Basic and applied research in Applied Mechanics, especially vibrations. 32 years on graduate faculty, Life Fellow ASME, Fellow AIAA and Ohio Academy of Science.
Journal of Bone and Joint Surgery, American Volume, Oct 1, 1974
The effects of altered levels of activity on the biomechanical properties of a ligament were inve... more The effects of altered levels of activity on the biomechanical properties of a ligament were investigated. After eight weeks of immobilization, anterior cruciate bone-ligament-bone preparations of wild primates tested in tension showed significant decreases in maximum failure load and energy absorbe
Mechanical properties were determined for three coating materials proposed as capable of providin... more Mechanical properties were determined for three coating materials proposed as capable of providing meaningful reductions in the vibratory amplitude of turbine blades by the internal dissipation of energy. Two were metallic materials applied by electron beam technology, one a magnetoelastic material, the other a layered material with a magnetoelastic component. The third coating was a plasma sprayed ceramic with a viscoelastic infiltrate. Properties obtained are the real and imaginary parts of a complex Young's modulus. As these are necessary for the inclusion of the influences of such coatings in preliminary design analyses, they are also the most relevant for the comparison of different materials. Values were obtained at several temperatures for strains to about 1000 ppm. A limited study of coating survivability through strains of about twice that value was also conducted.
Volume 3C: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration Control, Analysis, and Identification, Sep 17, 1995
The performance of a constrained layer damping treatment is greatly affected by its length, and t... more The performance of a constrained layer damping treatment is greatly affected by its length, and the damping effectiveness can be optimized by choosing a damping treatment length appropriate to the geometry and material properties of the viscoelastic and constraining layers. In this paper, the equilibrium equation and boundary conditions are formulated for a constraining layer on a substrate with a linearly varying strain distribution, and an analysis is developed that allows conclusions to be drawn about the optimal length of the constraining layer. Plunkett and Lee1 analyzed this problem for the special case of uniform strain in the substrate, and they showed that a loss coefficient depends only on the viscoelastic loss factor and a stiffness parameter that is a function of the material properties and thickness of the damping layers. In this paper, the uniform strain analysis is extended for the case of linearly varying substrate strain of the form ax+b, where a and b are arbitrary constants. The corresponding loss coefficient was shown to be a function of the parameters identified in the uniform strain problem, plus an additional parameter that accounts for the degree of non-uniformity of the substrate strain. It is shown that the non-uniformity of the substrate strain increases the length at which the damping treatment is optimized.
Roles for damping in vehicle design for noise suppression are identified in isolation of the vehi... more Roles for damping in vehicle design for noise suppression are identified in isolation of the vehicle from input disturbances, reducing the response to that disturbance, reducing the noise radiated due to that response, and reducing the transmission of noise. Various mechanisms for the dissipation of energy are discussed, and means of adding damping so as to reduce the dynamic response of structural elements, particularly thin sheets, are considered.
Anterior cruciate bone ligament-bone preparations of wild primates tested in tension failed at a ... more Anterior cruciate bone ligament-bone preparations of wild primates tested in tension failed at a higher load and greater elongation, and absorbed more energy, at a fast rate of deformation than at a slow rate. The major mode of specimen failure changed from a predominance of tibial avulsion fractures at the slow rate to ligament disruption at the fast rate. Failure at the two deformation rates commonly occurred by a serial mechanism involving from one to all components of the bone-ligament-bone unit to different degrees. Factors important in ligamentfailure properties included: (1) rate-dependent behaviors, (2) geometrical arrangement of collagen fibers, (3) surrounding ground-substance effects, (4) osseous insertion-site effects, and (5) the influence of non-physiological experimental loading conditions and disuse-induced changes in specimens. Because ofthe frequency and potential severity ofligament injuries, a need exists for information on the biomechanical properties of ligaments under loading conditions which occur at the time of trauma. That bone, ligaments, and other biological tissues exhibit viscoelastic behavior is now well known 2,8.11.14.15,1 719.23.25.33.52.54.56 Their load-extension behaviors are time-dependent, with the mechanical properties of the tissue dependent on the rate of loading, the rate of elongation, or both. In this regard, the change in failure properties of ligaments and bone at different rates of deformation is of particular interest to the orthopaedist in analyzing mechanisms of injury. In recent years, many studies have been performed to establish the mechanical properties and behavior of tendons and other collagenous structures 2.46,I3,172O.34.47.52,59.6o Prior studies on ligaments have provided important information 16.23.28.31.4042.43.495153.55.61; however, as yet our knowledge of their biomechanical properties is incomplete. The unique anatomical characteristics of individual ligaments, such as the twisting of the cruciates or the intricacy of the medial ligaments of the knee, impose specific structural properties which cannot be generalized to other ligaments. In addition, there appear to be important relations between macroscopic mechanical behavior and tissue microarchitecture The mechanical behavior of ligaments depends not only on the * Read in part at the Annual Meeting of the Orthopaedic Research Society, Las Vegas, Nevada, February 1, 1973. t This paper has been identified by the Aerospace Medical Research Laboratory as AMRL-TR-73-l 17. The experiments reported herein were conducted according to the “Guide for Laboratory Animal Facilities and Care” prepared by the Instituteof Laboratory Animal Resources, National Research Council. 1665 Randall Road, Yellow Springs, Ohio 45387. § Air Force Instituteof Technology, Wright-Patterson Air Force Base, Ohio 45433. 236 THE JOURNAL OF BONE AND JOINT SURGERY on April 5, 2007 www.ejbjs.org Downloaded from BIOMECHANICS OF ANTERIOR CRUCIATE LIGAMENT FAILURE 237 material properties of the fibers themselves, but also on the geometrical arrangement of collagen fibrils and fiber bundles, the proportioning of different types of fibrous constituents, and the relatively unknown effect of the surrounding ground substance 11,21,27,39,45 As will be shown in this study, the ligament insertion site and the underlying bone are additional parts of the ligament unit which must be considered in evaluating strength properties. In the analysis of ligament properties, it is often difficult to separate the effect ofthese different factors on macroscopic behavior. For these reasons, a great deal of caution is required in generalizing the mechanical properties of one ligament to other ligaments. An alternative to the approach of investigating each of the components of a ligament unit separately is afforded by using a bone-ligament-bone preparation, such as the femuranterior cruciate-tibia preparation used in this study. The mechanical properties of all components of the unit are then studied together in the same relationship that they have in the body, so that the combined interaction determines the properties of the structure, as in vivo. In the first section of this study, the effect of deformation rate (strain rate) on the ultimate failure properties of anterior cruciate bone-ligament-bone preparations was determined. In the second section we investigated the mechanism of specimen failure, in particular the failure properties of the bone and ligament components which comprise the functioning unit. Two studies were recently published on the deformation-rate sensitivity of boneligament-bone preparations 16.23 As specimens were not loaded to failure in those studies, ultimate properties were not determined. Other investigations have studied the failure properties of various ligaments, but the rate of deformation often was not controlled or recorded, and the studies often were performed under slow or quasi-static loading conditions. The slow rate…
24th Structures, Structural Dynamics and Materials Conference, May 2, 1983
ABSTRACT Fractional calculus is used to model the viscoelastic behavior of a damping layer in a s... more ABSTRACT Fractional calculus is used to model the viscoelastic behavior of a damping layer in a simply supported beam. The beam is analyzed by using both a continuum formulation and a finite element formulation to predict the transient response to a step loading. The construction of the finite element equations of motion and the resulting nontraditional orthogonality conditions for the damped mode shapes are presented. Also presented are the modified forms of matrix iteration required to calculate eigenvalues and mode shapes for the damped structure. The continuum formulation, also incorporating the fractional calculus model, is used to verify the finite element approach. The location of the poles (damping and frequency) are found to be in satisfactory agreement, as are the modal amplitudes for the first several modes.
The Journal of the Acoustical Society of America, 1971
The method employs the nonseparable solutions to the Helmholtz wave equation discovered by D. S. ... more The method employs the nonseparable solutions to the Helmholtz wave equation discovered by D. S. Moseley [Quart. Appl. Math. 27, 451–459 (1970)] as the elements of an expansion for membrane deflection. The boundary conditions for a membrane of any shape are then approximated by selecting the coefficients for the expansion so as to minimize the mean square error over a number of points on the boundary greater than or equal to the number of terms in the series representation. This procedure leads to an eigenvalue problem, and the minima in the eigenvalues lead to approximations of the natural frequencies. The resulting approximate solution satisfies the differential equation exactly and approximates the boundary condition. One advantage of the method is that it furnishes approximations to the frequencies of higher modes, as well as the first. When the method was applied to shapes for which the exact solutions are known, the results showed excellent agreement.
A method for estimating the damping of a vibratory system from the frequency of resonance and the... more A method for estimating the damping of a vibratory system from the frequency of resonance and the response amplitude at that resonant peak alone is reviewed and applied to the determination of the system loss or quality factors of uniform, rectangular cantilever bare titanium beams and beams with damping enhancing hard coatings. Using results from experiments with several different nonlinear coating systems vibrating in several modes and temperatures, comparisons are given for the damping measures obtained by this method with those obtained by the traditional method for determining system damping from the bandwidth (BW) of the frequency response functions (FRFs). These comparisons, made for strains of engineering interest (to strains over 1000 ppm), show that the BW method generally leads to inflated measures of system energy dissipation and that the inflation (10–70%) depends generally on the degree of nonlinearity, i.e., the extent to which the system loss factor varies with strai...
Journal of Bone and Joint Surgery, American Volume, Oct 1, 1974
The effects of altered levels of activity on the biomechanical properties of a ligament were inve... more The effects of altered levels of activity on the biomechanical properties of a ligament were investigated. After eight weeks of immobilization, anterior cruciate bone-ligament-bone preparations of wild primates tested in tension showed significant decreases in maximum failure load and energy absorbe
Mechanical properties were determined for three coating materials proposed as capable of providin... more Mechanical properties were determined for three coating materials proposed as capable of providing meaningful reductions in the vibratory amplitude of turbine blades by the internal dissipation of energy. Two were metallic materials applied by electron beam technology, one a magnetoelastic material, the other a layered material with a magnetoelastic component. The third coating was a plasma sprayed ceramic with a viscoelastic infiltrate. Properties obtained are the real and imaginary parts of a complex Young's modulus. As these are necessary for the inclusion of the influences of such coatings in preliminary design analyses, they are also the most relevant for the comparison of different materials. Values were obtained at several temperatures for strains to about 1000 ppm. A limited study of coating survivability through strains of about twice that value was also conducted.
Volume 3C: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration Control, Analysis, and Identification, Sep 17, 1995
The performance of a constrained layer damping treatment is greatly affected by its length, and t... more The performance of a constrained layer damping treatment is greatly affected by its length, and the damping effectiveness can be optimized by choosing a damping treatment length appropriate to the geometry and material properties of the viscoelastic and constraining layers. In this paper, the equilibrium equation and boundary conditions are formulated for a constraining layer on a substrate with a linearly varying strain distribution, and an analysis is developed that allows conclusions to be drawn about the optimal length of the constraining layer. Plunkett and Lee1 analyzed this problem for the special case of uniform strain in the substrate, and they showed that a loss coefficient depends only on the viscoelastic loss factor and a stiffness parameter that is a function of the material properties and thickness of the damping layers. In this paper, the uniform strain analysis is extended for the case of linearly varying substrate strain of the form ax+b, where a and b are arbitrary constants. The corresponding loss coefficient was shown to be a function of the parameters identified in the uniform strain problem, plus an additional parameter that accounts for the degree of non-uniformity of the substrate strain. It is shown that the non-uniformity of the substrate strain increases the length at which the damping treatment is optimized.
Roles for damping in vehicle design for noise suppression are identified in isolation of the vehi... more Roles for damping in vehicle design for noise suppression are identified in isolation of the vehicle from input disturbances, reducing the response to that disturbance, reducing the noise radiated due to that response, and reducing the transmission of noise. Various mechanisms for the dissipation of energy are discussed, and means of adding damping so as to reduce the dynamic response of structural elements, particularly thin sheets, are considered.
Anterior cruciate bone ligament-bone preparations of wild primates tested in tension failed at a ... more Anterior cruciate bone ligament-bone preparations of wild primates tested in tension failed at a higher load and greater elongation, and absorbed more energy, at a fast rate of deformation than at a slow rate. The major mode of specimen failure changed from a predominance of tibial avulsion fractures at the slow rate to ligament disruption at the fast rate. Failure at the two deformation rates commonly occurred by a serial mechanism involving from one to all components of the bone-ligament-bone unit to different degrees. Factors important in ligamentfailure properties included: (1) rate-dependent behaviors, (2) geometrical arrangement of collagen fibers, (3) surrounding ground-substance effects, (4) osseous insertion-site effects, and (5) the influence of non-physiological experimental loading conditions and disuse-induced changes in specimens. Because ofthe frequency and potential severity ofligament injuries, a need exists for information on the biomechanical properties of ligaments under loading conditions which occur at the time of trauma. That bone, ligaments, and other biological tissues exhibit viscoelastic behavior is now well known 2,8.11.14.15,1 719.23.25.33.52.54.56 Their load-extension behaviors are time-dependent, with the mechanical properties of the tissue dependent on the rate of loading, the rate of elongation, or both. In this regard, the change in failure properties of ligaments and bone at different rates of deformation is of particular interest to the orthopaedist in analyzing mechanisms of injury. In recent years, many studies have been performed to establish the mechanical properties and behavior of tendons and other collagenous structures 2.46,I3,172O.34.47.52,59.6o Prior studies on ligaments have provided important information 16.23.28.31.4042.43.495153.55.61; however, as yet our knowledge of their biomechanical properties is incomplete. The unique anatomical characteristics of individual ligaments, such as the twisting of the cruciates or the intricacy of the medial ligaments of the knee, impose specific structural properties which cannot be generalized to other ligaments. In addition, there appear to be important relations between macroscopic mechanical behavior and tissue microarchitecture The mechanical behavior of ligaments depends not only on the * Read in part at the Annual Meeting of the Orthopaedic Research Society, Las Vegas, Nevada, February 1, 1973. t This paper has been identified by the Aerospace Medical Research Laboratory as AMRL-TR-73-l 17. The experiments reported herein were conducted according to the “Guide for Laboratory Animal Facilities and Care” prepared by the Instituteof Laboratory Animal Resources, National Research Council. 1665 Randall Road, Yellow Springs, Ohio 45387. § Air Force Instituteof Technology, Wright-Patterson Air Force Base, Ohio 45433. 236 THE JOURNAL OF BONE AND JOINT SURGERY on April 5, 2007 www.ejbjs.org Downloaded from BIOMECHANICS OF ANTERIOR CRUCIATE LIGAMENT FAILURE 237 material properties of the fibers themselves, but also on the geometrical arrangement of collagen fibrils and fiber bundles, the proportioning of different types of fibrous constituents, and the relatively unknown effect of the surrounding ground substance 11,21,27,39,45 As will be shown in this study, the ligament insertion site and the underlying bone are additional parts of the ligament unit which must be considered in evaluating strength properties. In the analysis of ligament properties, it is often difficult to separate the effect ofthese different factors on macroscopic behavior. For these reasons, a great deal of caution is required in generalizing the mechanical properties of one ligament to other ligaments. An alternative to the approach of investigating each of the components of a ligament unit separately is afforded by using a bone-ligament-bone preparation, such as the femuranterior cruciate-tibia preparation used in this study. The mechanical properties of all components of the unit are then studied together in the same relationship that they have in the body, so that the combined interaction determines the properties of the structure, as in vivo. In the first section of this study, the effect of deformation rate (strain rate) on the ultimate failure properties of anterior cruciate bone-ligament-bone preparations was determined. In the second section we investigated the mechanism of specimen failure, in particular the failure properties of the bone and ligament components which comprise the functioning unit. Two studies were recently published on the deformation-rate sensitivity of boneligament-bone preparations 16.23 As specimens were not loaded to failure in those studies, ultimate properties were not determined. Other investigations have studied the failure properties of various ligaments, but the rate of deformation often was not controlled or recorded, and the studies often were performed under slow or quasi-static loading conditions. The slow rate…
24th Structures, Structural Dynamics and Materials Conference, May 2, 1983
ABSTRACT Fractional calculus is used to model the viscoelastic behavior of a damping layer in a s... more ABSTRACT Fractional calculus is used to model the viscoelastic behavior of a damping layer in a simply supported beam. The beam is analyzed by using both a continuum formulation and a finite element formulation to predict the transient response to a step loading. The construction of the finite element equations of motion and the resulting nontraditional orthogonality conditions for the damped mode shapes are presented. Also presented are the modified forms of matrix iteration required to calculate eigenvalues and mode shapes for the damped structure. The continuum formulation, also incorporating the fractional calculus model, is used to verify the finite element approach. The location of the poles (damping and frequency) are found to be in satisfactory agreement, as are the modal amplitudes for the first several modes.
The Journal of the Acoustical Society of America, 1971
The method employs the nonseparable solutions to the Helmholtz wave equation discovered by D. S. ... more The method employs the nonseparable solutions to the Helmholtz wave equation discovered by D. S. Moseley [Quart. Appl. Math. 27, 451–459 (1970)] as the elements of an expansion for membrane deflection. The boundary conditions for a membrane of any shape are then approximated by selecting the coefficients for the expansion so as to minimize the mean square error over a number of points on the boundary greater than or equal to the number of terms in the series representation. This procedure leads to an eigenvalue problem, and the minima in the eigenvalues lead to approximations of the natural frequencies. The resulting approximate solution satisfies the differential equation exactly and approximates the boundary condition. One advantage of the method is that it furnishes approximations to the frequencies of higher modes, as well as the first. When the method was applied to shapes for which the exact solutions are known, the results showed excellent agreement.
A method for estimating the damping of a vibratory system from the frequency of resonance and the... more A method for estimating the damping of a vibratory system from the frequency of resonance and the response amplitude at that resonant peak alone is reviewed and applied to the determination of the system loss or quality factors of uniform, rectangular cantilever bare titanium beams and beams with damping enhancing hard coatings. Using results from experiments with several different nonlinear coating systems vibrating in several modes and temperatures, comparisons are given for the damping measures obtained by this method with those obtained by the traditional method for determining system damping from the bandwidth (BW) of the frequency response functions (FRFs). These comparisons, made for strains of engineering interest (to strains over 1000 ppm), show that the BW method generally leads to inflated measures of system energy dissipation and that the inflation (10–70%) depends generally on the degree of nonlinearity, i.e., the extent to which the system loss factor varies with strai...
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