Transient Response of Continuous Elastic Structures With Viscous Damping

1978 ◽  
Vol 45 (4) ◽  
pp. 877-882 ◽  
Author(s):  
J. Strenkowski ◽  
W. Pilkey
Keyword(s):  
Transient Response ◽  
Equations Of Motion ◽  
Theoretical Development ◽  
Elastic Cylindrical Shell ◽  
Viscous Damping ◽  
Structural Members ◽  
Displacement Boundary ◽  
Adjoint Systems ◽  
Nonhomogeneous Boundary ◽  
Complex Structural

A comprehensive theory is presented for the dynamic response of continuous structural members with viscous damping using a modal analysis. The theoretical development provides a concise set of formulas that may be used for any structural member for which the equations of motion are known. These formulas are appropriate for both self-adjoint and nonself-adjoint systems of equations, which may include viscous damping, nonhomogeneous boundary and in-span conditions, and arbitrary forcing functions. The axisymmetric transient response of a thick elastic cylindrical shell subjected to displacement boundary conditions is included to demonstrate the usefulness of the general formulation in uncoupling the response of complex structural members.

scholarly journals Transient Response of Continuous Viscoelastic Structural Members

1979 ◽  
Vol 46 (3) ◽  
pp. 685-690 ◽  
Author(s):  
J. Strenkowski ◽  
W. Pilkey
Keyword(s):  
Dynamic Response ◽  
Circular Plate ◽  
Transient Response ◽  
Equations Of Motion ◽  
Structural Members ◽  
Governing Equations ◽  
Adjoint Systems ◽  
Comprehensive Theory ◽  
Hereditary Integral ◽  
Excitation Force

In this paper a comprehensive theory is formulated for the dynamic response of structural members with a constitutive relation in the form of a hereditary integral. A modal approach is taken to uncouple the response due to an arbitrary excitation force and general nonhomogeneous surface tractions. The result of this theory is a general set of formulas which may be used for both nonself-adjoint and self-adjoint systems of governing equations of motion. This general formulation is applied to the specific cases of a Voigt-Kelvin beam and a viscoelastic circular plate.

Heteroclinic Bifurcations in Rigid Bodies Containing Internally Moving Parts and a Viscous Damper

1999 ◽  
Vol 66 (3) ◽  
pp. 720-728 ◽  
Author(s):  
G. L. Gray ◽  
D. C. Kammer ◽  
I. Dobson ◽  
A. J. Miller
Keyword(s):  
Chaotic Dynamics ◽  
Equations Of Motion ◽  
Major Axis ◽  
Rigid Bodies ◽  
Necessary Condition ◽  
Viscous Damping ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Melnikov Criterion ◽  
Analytical Criterion

Melnikov’s method is used to analytically study chaotic dynamics in an attitude transition maneuver of a torque-free rigid body in going from minor axis to major axis spin under the influence of viscous damping and nonautonomous perturbations. The equations of motion are presented, their phase space is discussed, and then they are transformed into a form suitable for the application of Melnikov’s method. Melnikov’s method yields an analytical criterion for homoclinic chaos in the form of an inequality that gives a necessary condition for chaotic dynamics in terms of the system parameters. The criterion is evaluated for its physical significance and for its application to the design of spacecraft. In addition, the Melnikov criterion is compared with numerical simulations of the system. The dependence of the onset of chaos on quantities such as body shape and magnitude of damping are investigated. In particular, it is found that for certain ranges of viscous damping values, the rate of kinetic energy dissipation goes down when damping is increased. This has a profound effect on the criterion for chaos.

A NEW NONLOCAL BEAM THEORY WITH THICKNESS STRETCHING EFFECT FOR NANOBEAMS

2013 ◽  
Vol 12 (04) ◽  
pp. 1350025 ◽  
Author(s):  
ABDELOUAHED TOUNSI ◽  
SOUMIA BENGUEDIAB ◽  
MOHAMMED SID AHMED HOUARI ◽  
ABDELWAHED SEMMAH
Keyword(s):  
Shear Deformation ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Dynamic Responses ◽  
Theoretical Development ◽  
Small Scale ◽  
Small Scale Effect ◽  
Nonlocal Beam

This paper presents a new nonlocal thickness-stretching sinusoidal shear deformation beam theory for the static and vibration of nanobeams. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and it accounts for both shear deformation and thickness stretching effects by a sinusoidal variation of all displacements through the thickness without using shear correction factor. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanobeam are derived using Hamilton's principle. The effects of nonlocal parameter, aspect ratio and the thickness stretching on the static and dynamic responses of the nanobeam are discussed. The theoretical development presented herein may serve as a reference for nonlocal theories as applied to the bending and dynamic behaviors of complex-nanobeam-system such as complex carbon nanotube system.

Transient Response of Inelastically Constrained Rigid-Body Systems

1974 ◽  
Vol 96 (3) ◽  
pp. 1041-1047 ◽  
Author(s):  
K. C. Park ◽  
K. J. Saczalski
Keyword(s):  
Structural Material ◽  
Rigid Body ◽  
Transient Response ◽  
Equations Of Motion ◽  
Coupling Mechanism ◽  
System Of Equations ◽  
Structural System ◽  
Lagrangian Multipliers ◽  
Nonlinear Geometric ◽  
Incremental Equations

An energy rate balance is employed to develop the incremental equations of motion for a shock loaded, inelastically constrained rigid-body structural system. Lagrangian multipliers provide the coupling mechanism necessary to reduce the overall system of equations to a set of modified rigid-body equations which include the nonlinear geometric and structural material effects. Kinematic material hardening and a modified yield criteria are used. Examples illustrate the technique and are compared with experimental results.

Flow-Induced Vibration of Long-Span Gates

2017 ◽  
pp. 294-386
Keyword(s):  
Vortex Shedding ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Full Scale ◽  
Degree Of Freedom ◽  
Theoretical Development ◽  
Flow Induced Vibration ◽  
Long Span ◽  
Free Discharge ◽  
Two Degree Of Freedom

In this chapter the theoretical equations for fluctuating pressures due to vertical and streamwise gate motions developed in Chapters 4 and 5 are used to derive equations of motion for long-span gates with underflow, overflow and simultaneous over- and underflow. Theoretical development of analysis methods is supported by laboratory and full-scale measurements. Specifically, this chapter considers long-span gate instabilities including one degree-of-freedom vibration of gates with underflow and free discharge, one degree-of-freedom vibration of a gate with submerged discharge and vortex shedding excitation, a two degree-of-freedom vibration of long-span gates with only underflow, and two degrees-of-freedom vibration of long-span gates with simultaneous over and underflow. A method is developed to predict pressure loading on the crest of the gate with overflow.

Particulate Enhanced Damping in Sandwich Structures

1999 ◽  
Author(s):  
Scott Maley ◽  
C. T. Sun
Keyword(s):  
Sandwich Structures ◽  
Equations Of Motion ◽  
Viscous Damping ◽  
Honeycomb Core ◽  
Moderate Amount ◽  
Damping Effect ◽  
The Core ◽  
Plate Equations ◽  
Aluminum Honeycomb ◽  
Vibration Tests

Abstract This paper investigates the damping effect of loose particulate within the core of sandwich structures. Beam specimens fabricated from aluminum honeycomb core and IM7 carbon fiber face sheets with various amounts of loose particulate are experimentally examined. Both free vibration and forced vibration tests are performed. It is shown that a moderate amount of particulate can cause a large increase in damping. The effect of varying amounts of particulate is also investigated. Plate equations of motion with damping and inertia terms are derived to model the beam and compare with experimental results. Effective mass and effective viscous damping are generated by matching the theoretical model to the experimental data.

scholarly journals Transient Response of Three-Layered Rings

1977 ◽  
Vol 44 (2) ◽  
pp. 299-304 ◽  
Author(s):  
M. J. Sagartz
Keyword(s):  
Transient Response ◽  
Theoretical Calculations ◽  
Equations Of Motion ◽  
Radial Strain ◽  
Middle Layer ◽  
Computational Technique ◽  
Linear Elastic ◽  
Time Histories ◽  
Measured Strain ◽  
Low Modulus

Hamilton’s principle is used to derive equations of motion for a linear elastic three-layered ring. The theory includes the effects of shear deformation and rotatory inertia in each layer and radial strain effects in the middle layer. A convenient computational technique is developed for transient response evaluation. A companion experimental study was conducted using two different rings. Both rings had aluminum inner and outer layers, but each had a different low-modulus middle layer. Radial impulse loads distributed as a cosine over half the ring circumference, were applied to the outer ring surface, and the transient response was monitored with strain gages mounted on the aluminum layers. Measured strain-time histories were compared with theoretical calculations, and good agreement was obtained.

Transient response of cracked nonhomogeneous substrate with piezoelectric coating by dislocation method

2018 ◽  
Vol 23 (12) ◽  
pp. 1525-1536 ◽  
Author(s):  
H Ershad ◽  
R Bagheri ◽  
M Noroozi
Keyword(s):  
Transient Response ◽  
Mass Density ◽  
Singular Integral Equations ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Multiple Cracks ◽  
Viscous Damping ◽  
Gradual Change ◽  
Dynamic Stress Intensity Factors ◽  
Orthotropic Strip

The transient response of a functionally graded material (FGM) orthotropic strip with a piezoelectric coating weakened by multiple cracks is investigated. The system is subjected to out-of-plane mechanical and in-plane electrical loading. The properties of the nonhomogeneous substrate are assumed to vary exponentially along the thickness and the energy dissipation is modeled by viscous damping. In this study, the rate of the gradual change of the shear moduli, mass density, and damping constant are assumed to be same. At first, the transient response of a Volterra-type dislocation in an FGM orthotropic strip is obtained analytically. Imposing a distributed dislocation density on the crack surface and using the Fourier and Laplace integral transforms, the problem is reduced to a system of singular integral equations for a substrate weakened by multiple cracks in the form of Cauchy singularity; which are solved numerically to obtain the dynamic stress intensity factors at the crack tips. Finally, the effects of the geometrical parameters, material properties, viscous damping and cracks arrangement on the dynamic fracture behavior of the interacting cracks are studied.

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