future work. The main goal of validating the abdominal response of the dummy model is to enable its use in assessing injury potential in dynamic sled testing of crashworthy workstation tables, the results of which are presented in a companion paper [3]. The authors used the model of the H3-RS ATD to study the 8G sled test specified in the American Public Transportation Association (APTA) workstation table safety standard [4]. The 8G sled test is intended to simulate the longitudinal crash accleration in a severe train-to-train collision involving U.S. passenger equipment. Analyses of the dynamic sled test are useful for studying the sensitivity of the sled test to factors such as table height, table force-crush behavior, seat pitch, etc., which help to inform discussions on revisions to the test requirements eventually leading to safer seating environments for passengers.

Fixed workstation tables in passenger rail coaches can pose a potential injury hazard for passengers seated at them during an accident. Tables designed to absorb impact energy while minimizing contact forces can reduce the risk of serious injury, while helping to compartmentalize occupants during a train collision. The Rail Safety and Standards Board (RSSB) in the U.K. issued safety requirement GM/RT2100, Issue 5 [1] and the American Public Transportation Association (APTA) in the U.S. issued safety standard APTA PR-CS-S-018-13, Rev. 1 [2] with the goals of setting design and performance requirements for energy-absorbing workstation tables. The U.S. Department of Transportation, Federal Railroad Administration (FRA) Office of Research, Development and Technology directed the Volpe National Transportation Systems Center (Volpe Center) to evaluate the performance of the Hybrid-III Rail Safety (H3-RS) anthropomorphic test device (ATD), also known as a test dummy, in the APTA sled test in order to incorporate a reference to the H3-RS in the safety standard. The Volpe Center contracted with the manufacturer of the H3-RS, Transport Research Laboratory (TRL), in the U.K. to conduct a series of sled tests [3] with energy-absorbing tables, donated by various table manufacturers. The tables were either already compliant with the RSSB table standard or were being developed to comply with the APTA table standard. The sled test specified in Option A of the APTA table standard involves the use of two different 50th percentile male frontal impact ATDs. The H3-RS and the standard Hybrid-III (H3-50M) ATDs performed as expected. The H3-RS, which features bilateral deflection sensors in the chest and abdomen, was able to measure abdomen deflections while the H3-50M, which features a single sensor measuring chest compression, was not equipped to measure abdomen deflection. This study attempts to validate a finite element (FE) model of the APTA 8G sled test with respect to the thorax response of the H3-RS and H3-50M. The model uses a simplified rigid body-spring representation of one of the energy absorbing tables tested by TRL. The FE models of the H3-RS ATD and the H3-50M ATD were provided by TRL and LSTC, respectively. Results from the sled tests and FE simulations are compared using data obtained from the chest accelerometer, the chest and abdomen deflection sensors, and the femur load cells. Using video analysis, the gross motion of the dummies and table are also compared. Technical challenges related to model validation of the 8G sled test are also discussed. This study builds on previous analyses conducted to validate the abdomen response of the H3-RS FE model, which are presented in a companion paper [4].

Linkage or cam follower types of mechanisms are designed to create dwell motion when the interest of point on the mechanism is expected to stay at rest while the input is constantly supplied to the driven link. Generally, six bar linkages consisting of a four bar crank rocker mechanism actuating a slider crank are considered for linkage type mechanisms. A novel compliant translational double exact dwell mechanism incorporating the buckling motion of an initially straight flexible member as its members is introduced in this paper. Buckling members are designed to create dwell motion as a compliant mechanism that is easy to manufacture and require minimum number of components and assembly. This partially compliant five bar mechanism consists of two rigid links as the crank and the slider, and two flexible links as the coupler and the last link. Kinematic analysis of the mechanism is broken into two parts. The first one is a flexible pinned-pinned beam attached to a slider and the second one is the pinned-pinned flexible beam which is attached to a rotating crank. Large deflection analysis of pinned-pinned buckling beam is obtained by solving first and second kind of elliptic integrals in Matlab. Load required to displace the slider and the maximum bending moment restored on the pinned-pinned beam are analyzed by changing the normalized offset from 0 to 1. A mechanism is said to be linear if the slope of the load-deflection curve remains positive during deformation. Slope of the normalized load deflection curves at various offsets are explored and design limitations providing a stable buckling behavior is discussed. Pinned-pinned buckling beams are represented by springs possessing the same load-deflection characteristics as the compliant beams where the nonlinear spring function is described by a 4 th order polynomials fitted to the load-deflection curves both for the beam attached to the slider and the beam attached to the driven crank. The emphasis is placed on the dynamic response of the double exact dwell motion profile. Simulation results are studied using Solidworks model, and Matlab. Slider stays at rest until the maximum bending moment of the coupler flexible link is achieved creating the dwell, snaps to its maximum position and on the return creates a momentary dwell since the flexible follower behaves like a rigid link. Desired dwell motion can be accomplished by changing the flexible beam parameters such as its length, thickness and offset ratio.

This paper presents a numerical study of the influence of different factors on tumor detection via a 2D tactile sensor. The 2D tactile sensor entails a polydimethylsiloxane (PDMS) microstructure embedded with a 3 × 3 sensing-plate/transducer array. By pressing the sensor against a tissue region with a predefined indentation depth pattern, the tissue stiffness distribution is extracted from the measured slopes of the deflections of the sensing-plate array versus the indentation depth. In this work, we numerically investigate the influence of curved tissue surface, curved substrate and tissue viscoelasticity on the measured sensor deflection distribution, which is representative of the tissue stiffness distribution. A set of numerical models are created in COMSOL Multiphysics to investigate the influence of the above-mentioned factors separately. A purely elastic numerical model with a flat substrate and a flat tissue surface is created as the reference model. Two other numerical models are created with one having a curved surface and the other having a curved substrate. The same tumor is embedded in these three models. Given the same 2D sensor, how the measured sensor deflection distribution is affected by different curved surfaces and curved substrates is compared with the results from the reference model. The three tumor parameters (elasticity, size and depth) are also varied for their influence on the measured results. A separate viscoelastic numerical model is created to study how the time-dependent behavior of a tumor varies with its viscoelasticity. This model provides the guidance on tailoring the testing parameters in a pre-defined indentation protocol for quantitatively maximizing the difference in viscoelasticity among different tumors.

This work explores the effects of geometrical nonlinearities in the vibration analysis of rotating structures and helicopter blades. Structures are modelled via higher-order beam theories with variable kinematics. These theories fall in the domain of the Carrera Unified Formulation (CUF), according to which the nonlinear equations of motion of rotating blades can be written in terms of fundamental nuclei, whose formalism is an invariant of the theory approximation. The inherent three-dimensional nature of CUF enables one to include all Green-Lagrange strain components as well as all coupling effects due to the geometrical features and the three-dimensional constitutive law. Numerical solutions are considered and opportunely discussed. Also, linearized and full nonlinear solutions for vibrating rotating blades are compared both in case of small amplitudes and in the large deflections/rotations regime.

A concept for an innovative wind turbine blade with an actively transformable twist distribution is presented. A simulation model demonstrates that adapting the blade twist distribution can increase the aerodynamic efficiency during partial-load operation. A blade concept consisting of a rigid spar that is surrounded by deformable modular shells is also proposed. The outer shells are assumed to be produced using additive manufacturing (AM) technology. Integrated features enabled by the AM process tune the stiffness, and thus the degree of flexibility for each surrounding segment. The unique local stiffness and the placement of actuators establishes a nonlinear twist angle distribution (TAD). An optimal design procedure is devised for setting the stiffness and actuator locations. It maximizes the aerodynamic efficiency for a discrete range of wind speed. The blade performance is quantified using data acquired from the National Renewable Energy Laboratory (NREL) Aerodyn software. A computer cluster is used to facilitate this process. It must consider the TAD for the range of wind speed that corresponds to the partial-load operation. The design procedure first establishes the TAD geometry based on the theoretical aerodynamic modeling. The TAD geometry is then passed to a mechanical design algorithm. At this point, the actuator positions are set, and the stiffness ratios of the adaptable shells are defined using the objective function. It minimizes the amount of deviation between the actual TAD and that found in the aerodynamic analysis. The free-shape TAD is determined in the final step. This is the shape of the blade when no actuation force is applied to the shells. This shape is then selected to minimize the amount of deflection needed to shape the TAD between its extreme positions. A case study demonstrates the ability of the blade and the proposed design process. The study indicates that a blade with five actuators can achieve the full range of TAD motion. The final solution shows that the adaptive TAD can increase the efficiency by 3.8 and 3.3%, respectively, at the cut-in and rated speeds.

Engine turbine blades operate at a high speed of rotation and are subjected to high temperature and pressure prevailing gas from the combustion chamber, making the working condition very harsh. In particular, the leading edge of the blade, which is directly subjected to high-temperature gas impacts, is the hottest part of the turbine. Therefore, it is of great importance to improve the protection of the blade leading edge and enhance the understanding of this part of the flow field and temperature field. This paper will focus on the phenomenon of wake deflection and study the film cooling characteristics of the turbine blade under rotating condition. The characteristics of pressure surface and suction surface of the blade are verified by numerical simulation. The contents cover the influence of the film hole diameter, pitch, blowing ratio, rotation number and the development process, the film cooling efficiency on the outflow of coolant film. The result shows that Coriolis force, centrifugal force and secondary flow induced by rotation will change the mainstream flow along the blade, which will lead to changes of pattern concerning the development of the film on the blade surface. In the process of wake development, deflection occurs in different directions at different positions, and the greater the rotation number is, the more obvious the degree of deflection will be. Studying the model with film holes on the leading edge of the blade, these phenomena can be observed along the downstream on the pressure and suction surfaces. Also, models with film holes independently set on the pressure and suction surfaces can be used as proof of these features. At the same time, this paper studies the flow and heat transfer characteristics of the leading-edge gas film under rotating condition and focuses on the influence of rotation on the outflow and the development processes of the wake. The gas film cooling models in rotating state of different film hole diameters and film hole radial spacing will also be compared to further understand the flow and heat transfer characteristics of film cooling on the leading edge of the blade.

This paper reports the experimental and numerical studies on the effects of rotating speed and blowing ratio on the film cooling performance of the hole near the leading edge on the suction side of the turbine blade. The chord and height of the blade are 60mm and 80mm respectively. The film hole with diameter of 0.8mm is located in the mid span on the suction side at axial location of 8%. The injection angle of the hole is 45° to the suction surface of the blade and is nearly perpendicular to the axial direction. Both experimental and numerical studies were carried out with rotating speeds of 300rpm, 450rpm and 600rpm, and with blowing ratios of 0.5, 1.0, 1.5 and 2.0. CO 2 was used as the coolant. Experimental data was measured by applying the Thermochromic Liquid Crystal (TLC) technique and the Stroboscopic Imaging Technique. Mainstream and coolant were heated to 308K and 318K respectively. Numerical studies were performed to assist the analysis of the experimental results. The SST turbulence model was applied in the simulations. Results show that the film cooling performance of the hole near the leading edge is different from that of the hole further downstream on the suction side. This is because the direction of the jet is nearly perpendicular to the axial direction, which increases the effect of the Coriolis force. Besides, the mainstream from leading edge also has effects on film cooling performance. With the increase of the blowing ratio, the film coverage area and spatially averaged film cooling effectiveness increase first and then decrease. The maximum film coverage and averaged film cooling effectiveness appear at blowing ratio of 1.0 and rotating speed of 300rpm. Moreover, the upward deflection angle of the film trajectory increases slightly with the increase of the blowing ratio. Higher rotating speed intensifies the deflection of the film trajectory. Therefore, the film coverage and the averaged film cooling effectiveness decrease rapidly.

For the laminated piezoelectric rectangular plate with large deflection and large rotation, the nonlinear equilibrium differential equations are derived and solved. Firstly, the global Cartesian coordinate system to describe the undeformed geometry and the local orthogonal curvilinear coordinate system to describe the deformed geometry are established respectively on the mid-plane of the plate before and after the deformation, and the relationship between the two coordinates is expressed by transformation matrix. For the convenience of calculation, the expressions of the nonlinear curvatures and inplane strains are obtained by Taylor series expansion. Considering the piezoelectric effect, three equilibrium partial differential equations describing nonlinear bending problems are obtained by the principle of virtual work. Furthermore, in order to simplify the solution process, the stress function is introduced to automatically satisfy the first two equations for the large deformation of the cantilever plate, and the relationship between stress function, the mid-plane internal force and shear force is also given for the first time. Therefore, the stress function and the transversal displacement are the main unknowns of the governing equation and compatibility equation. Additionally, the approximate deflection function and stress function are given which can satisfy all the displacement boundary conditions and only part of the force boundary conditions. Thereby, the generalized Galerkin method is used to obtain the approximate solution of the nonlinear bending problem. Finally, the results in the study are verified by comparison with the results obtained from the finite element method. It also provides a theoretical basis for the engineering application of the large deformation of the piezoelectric cantilever plate.

With approximately 12% of adults in the United States affected by osteoarthritis (OA), constant research is being performed to advance treatment techniques for this ailment. 3D printed bio-polymer caps have been proposed as a potential treatment for severe cases of OA, and are an alternative to traditional implants. This report considers the feasibility of one such bio-polymer cap using a simplified, linear, finite element analysis (FEA) model. Material properties for both Bionate 80A and articular cartilage are considered for comparison. The simulation modeled joint loading for a 195 lb, 867.4 N, adult male squatting from 0 to 90-degrees flexion with a mathematical model governing the changing contact area on the medial and lateral condyles. Menisci effects were neglected as a part of the model reduction. For Bionate 80A, minimum and maximum stress values of 1.124 MPa and 3.555 MPa were obtained, with corresponding deflections of 126.8 μm and 316.8 μm. The articular cartilage model gave stress values of 1.102 MPa and 3.623 MPa, with deflections of 170.2 μm and 420.8 μm. A maximum shear stress value of 1.988 MPa was obtained in the Bionate 80A simulation. From these results, it was determined that the Bionate cap is comparable to articular cartilage and could be a viable replacement in the cases of advanced OA, but the Bionate cap may have limitations on joint flexibility due to the relatively small 1.65 factor of safety at 90-degree. The maximum shear stress value indicates it would be viable to use specific biocompatible cements as a method of fixture.

Cocquilhat’s first documented (1851) how heat in a tool shortens the life of the tool. Research since his time has generally concluded that the tool gives up a relatively higher percentage of it’s “cold hardness and toughness” as compared to the work stock. This paper looks at the previously unstudied advantages/disadvantages which may be gained by pre-heating the work stock to a relatively modest temperature, thereby preferentially shifting the ratio/percentages back toward the tool. A widely-used body centered cubic (BCC) steel and a widely-used face centered cubic (FCC) aluminum were chosen to test common commercially machined crystalline structures. The materials were heat treated and/or aged to provide various levels of hardness within the crystalline structures. The selection of two cutting speeds, two levels of cut and three tool rake angles completed the factor level combinations chosen for the study. Parts were preheated immediately prior to the machining operations with an additional resistance heater mounted in the work holder to maintain the temperatures during the trial run. Tensile specimens of all the samples were undertaken to establish the cold working flow stress values of the materials tested. Machining was conducted in a specially modified Cincinnati Horizontal Milling machine using an improved Videographic Quick Stop Device (VQSD) to capture the geometry of the cutting formation simultaneously with the forces in the X, Y and Z-axes using a standard Kistler force plate dynamometer. Utilizing the VQSD greatly increases the number of replicates available for statistical analysis by the metal cutting researcher. This allows for comprehensive multivariate analysis of the data with high confidence (> 95%) in the obtained results. Forces and geometry were collected and analyzed. Wear was measured on the face of each tool using surface profilometers and white light microscopy. The specific horsepower (HPs), also known as the specific cutting energy, normal force (N), and wear rate data indicated there is a definite advantage to be had in pre-heating the workpiece by even a modest amount. In fact, the temperature was a significant prime factor (p-value <= 0.0001, Fstat > 5 with 95% certainty) in all factor level combinations. It was often ranked as the primary number one factor or the number two ranked factor. Many interactions with the temperature were also significant. This, combined with improved tool cooling methods, should result in all tools living a longer time while undergoing less chatter and/or deflection.

In this study, two degrees of freedom planar compliant five-bar mechanism design is explored and synthesized to achieve a desired trajectory and to perform various defined tasks. The mechanism consists of five rigid links (including the ground) connected by the compliant large deflecting short beam joints and it is excited by the applied torques at the base links. The compliant five bar mechanism has not been explored in the literature for either a path tracking task or a function generation problem. The novelty of the compliant five bar mechanism presented in this paper is its large deflecting/rotating pivots joining the mechanism links. The mathematical model of the compliant five-bar mechanism is derived by using vector loop closures and dynamic inertia equations of the mechanism links. The dynamic response of the mechanism is investigated under the applied torques to the corresponding base links, using numerical 4 th order Runge-Kutta methods. Compliant joints are represented by their equivalent torsional spring parameters so that the nonlinear large deflection equations of short beam joints are eliminated from the kinematic equations of the system using its equivalent Pseudo Rigid Body Model (PRBM). The torsional spring constants can be obtained, either by using nonlinear exact mathematical equations or by using geometrically nonlinear Finite Element Method software. The scope of this research is to derive a mathematical model of the system and to analyze the compliant five bar mechanism including the controller design for arbitrary predefined tasks to achieve the desired path for the end effector. The compliant five-bar mechanisms are superior to traditional rigid five-bar mechanisms in high precision tasks since compliant joints and links have no backlash and friction. This study explores path generation of compliant five bar mechanism resulting in high precision path tracking. The presented mechanism might be manufactured as a single piece using an injection molding technique or 3D printing by polypropylene and it is also suitable for a fully compliant Micro Electro Mechanical System fabrication. The mathematical model of the mechanism is validated by utilizing inverse-forward dynamic model. The tip point of the mechanism successfully follows the reference trajectory by employing model based PID controller.

In recent years, piezoelectric actuators have been extensively utilized in novel technologies such as insect-sized micro air vehicles. Utilization of common piezoceramics and high performance nanocomposite materials coupled with special geometry like trapezoidal plates which are driven at high electric field yields suitable actuators for use in such applications. First, in this paper the nonlinear vibrations of the carbon nanotube reinforced composites cantilever trapezoidal plate with two surface-bonded piezoelectric layers is modeled in accordance to classical laminate plate theory and large deflection Von Karman type equations for the geometric nonlinearity by using the Hamilton’s principle. The geometry of trapezoidal plate is mapped into rectangular computational domain. Second, the Galerkin discretization method is used for changing the partial differential equations into ordinary differential equations. Finally, the governing equations of the motion of piezoelectric laminated carbon nano-tube reinforced composite trapezoidal actuator with cubic nonlinearities under the external excitation and strong electric field with considering electroelastic and electrostrictive effects, is modeled and the linear natural frequency of transversal deflection is obtained.

Static deflections due to static loadings limit the isolation performance of linear vibration isolation systems. Therefore, quasi-zero stiffness (QZS) mechanisms, i.e. nonlinear isolators with high static and low dynamic stiffness characteristic, are used to decrease the natural frequency of the isolation structure and improve the isolation performance of the system while having the same loading capacity. However, the resulting system is highly nonlinear and unstable solutions may as well occur. Although increasing the amount of linear viscous damping in the system reduces the nonlinearity, it has adverse effect on the isolation region. Geometrically nonlinear damping is effective when the response of the isolation system increases; hence, isolation region is unaffected. Combination of position depended nonlinear damping and QZS mechanism eliminates highly input depended response of QZS mechanism. In this study, a single degree of freedom system with a nonlinear isolator having QZS mechanism and geometrically nonlinear damping is considered. The nonlinear differential equations of motion of the isolation system are converted into a set of nonlinear algebraic equations by using harmonic balance method, which are solved by using Newton’s method with arc-length continuation. Several case studies are performed and the effect of stiffness and loading deviations on the isolation performance is studied.

During the discharge of large cylindrical silos, significant vibrations, pulsations and quaking are often created. The vibrations are typically accompanied by acoustical emissions referred to as silo honking. Such noise pollution is a health and safety concern for workers at site (e.g., hearing loss due to prolonged exposure). From a structural integrity standpoint, the vibrations contribute to the fatigue failure of the load carrying members and connections and endanger the safety and integrity of the overall system. The associated forces and deflections are often further amplified due to resonance between the silo support structure and the discharge loading frequencies. In order to avoid exciting one of the silo support structure modes, researchers and engineers often employ simplified mass-spring models to predict the natural frequencies of the structure. However, these models do not always capture all of the important modes of the silo system. In this paper, a detailed finite element model is developed to predict all of the dominant modes (vertical and side-way swaying) of the system. Beam, shell, and solid elements are used to model the silo support structure, silo walls, and the potash mass, respectively. For the experimental study, several strain gauges and accelerometers were installed on a full-scale silo support structure to determine the frequency of loading during material discharge. This paper summarizes the results of the numerical and experimental study that has been performed.

A mechanical system sliding on a moving surface with Coulomb friction is a rich area for study. Despite much past work, there is still something to be gleaned by closed-form expressions for the system behavior. Consider a spring-mass-damper system (K, M, C) with deflection x, base moving in the +x direction at velocity V , sliding friction F , and sticking friction F s . An initial condition of x 0 at rest can be considered general because all possible motions will follow. Two dimensionless schemes are used. For the abstract, we focus on the scheme normalized by x 0 with variable z = x/x 0 , τ = ( ω n t , ω n = [ K/M ] 1/2 , ζ = c /[2( KM ) 1/2 ], ν̄ = V / ( ω n x 0 ), f = F /( Kx 0 ), and f s = F s /( Kx 0 ). Since the solution is piecewise linear, this allows closed-form results. For this abstract, we consider C = 0, F s = F . (Other cases are in the paper.) There are three critical ground speeds. The first, ν̄ d , is when sticking first occurs (at z = f ). At the second speed, ν̄ c , sticking has moved to z = − f . Thereafter, the sticking point again increases, reaching z = f at the third speed, ν̄ b . For higher ν̄ , there is no sticking. In this paper, closed form expressions are presented for the three critical speeds: (1) ν ¯ d = [ ( 1 + 3 f ) ( 1 − 5 f ) ] 1 2 , ν ¯ c = [ ( 1 + f ) ( 1 − 3 f ) ] 1 2 , ν ¯ b = 1 − f These formulas are verified by numerical simulation. The insight is that there is a limited range of f for which certain critical points can be reached. Thus, 0 < f < 1/5 has different dynamics than 1/5 < f < 1/3. Formulas are also derived for the second maximum of z, which gives an indication of decay or growth of the system. For example, with f = f s and C = 0, the second maximum z with f < 1/5 is: (2) z max = f + ( ( 1 − f ) 2 − ν ¯ 2 − 4 f ) 2 + ν ¯ 2 ν ¯ d < ν ¯ < ν ¯ c z max = ν ¯ + f ν ¯ c < ν ¯ < ν ¯ b z max = 1 ν ¯ > ν ¯ c Formulas will also be given for the times at which the maximum occurs and the times at which a transition occurs from static to sliding for all cases.