Viscoelastic Spring Research Articles

The dynamic stress analysis of a viscoelastic non-cylindrical coil spring to base excitations with consideration of end effects.

This paper deals with a method for solving dynamic stress problems of a non-cylindrical viscoelastic coil spring subjected to base excitations. The analysis considers the effects of ends of the coil, and applies the three dimensional curved beam theory for obtaining the exact solution of the element of the coil. The resultant forces and the resultant moments in the vibrant coil are decided by means of the transfer matrix method for an arbitrary shape. Both the shear and the normal stresses are obtained by use of the curved beam theory as just mentioned. Numerical calculations have been carried out for two cases of a barrel spring and a hyperboloidal spring.

Sensitive force transducer system for mechanical studies of single isolated vascular smooth muscle cells.

To measure forces of the order of 0·1 μN, generated by single isolated vascular smooth muscle cells, a sensitive transducer system has been developed. A video displacement detection system and an inductive position detector were used to control the tip displacement of a glass microneedle. The bending of the microneedle was used as a measure of the force generated by a single smooth muscle cell attached to the tip. During isometric contractions the stiffness of the system was 0·7 μN μm−1. A signal limiter in one of the feedback loops made it possible to reduce the stiffness of the system to 4 nN μm−1 when an adjustable force limit was exceeded. These two conditions of the system made it possible to measure both isometric and isotonic contractions of a single muscle cell. The force limiter may also be used to protect the preparation against excessive forces developed during contraction. A mechanical model of the system and the vascular smooth muscle cell was simulated and verified. The parameters of the model for a single vascular smooth muscle cell, two viscoelastic springs in parallel, could be estimated from the measurements. The bandwidth of the system during isometric contraction was 17 Hz.

Studies of relaxation phenomena in polymers. I. The use of periodic square and triangular stress functions

AbstractIn order to evolve the methods of mechanical spectroscopy and find new methods of studying the rise of nonlinear viscoelasticity, periodic square and triangular stress functions have been used. A “new” viscoelastic function is defined, log J2 = g{log J1}, where J1 and J2 are the compliances at the time (ζ/2 + 2nζ)n→∞ for an odd, periodic, square function and an even, periodic, triangular function, respectively, with periods of 2ζ. The function shows characteristic shapes for viscoelastic spring and dashpot models. The interrelations between the complex compliance and J1 and J2 are developed; and since the sum of J1 and J2 at the time ζ/2 agrees very well with the creep compliance at the same time, J1 and J2 can be used as an interrelation between complex compliance and creep compliance. Special equipment for measuring the compliances J1 nd J2 is described.

Free damped vibrations of linear viscoelastic materials

A mechanical system consisting of an inert component, attached to a linear viscoelastic spring, is studied theoretically. Basic assumptions about the viscoelastic material areBoltzmann's superposition principle and a positive discrete relaxation spectrum. The equation of motion and its formal solution for free damped vibrations are discussed.

Wave Effects in Viscoelastic Leaf and Compression Spring Mounts

Transmissibility expressions that take wave effects into account are derived for masses mounted on highly viscoelastic leaf springs and compression springs. Approximations suitable for large ratios of mounted mass to spring mass are introduced, and equations are derived that give the approximate magnitudes of the transmissibility peaks associated with standing wave resonances and the corresponding frequencies. The validity of these approximations is verified by comparison with directly computed results. It is shown that a leaf spring results in a higher first standing wave frequency, in lower density of transmissibility peaks, and in a higher envelope of these peaks than a compression spring of the same mass, loss factor, and static stiffness.

Loss Factors of Viscoelastic Systems in Terms of Energy Concepts

The definition of loss factor in terms of energy quantities is reexamined, particularly as it applies to composite viscoelastic systems. A restatement of this definition in terms of a corresponding viscoelastic spring is used to show that this definition is extremely useful for massless (ideal viscoelastic spring) systems, but may be applied unambiguously to spring systems with a single attached mass only at resonance. Simple relations are derived which express the loss factors of series-parallel arrays of massless viscoelastic springs in terms of properties of the individual components; application of these relations to damping analyses of composite structures should result in considerable economy of effort.

Loss Factors of Viscoelastic Systems in Terms of Energy Concepts

The definition of loss factor in terms of energy quantities is re-examined, particularly as it applies to composite viscoelastic systems. A restatement of this definition in terms of a corresponding viscoelastic spring is used to show that this definition is extremely useful for massless (ideal viscoelastic spring) systems, but may be applied unambiguously to spring systems with a single attached mass only at resonance. Simple relations are presented which express the loss factors of series-parallel arrays of massless viscoelastic springs in terms of properties of the individual components. Implications of these relations in damping of composite structures are discussed. (This work was supported in part by the Aeronautical Systems Division, U. S. Air Force.)