Taper Parameter Research Articles

Parametric Stability Analysis of a Spring Attached, Pre-Twisted, Rotating Sandwich Beam with Tip Mass and Viscoelastic Support

This paper inspects the influence of a spring attachment provided on the top elastic layer on the stability of a pre-twisted, rotating sandwich beam having viscoelastic supports at the root under the impact of a periodically varying axial load. The spring is deployed on the beam to achieve more strength to weight ratio without compromising the stability. The beam is exponentially tapered, and a tip mass is at the free end to represent the rotating members in various types of machinery as closely as possible. The ruling equations and inter-related boundary conditions are attained by applying Hamilton’s principle. To obtain the solution, a matrix equation was developed through the assumed-mode variational method. The resulting matrix equation was converted to a coupled Hill’s equation of parametric vibration through the modal matrix corresponding to the free vibration problem. Finally, static and dynamic stability graphs were obtained for several system parameters such as position and length of the attached spring on the top elastic layer, the mass of the spring attachment, stiffness of the spring attachment, angle of pre-twist, tip mass, taper parameter, temperature gradient parameter, setting angle, viscoelastic spring stiffness, etc. to analyze their impact on the system’s stability. Saito and Otomi conditions were used to obtain dynamic stability plots. Greater stability is achieved due to the spring attachment on the top of the top elastic layer.

Effect of taper parameters on mechanical seal performance of taper/pores composite mechanical seal

a new combination fluid seal with the cone/pores is given, and the 3D fluid/solid coupling theory model is constructed, considering the interaction between the liquid pressure field and the stress deformation of the seal rings, led to seal clearance unceasingly change. Through the corresponding numerical calculation, film pressure distribution and end face deformation situation are obtained between the seal end faces, the influence rule of taper on sealing performance under the high and low pressure conditions is analyzed. The results show that the dynamic pressure effect caused by rhomboid pores can produce circumferential and radial wavy deformation of the seal end faces, while the static pressure effect also changes with the taper change of the end faces. For the low pressure and medium speed equipment, the conical end face which the taper is 0-2.4 should be chosen priority. For higher pressure and rotational speed device, the convergence end face seal which the taper is 0-2.4 should first be chosen.

Parametric Analysis of a Rotational Piezoelectric-Coupled Tapered-Bimorph Structure with Various Boundary Conditions Under Transient Axial Loading

The steady-state parametric analysis of a piezoelectric-coupled rotating tapered-bimorph system consists of a central host beam and two piezoelectric ceramic patches above and below it, tapering along positive X-direction and rotating in the X–Y plane, subjected to axial dynamic as well as static loading at its one end is done. The influence of three boundary conditions and various system parameters are also studied. The mathematical modeling of the rotating tapered-bimorph system is formulated with the help of Hamilton's equation. The parametric analysis of the axially loaded system is done for clamped-free (C-F), pinned-pinned (P-P), and clamped-pinned (C-P) boundary conditions. A number of parametric instability regions along with static buckling load plots are obtained and analyzed for various values of the piezoelectric patches to the host beam thickness ratio, taper parameter, and rotational frequency using MATLAB software and depicted through a series of diagrams. The results illustrate that the principal modal frequencies of the tapered-bimorph rotating system are increased rapidly with an increase in the thickness ratio, whereas increase less significantly with a rise in taper parameter and spinning speed for both the static and dynamic loading conditions. The lowest first modal frequency is observed for the P-P system under any given system configurations and operating conditions, which can be used for low-frequency rotational vibration energy harvester over the orthodoxly used C-F system. Designing low-frequency rotational vibration energy harvester and rotor blades can be done by selecting appropriate dimensions and parameters presented in this article.

Study of dynamic stability of exponentially tapered asymmetric sandwich beam on Pasternak foundation

Abstract The work aims at the investigation of dynamic stability of an asymmetric sandwich beam varying exponentially and resting on a Pasternak foundation. The stiffness of the Pasternak foundation varies linearly with displacement. The extended Hamilton’s principle is used to derive the governing equations of motion and associated boundary conditions. The system of equations is non-dimensionalized. Using Galerkin’s method, a set of Hill’s equations are obtained. The dynamic stability is analyzed using Saito-otomi conditions. The effects of elastic foundation parameter, thermal gradient, shear parameter, taper parameter, core-loss factor and modulus ratios on dynamic stability of the system is studied for pinned–pinned boundary condition. The results are represented graphically using suitable MATLAB program.

Analysis of dynamic stability of a tapered two layer elastic beam resting on a variable Pasternak foundation subjected to axial pulsating load

The main aim of this work is to investigate the dynamic stability of a tapered two layer beam resting on a Pasternak foundation is subjected to axial pulsating load. The analysis is done for two boundary conditions i.e. Clamped-Clamped and Clamped-Pinned using computational method. The equation of motion and boundary conditions are derived using Hamilton’s principle. A set of Hill’s equation is obtained from generalized Galerkin’s method. The dynamic stability of the system is analyzed by using the Saito-Otomi conditions. The effects of different geometrical parameters, modulus ratio, taper parameter and elastic foundation parameter on the regions of parametric instability of the system are investigated using required MATLAB code.

Free vibration response of internally-thickness-tapered laminated composite square plates based on an energy method

In the present work, the free vibration response of symmetric linearly-thickness-tapered laminated composite square plates is considered for a variety of taper configurations. Since exact and closed-form solutions for the natural frequencies and mode shapes of the plates could not be obtained from the corresponding complex partial differential equations in space and time coordinates, the Ritz method in conjunction with the Classical Laminated Plate Theory (CLPT) and then the First-order Shear Deformation Theory (FSDT) is used to obtain the system’s mass and stiffness matrices for out-of-plane bending vibrations. The free vibration analysis of the plates is conducted using these system matrices and the natural frequencies and mode shapes are determined. Different boundary conditions are considered for the free vibration response of the plates and the computational work is performed in the MATLAB® environment. The convergence of the series expansions used for the out-of-plane displacement functions and the Ritz solutions for plates with various boundary conditions are established. The demonstration of solution accuracy is performed by conducting a so-called “layer reduction test” and also by comparing the results obtained by using the Ritz method with the solution obtained based on the Finite Element Method (FEM) using ANSYS®. A parametric study is then conducted to investigate the influences of taper configurations and taper parameters on the free vibration response of the composite plates.

A numerical study on the thermal buckling of variable thickness Mindlin circular FGM plate on a two-parameter foundation

In the present work, the symmetric thermal buckling behavior of shear deformable heterogonous circular plates of variable thickness resting on a two parameter foundation is studied. The plate material properties assumed to be graded across the thickness direction according to a simple power law, and the plate thickness assumed to be varied along the radial direction within another power function. Implementing Mindlin's plate theory and the nonlinear von-Karman strain field, the plate stability equations together with the membrane equilibrium equation are derived and expressed in terms of the displacement field components. Then the nondimensionalized forms of the equations are discretized along with their corresponding boundary conditions by employing differential quadrature method (DQM). The resulting set of linear algebraic equations constitutes an eigenvalue problem, which can be solved to evaluate the plate critical buckling temperature difference. The present DQ formulation has fast convergence with more accurate results than those of recent references. The influences of some important parameters including the plate taper parameter and Pasternak bed coefficients on the buckling load and mode shape are investigated, which comprise some novel results useful for design optimization of such structural elements.

Effect of Winkler Foundation on Radially Symmetric Vibrations of Bi-Directional FGM Non-Uniform Mindlin’s Circular Plate Subjected to In-Plane Peripheral Loading

An analysis has been presented of the effect of elastic foundation and uniform in-plane peripheral loading on the natural frequencies and mode shapes of circular plates of varying thickness exhibiting bi-directional functionally graded characteristics, on the basis of first order shear deformation theory. The material properties of the plate are varying following a power-law in both the radial and transverse directions. The numerical solutions of the coupled differential equations leading the motion of simply supported and clamped plates acquired by using Hamilton’s principle, is attained by harmonic differential quadrature method. The effect of different plate parameters namely gradient index, heterogeneity parameter, density parameter, taper parameter and thickness parameter is illustrated on the vibration characteristics for the first three modes of vibration for various values of in-plane peripheral loading parameter together with foundation parameter. Critical buckling loads in compression are calculated for both the boundary conditions by putting the frequencies to zero. The reliability of the present technique is confirmed by comparing the results with exact values and results of published work.

Numerical Computation of First Three Frequencies for Circular Plate with Transcendental Thickness

In the present work, a very important approach Rayleigh-Ritz method has been used to compute the first few frequencies of a circular plate. The boundary conditions of circular plate are considered as a clamped and simply-supported. Different types of thickness variation of circular plate have been considered by researchers and a vast numbers of numerical results are available in the literature but none of the researchers consider the transcendental thickness variation which has been considered in the present work. The type of circular plate is considered as isotropic plate and significant numerical computations have been done for finding first three frequencies by varying the order of approximation and also the taper parameter. In special cases, results have been compared for uniform, linearly varying and transcendental thickness variations of circular plate and computed result are presented in the form of tables and graphs.

Stability analysis of an exponentially tapered, pre-twisted asymmetric sandwich beam on a variable Pasternak foundation with viscoelastic supports under temperature gradient

The purpose of this work is to study the stability of an exponentially tapered, pre-twisted and asymmetric sandwich beam on a variable Pasternak foundation, propped at ends. Viscoelastic translational and rotational springs have been employed to include the resistance offered by pinned–pinned end supports. The system is subjected to pulsating axial loads, and the elastic layers are subjected to a temperature gradient due to steady heat flow. A set of equations of motion was obtained by using Hamilton’s principle, and instability regions were plotted using formulae developed by Saito and Otomi. The effects of pre-twist angle, temperature gradient, taper parameter, shear modulus of the core, core loss factor, stiffness of the Pasternak foundation and rotational spring stiffness on static stability and regions of parametric instability were studied. Increase in the value of pre-twist angle was observed to be detrimental to both dynamic and static stability of the system. It was found that the dynamic stability of the system also degraded with an increase in the taper parameter.

Vibrational Behavior of Tapered Triangular Plate with Clamped Ends under Thermal Condition

In the present study, the effect of thermal gradient on the vibration of different types of triangular plates is discussed. Tapering in triangular plate is assumed bilinear. Variation in temperature of plate material is considered as linear in x-direction. The Rayleigh–Ritz technique is employed to evaluate the first two modes of frequency parameter for different values of thermal gradient, taper parameters and aspect ratios. The author reported frequency for both the modes of vibration for different types of clamped triangular plates, i.e., an isosceles triangular plate, right-angled isosceles triangular plate and scalene triangular plate. All numerical results are presented in tabular form.

Static and Dynamic Stability Analysis of an Asymmetric Rotating Tapered Sandwich Beam Subjected to Pulsating Axial Load with Thermal Gradient

The static and dynamic stability of an asymmetric rotating tapered sandwich beam subjected to pulsating axial load in temperature environment is studied under two different boundary conditions. The non-dimensional equations of motion and the boundary conditions are derived by applying Hamilton's energy principle. A coupled Hill's equations with complex coefficients are derived from the non-dimensional equations of motion by the application of the generalized Galerkin method. By the application of the Saito-Otomi conditions, zones of instabilities are obtained and presented graphically. For the calculation of the Young's module for the elastic layers, the effect of temperature has been taken in to consideration by means of a uniform thermal gradient along the longitudinal axes for both the upper and lower elastic layers. The effects of the taper parameter, core loss factor, thermal gradient, rotational speed, hub radius, and core density parameter on the static buckling loads and the regions of instability are investigated.

Nanoimprinting and tapering of chalcogenide photonic crystal fibers for cascaded supercontinuum generation.

Improved long-wavelength transmission and supercontinuum (SC) generation is demonstrated by antireflective (AR) nanoimprinting and tapering of chalcogenide photonic crystal fibers (PCFs). Using a SC source input spanning from 1 to 4.2μm, the total transmission of a 15μm core diameter PCF was improved from ∼53% to ∼74% by nanoimprinting of AR structures on both input and output facets of the fiber. Through a combined effect of reduced reflection and redshifting of the spectrum to 5μm, the relative transmission of light >3.5 μm in the same fiber was increased by 60.2%. Further extension of the spectrum to 8μm was achieved using tapered fibers. The spectral broadening dynamics and output power were investigated using different taper parameters and pulse repetition rates.

Improved filter bank on multitaper framework for robust Punjabi-ASR system

Robustness of the automatic speech recognition (ASR) system relies upon the accuracy of feature extraction and classification in training phase. The mismatch between training and testing conditions during classification of large feature vectors causes a low performance. In this paper, the issue of robustness of acoustic information is addressed for practical Punjabi dataset. Traditional feature extraction approaches: mel frequency cepstral coefficients (MFCC) and gammatone frequency cepstral coefficients (GFCC) face the issue of high variance with leakage of spectral information. Also, handling of the huge number of feature information creates chaos for large speech vocabulary. To overcome this dilemma, a Principal component analysis (PCA) based multi-windowing technique is proposed with the incorporation of baseline GFCC and MFCC based feature approaches after the tuning of taper parameter. The proposed integrated approaches result in better feature vectors, which are further processed using differential evolution + hidden Markov model (DE + HMM) based modelling classifier. The integrated approaches show substantial performance for word recognition as compared to the conventional or fused feature extraction systems.

Static and Dynamic Stability Analysis of a Rotating Taper Beam Having Elliptical Cross Section Subjected to Pulsating Axial Load With Thermal Gradient

The static and dynamic stability of a rotating tapered beam having an elliptical cross-section subjected to a pulsating axial load with a thermal gradient is investigated under three different boundary conditions, such as clampedclamped (C-C), clamped-pinned (C-P), and pinned-pinned (P-P). The governing equations of motion have been derived by using Hamilton’s energy principle. A set of Hill’s equations have been obtained by the application of generalized Galerkin’s method. The effects of taper parameter, hub radius, rotational speed, thermal gradient, and geometric parameter on the static buckling loads and the regions of instability have been studied and the results are presented graphically

Influence of wedge shape on the performance of air foil thrust bearings

PurposeThe purpose of this paper is to investigate the effect of different wedge shapes on the performance of air foil thrust bearing (AFTB).Design/methodology/approachDuring the study, a bump foil stiffness model considering slip deformation and a two-dimensional sheet top foil model is established, and the Reynolds equation and film thickness equation is solved using the finite difference method and finite element method. The static performance such as load carrying capacity, friction torque and power loss of AFTB under different taper parameters is obtained. The influence of different pitch ratio, film thickness ratio and wedge shapes on the bearing characteristics is studied.FindingsThere is an optimal height and a pitch ratio for the taper of AFTB with certain tile number. Compared to the plane and concave wedge shape, the upper convex shape can enhance the convergence effect of the wedge region, increase the effective film pressure distribution area of the bearing and reduce the local concentrated load of the top foil, which is more conductive to the increase of load capacity.Originality/valueThe wedge shape parameters bring a fundamental difference in the static performance of AFTB. The results are expected to be helpful to bearing designers, researchers and academicians concerned.

Longitudinal vibration responses of axially functionally graded optimized MEMS gyroscope using Rayleigh–Ritz method, determination of discernible patterns and chaotic regimes

Axial vibration analysis of an optimized MEMS gyroscope is investigated in this paper. For this purpose; a model of rotating, axially functionally graded (tapered) nano-rod is represented. Along with classical continuum mechanics, Eringen’s non-local theory is adopted. Using Hamilton’s variational approach along with coupled displacement field concept which is derived from Babaei and Yang, governing equations of motion are derived. Rayleigh–Ritz approximate method is used to solve the equation for both clamped–clamped and clamped-free rod model. Verification of current results is ratified by comparison with results available in technical literature. Incorporation of taper parameter, non-local effect and rotation effects reveals predictable patterns along with unpredictable chaotic behavior of the optimized gyroscope. Such outcomes report necessity of precise and case-by-case perusal as for some specific values of taper and non-local parameters; system results unpredictable responses. In such chaotic regimes, pattern detection based on response of the gyroscope is impossible and a kind of real-time monitoring and analysis is required. Excluding critical values of the mentioned parameters of non-locality and taper; generally rotations around a fixed axis leads to lessening the oscillations, enhancing the non-locality yields weak vibrations, and intensifying the taper effects makes the system oscillate with greater frequencies wherein for quite high values of taper parameter, gyroscope model behavior turns out independent. It is good to mention that only case in which increment of taper parameter suppresses vibrations occurs when cross-section area of clamped-free nano-rod model is increasing. Eventually, influential factors of current model are revealed.

Thermal effect on radially symmetric vibrations of temperature-dependent FGM circular plates with nonlinear thickness variation

Thermo-elastic analysis for the free axisymmetric vibration of functionally graded circular plates with quadratic thickness variation along radial direction has been presented on the basis of classical theory of plates. Following a power law model, the plate is assumed to be graded in thickness direction and mechanical properties of the material are temperature-dependent. The plate is subjected to a non-linear temperature distribution in thickness direction while the thermal environment over the top and bottom surfaces is uniform. The equations for thermo-elastic equilibrium and axisymmetric motion for such a plate model have been derived using Hamilton’s principle. Employing differential quadrature method, the numerical values of thermal displacements and frequencies for clamped and simply supported plates have been computed. The influence of thickness parameters, material graded index and temperature difference on the vibration characteristics for the first three modes of vibration has been analyzed. The benchmark results for uniform and linear temperature distributions have been computed. A study with the plate material having temperature-independent mechanical properties has also been performed. Because, functionally graded materials inherently withstand high temperature gradients due to low thermal conductivity, core ductility, low thermal expansion coefficient, etc, the performance of results can help for optimal designing of non-uniform circular plates by controlling one or both the taper parameters. In special cases, the results have been compared with those obtained by other methods.

Stability Analysis of a Tapered Symmetric Sandwich Beam Resting on a Variable Pasternak Foundation

The static and dynamic stability analysis of a three-layered, tapered and symmetric sandwich beam resting on a variable Pasternak foundation and undergoing a periodic axial load has been carried out for two different boundary conditions by using a computational method. The governing equation of motion has been derived by using Hamilton’s principle along with generalized Galerkin’s method. The effects of elastic foundation parameter, core-loss factor, the ratio of length of the beam to the thickness of the elastic layer, the ratio of thickness of shear-layer of Pasternak foundation to the length of the beam, different modulus ratios, taper parameter, core thickness parameter, core-density parameter and geometric parameter on the non-dimensional static buckling load and on the regions of parametric instability are studied. This type of study will help the designers to achieve a system with high strength to weight ratio and better stability which are the desirable parameters for many modern engineering applications, such as in the attitude stability of spinning satellites, stability of helicopter components, stability of space vehicles etc.

On radially symmetric vibrations of functionally graded non-uniform circular plate including non-linear temperature rise

In this study, the free axisymmetric vibrations of functionally graded circular plate of linearly varying thickness controlled by a taper parameter in radial direction and non-linear temperature rise along the thickness have been investigated on the basis of classical plate theory. The plate material is graded in transverse direction and its mechanical properties are temperature-dependent. The temperature over the top and bottom surfaces is assumed to be uniformly distributed. Hamilton's principle has been used to derive the governing equations for thermo-elastic equilibrium and axisymmetric motion of such a plate model. The generalized differential quadrature method has been employed to obtain the thermal displacements and characteristic equations, for clamped and simply supported plates. The lowest three roots of these equations have been computed and reported as the values of frequency parameter for the first three modes of vibration. Effect of thickness parameter, volume fraction index and temperature difference has been analyzed on the vibration characteristics of the plate. A study with temperature-independent material properties has also been performed. Results have been compared with the published work.