Tunable Three-Dimensional Vibrational Structures for Concurrent Determination of Thin Film Modulus and Density

2021 ◽  
pp. 1-15
Author(s):  
Hairui Wang ◽  
Chen Wei ◽  
Yao Zhang ◽  
Yinji Ma ◽  
Ying Chen ◽  
...  
Keyword(s):  
Thin Film ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Theoretical Models ◽  
Structural Vibration ◽  
Small Scale ◽  
Vibration Modes ◽  
Film Material ◽  
Film Properties ◽  
Out Of Plane

Abstract The real-time characterization of thin film properties can provide insights into the behavior of film material during process such as phase-transition, hydration and chemical reaction. The shift of reasonant frequency in structural vibration serves as the basis of an effective approach to determine film properties, but encounters the difficulty that multiple to-be-determined quantites (e.g. film modulus and density) are often related to the resonant frequency simultaneously and therefore cannot be determined by a structure with fixed shape and vibration mode. Determinsitic mechanical buckling provides an effective route for the vibrational structure to rapidly switch between designed shapes and vibration modes. Here, we adopt a ribbon structure in the flat state and buckled state to yield two distinct vibration modes. Theoretical models of the natural frequencies are established for first-order out-of-plane modes of the ribbon with patterned thin films in these two states, respectively. The model suggests that with optimized film pattern the sensitivity of the natural frequencies to the film modulus and density can be partially decoupled. The results lead to a simple and effective method based on tunable vibration to characterize the thin film modulus and density at small scale.

In-Plane Vibration Modes of Arbitrarily Thick Disks

1997 ◽  
Author(s):  
Kevin I. Tzou ◽  
Jonathan A. Wickert ◽  
Adnan Akay
Keyword(s):  
Natural Frequencies ◽  
Arbitrary Dimension ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Three Dimensional Model ◽  
Bending Vibration ◽  
Annular Disk ◽  
Out Of Plane ◽  
Plane Bending

Abstract The three-dimensional vibration of an arbitrarily thick annular disk is investigated for two classes of boundary conditions: all surfaces traction-free, and all free except for the clamped inner radius. These two models represent limiting cases of such common engineering components as automotive and aircraft disk brakes, for which existing models focus on out-of-plane bending vibration. For a disk of significant thickness, vibration modes in which motion occurs within the disk’s equilibrium plane can play a substantial role in setting its dynamic response. Laboratory experiments demonstrate that in-plane modes exist at frequencies comparable to those of out-of-plane bending even for thickness-to-diameter ratios as small as 10−1. The equations for three-dimensional motion are discretized through the Ritz technique, yielding natural frequencies and mode shapes for coupled axial, radial, and circumferential deformations. This treatment is applicable to “disks” of arbitrary dimension, and encompasses classical models for plates, bars, cylinders, rings, and shells. The solutions so obtained converge in the limiting cases to the values expected from the classical theories, and to ones that account for shear deformation and rotary inertia. The three-dimensional model demonstrates that for geometries within the technologically-important range, the natural frequencies of certain in- and out-of-plane modes can be close to one another, or even identically repeated.

In-Plane Vibration Modes of Arbitrarily Thick Disks

1998 ◽  
Vol 120 (2) ◽  
pp. 384-391 ◽  
Author(s):  
K. I. Tzou ◽  
J. A. Wickert ◽  
A. Akay
Keyword(s):  
Natural Frequencies ◽  
Arbitrary Dimension ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Three Dimensional Model ◽  
Bending Vibration ◽  
Annular Disk ◽  
Out Of Plane ◽  
Plane Bending

The three-dimensional vibration of an arbitrarily thick annular disk is investigated for two classes of boundary conditions: all surfaces traction-free, and all free except for the clamped inner radius. These two models represent limiting cases of such common engineering components as automotive and aircraft disk brakes, for which existing models focus on out-of-plane bending vibration. For a disk of significant thickness, vibration modes in which motion occurs within the disk’s equilibrium plane can play a substantial role in-setting its dynamic response. Laboratory experiments demonstrate that in-plane modes exist at frequencies comparable to those of out-of-plane bending even for thickness-to-diameter ratios as small as 10−1. The equations for three-dimensional motion are discretized through the Ritz technique, yielding natural frequencies and mode shapes for coupled axial, radial, and circumferential deformations. This treatment is applicable to “disks” of arbitrary dimension, and encompasses classical models for plates, bars, cylinders, rings, and shells. The solutions so obtained converge in the limiting cases to the values expected from the classical theories, and to ones that account for shear deformation and rotary inertia. The three-dimensional model demonstrates that for geometries within the technologically-important range, the natural frequencies of certain in- and out-of-plane modes can be close to one another, or even identically repeated.

Free Vibration of Coupled Disk-Hat Structures

1999 ◽  
Author(s):  
Jun-Chul Bae ◽  
Jonathan Wickert
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Phase Relationship ◽  
Vibration Modes ◽  
Pure Bending ◽  
Brake Rotors ◽  
Automotive Brake ◽  
Ordered Pairs

Abstract The free vibration of disk-hat structures, such as automotive brake rotors, is investigated analytically and through laboratory experimentation. Of particular interest are the role played by the hat element’s depth in influencing the three-dimensional vibration of the disk, and the manner in which the bending and in-plane modes of the disk alone evolve as a hat of increasing depth is incorporated in the model. The lower vibration modes of disk-hat structures are shown to be characterized by the numbers of nodal circles NC and diameters ND present on the disk, as well as the phase relationship between the disk’s transverse and radial displacements due to coupling with the hat element. Such modes map continuously back to the pure bending and in-plane modes of the disk alone, appear in ordered pairs, and can exist at close frequencies. Those characteristics are explored particularly with respect to sensitivities in the disk’s thickness and the hat’s depth with a view towards shifting particular natural frequencies, or minimizing transverse disk motion in certain vibration modes. Results obtained through analysis and measurement of a prototypical disk-hat structure are applied in a case study with a ventilated automotive brake rotor.

The Three-Dimensional Dynamics for Toroidal Drive

2012 ◽  
Vol 562-564 ◽  
pp. 536-539
Author(s):  
Li Zhong Xu ◽  
Jin Liang Li ◽  
Ya Jun Li
Keyword(s):  
Natural Frequencies ◽  
Cone Angle ◽  
Three Dimensional ◽  
Drive System ◽  
Vibration Modes ◽  
Mesh Stiffness ◽  
Coupled Modes ◽  
Bearing Stiffness ◽  
Rigid Body Motions ◽  
Half Cone

In this paper, a model to simulate the dynamic behavior of the toroidal drive is developed. The three-dimensional dynamic model includes all six rigid body motions of the stator, worm, rotor and the planets. Using the model, the natural frequencies and vibration modes of the drive system are investigated. The vibration modes are classified into single modes and coupled modes. The single modes include planet mode, worm mode and stator mode. The vibration and frequency characteristics of different modes are obtained. The relation between modes and half cone angle of the planet tooth is discussed. The relation between vibrations and bearing stiffness is also discussed. When the bearing stiffness is about 10 times of the mesh stiffness, some vibration displacements of the drive system are quite small and can be neglected. Meanwhile, the dynamic equations for the drive system can be simplified.

Feasibility of Two-Dimensional Control for Ship-Mounted Cranes

2001 ◽  
Author(s):  
Eihab M. Abdel-Rahman ◽  
Ali H. Nayfeh
Keyword(s):  
Natural Frequencies ◽  
Three Dimensional ◽  
Major Axis ◽  
Double Pendulum ◽  
Spherical Pendulum ◽  
Safe Operation ◽  
Control Effort ◽  
Pendulum System ◽  
Out Of Plane ◽  
The One

Abstract We test the feasibility of employing an exclusively planar control effort to suppress unsafe ship-mounted crane pendulations induced by sea motions. The new crane configuration, designed to apply the control effort, is modeled and the proposed control effort, employing Coulomb friction and viscous damping, is applied. The three-dimensional nonlinear dynamics of the crane is then investigated. The new crane configuration, dubbed Maryland Rigging, transforms a crane from a single spherical pendulum to a double pendulum system. The upper pendulum, a pulley riding on a cable suspended from the boom, is constrained to move over an ellipsoid. The major axis of the ellipsoid is the boom and the foci are the two points at which the riding cable attaches to it. The lower pendulum, the payload suspended by a cable from the pulley, continues to act as a spherical pendulum. Due to the geometry of the ellipsoid, the natural frequencies of the crane in the plane of the boom (in-plane) are almost equal to the out-of-plane natural frequencies. The model is used to examine the response of a Maryland rigged crane to direct, in-plane, harmonic forcing. The frequency of the excitation is set almost equal to the crane’s lowest natural frequency. It is found that under this excitation and due to the one-to-one internal resonance between the lowest in-plane and out-of-plane natural frequencies, significant out-of-plane motions are induced by applying a purely in-plane forcing. Thus an in-plane control mechanism is not adequate for safe operation of the crane. To guarantee safe operation of a ship-mounted crane, one must apply both in-plane and out-of-plane control efforts.

scholarly journals Component Mode Synthesis Method Applied to Acoustic Resonators in Ducts for Structural Vibration Analysis

2020 ◽  
Vol 25 (4) ◽  
pp. 498-503
Author(s):  
Jose Manuel Bautista Ordóñez ◽  
Maria Alzira de Araújo Nunes
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Modal Analysis ◽  
Natural Frequencies ◽  
Component Mode Synthesis ◽  
Structural Vibration ◽  
Structural Systems ◽  
Vibration Modes ◽  
The Finite Element Method ◽  
Element Method

Tubular structural systems appear in many industrial applications, such as heating, ventilation, and air conditioning systems, which are responsible for making any enclosed environment remain within a temperature, humidity, and cleanliness range. This kind of system has its applications in the internal environmental comfort of industrial spaces, buildings, and vehicles. Several of these spaces have industrial processes that generate high sound frequencies and mechanical vibrations that need to be adequately controlled to meet both environmental and health norms. With the intention to analyze the structural vibration of tubular systems, the modal analysis technique is a classical methodology for the extraction of natural frequencies and vibration modes. Among the various techniques of modal analysis, numerical methodologies such as the finite element method, and also analytical methodologies such as the Component Mode Synthesis (CMS) can be found. CMS is one of the leading modeling tools for complex systems that are applied to large systems. The method uses a modal superset and consists of separately modeling individual components of a structure and coupling them into a single system. The objective of this work is to demonstrate the application of the CMS technique through the estimation of natural frequencies and vibration modes in a simplified tubular structural system formed by two substructures, using MATLAB and ANSYS. The validation of the results was done through numerical modeling using the finite element method using and ANSYS software. The results obtained were satisfactory, thus demonstrating the feasibility of applying the CMS technique to an analysis of structural vibration in tubular structural systems.

Two-Dimensional Control for Ship-Mounted Cranes: A Feasibility Study

2003 ◽  
Vol 9 (12) ◽  
pp. 1327-1342 ◽  
Author(s):  
Eihab Abdel-Rahman ◽  
Ali H Nayfeh
Keyword(s):  
Natural Frequencies ◽  
Three Dimensional ◽  
Major Axis ◽  
Double Pendulum ◽  
Spherical Pendulum ◽  
Safe Operation ◽  
Control Effort ◽  
Pendulum System ◽  
Out Of Plane ◽  
The One

We test the feasibility of employing an exclusively planar control effort to suppress unsafe ship-mounted crane pendulations induced by sea motions. The new crane configuration, designed to apply the control effort, is modeled and the proposed control effort, employing Coulomb friction and viscous damping, is applied. The three-dimensional nonlinear dynamics of the crane is then investigated. The new crane configuration, dubbed Maryland rigging, transforms a crane from a single spherical pendulum to a double pendulum system. The upper pendulum, a pulley riding on a cable suspended from the boom, is constrained to move over an ellipsoid. The major axis of the ellipsoid is the boom and the foci are the two points at which the riding cable attaches to it. The lower pendulum, the payload suspended by a cable from the pulley, continues to act as a spherical pendulum. Due to the geometry of the ellipsoid, the natural frequencies of the crane in the plane of the boom (in-plane) are almost equal to the out-of-plane natural frequencies. The model is used to examine the response of a Maryland rigged crane to direct, in-plane, harmonic forcing. The frequency of the excitation is set almost equal to the crane's lowest natural frequency. It is found that under this excitation and due to the one-to-one internal resonance between the lowest in-plane and out-of-plane natural frequencies, significant out-of-plane motions are induced by applying a purely in-plane forcing. Thus, an in-plane control mechanism is not adequate for safe operation of the crane. To guarantee safe operation of a ship-mounted crane, both in-plane and out-of-plane control efforts must be applied.

Conjugate Analysis of Thin Film Heat Spreaders to Reduce Temperature at Hot Spots

2015 ◽  
Author(s):  
Sohail R. Reddy ◽  
Abas Abdoli ◽  
George S. Dulikravich ◽  
Rajesh Jha
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Hot Spot ◽  
Three Dimensional ◽  
Effective Area ◽  
Heat Transfer Analysis ◽  
Maximum Temperature ◽  
Film Material ◽  
Electric Circuits ◽  
Heat Spreaders

The effects of thin film coating on maximum temperature of integrated electric circuits are investigated. A fully three-dimensional conjugate heat transfer analysis was performed to investigate the effects of thin film material and thickness on the temperature of a hot spot. Two different materials, diamond and graphene nano-platelets were simulated as materials for thin films. The thin film heat spreaders were applied to the top wall of the three optimized arrays of micro pin-fins having circular, airfoil and convex cross sections. The electronic chip with a 4 × 3 mm footprint featured a 0.5 × 0.5 mm hot spot located on the top wall which was exposed to a uniform high-level background heat flux. The effective area of coverage of the thin films was also investigated computationally. It was found that thin film heat spreaders significantly reduce the hot spot temperature, allowing for increased thermal loads and therefore increased performance. Furthermore, it was found that thickness of the thin film heat spreader does not have to be greater than a few tens of microns.

Triangular relationship between vibration modes of an elastically supported rigid body with a plane of symmetry

2011 ◽  
Vol 226 (5) ◽  
pp. 1254-1262 ◽  
Author(s):  
S-J Jang ◽  
J W Kim ◽  
Y J Choi
Keyword(s):  
Rigid Body ◽  
Natural Frequencies ◽  
Vibration Modes ◽  
Geometrical Properties ◽  
Plane Vibration ◽  
Numerical Example ◽  
Mass Centre ◽  
Out Of Plane ◽  
Triangular Relationship ◽  
Elastically Supported

The geometrical properties of vibration modes of a single rigid body with one plane of symmetry are presented. When in-plane vibration modes are represented by the axes normal to the plane of symmetry, three intersecting points of those axes and the plane of symmetry constitute two triangles whose orthocentres are coincident with the mass centre and planar couple point, while the induced wrenches of three out-of-plane modes are found to form two triangles whose orthocentres are lying on the mass centre and the perpendicular translation point. Examining these triangles reveals that the triangular areas are proportional to the distributions of the mass and stiffness in the vibrating system and the shapes of the triangles are related to the natural frequencies. A numerical example is provided to verify the proposed findings.

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