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.

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.

Nonlinear Dynamic Response of Piezoelectric Cylindrical Shell with Delamination under Hygrothermal Conditions

2012 ◽  
Vol 204-208 ◽  
pp. 4698-4701
Author(s):  
Jin Hua Yang ◽  
De Liang Chen
Keyword(s):  
Cylindrical Shell ◽  
Finite Difference Method ◽  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Transverse Motion ◽  
Governing Equations ◽  
Nonlinear Dynamic Response ◽  
The Finite Difference Method ◽  
Delamination Length

Abstract. On the basis of the nonlinear plate-shell and piezoelectric theory, the governing equations of motion for axisymmetrical piezoelectric delaminated cylindrical shell under hygrothermal conditions were derived. The governing equation of transverse motion was modified by contact force and thus the penetration between two delaminated layers could be avoided. The whole problem was resolved by using the finite difference method. In calculation examples, the effects of delamination length, depth and amplitude of load on the nonlinear dynamic response of the axisymmetrical piezoelectric delaminated shell under hygrothermal conditions were discussed in detail.

Intrinsic Finite Element Modeling of Nonlinear Dynamic Response in Helical Springs

2012 ◽  
Vol 7 (3) ◽  
Author(s):  
Michael J. Leamy
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Complex Dynamics ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Intrinsic Curvature ◽  
Nonlinear Dynamic Response ◽  
Helical Springs ◽  
Secondary Resonances ◽  
Element Approach

This paper presents an efficient intrinsic finite element approach for modeling and analyzing the forced dynamic response of helical springs. The finite element treatment employs intrinsic curvature (and strain) interpolation and vice rotation (and displacement) interpolation and, thus, can accurately and efficiently represent initially curved and twisted beams with a sparse number of elements. The governing equations of motion contain nonlinearities necessary for large curvatures. In addition, a constitutive model is developed, which captures coupling due to nonzero initial curvature and strain. The method is employed to efficiently study dynamically-loaded helical springs. Convergence studies demonstrate that a sparse number of elements accurately capture spring dynamic response, with more elements required to resolve higher frequency content, as expected. Presented results also document rich, amplitude-dependent frequency response. In particular, moderate loading amplitudes lead to the presence of secondary resonances (not captured by linearized models), while large loading amplitudes lead to complex dynamics and transverse buckling.

Intrinsic Finite Element Modeling of Nonlinear Dynamic Response in Helical Springs

2010 ◽  
Author(s):  
Michael J. Leamy
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Intrinsic Curvature ◽  
Amplitude Response ◽  
Nonlinear Dynamic Response ◽  
Helical Springs ◽  
Secondary Resonances ◽  
Element Approach

This paper presents an efficient intrinsic finite element approach for modeling and analyzing the forced dynamic response of helical springs. The finite element treatment employs intrinsic curvature (and strain) interpolation vice rotation (and displacement) interpolation, and thus can accurately and efficiently represent initially curved and twisted beams with a sparse number of elements. The governing equations of motion contain nonlinearities necessary for large curvatures. In addition, a constitutive model is developed which captures coupling due to non-zero initial curvature and strain. The method is employed to efficiently study dynamically-loaded helical springs. Convergence studies demonstrate that a sparse number of elements accurately capture spring dynamic response, with more elements required to resolve higher frequency content, as expected. Presented results also document rich, amplitude-dependent frequency response. In particular, moderate amplitude response leads to the presence of secondary resonances not captured by linearized models.

Elastic System Moving on an Elastically Supported Beam

1984 ◽  
Vol 106 (2) ◽  
pp. 292-297 ◽  
Author(s):  
T. C. Huang ◽  
V. N. Shah
Keyword(s):  
Elastic System ◽  
Equations Of Motion ◽  
Variable Coefficients ◽  
Structural Members ◽  
Governing Equations ◽  
Linear Spring ◽  
Inertia Properties ◽  
Elastically Supported ◽  
Predictor Corrector ◽  
Unsprung Mass

The problem of a two-dimensional elastic system moving on a beam is considered. The moving elastic system or vehicle is represented by the structural members with distributed stiffness, damping, and inertia properties, and it is supported by the suspension units. Each suspension unit consists of a linear spring, a viscous damper, and an unsprung mass. The beam is supported at discrete points along its length, and/or by an elastic foundation. The deformations of the moving system and the beam are represented by their corresponding eigenfunction series. The resulting governing equations are represented by the coupled, ordinary differential equations with variable coefficients. The equations of motion for an elastic platform moving with constant velocity on a beam are derived and solved by the Hamming’s predictor-corrector method. Numerical examples are presented.

Dynamic Response of a Double Articulated Offshore Loading Structure to Noncollinear Waves and Current

1981 ◽  
Vol 103 (1) ◽  
pp. 41-47 ◽  
Author(s):  
R. K. Jain ◽  
C. L. Kirk
Keyword(s):  
Dynamic Response ◽  
Nonlinear Equations ◽  
Relative Motion ◽  
Integration Method ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Governing Equations ◽  
Steady Current ◽  
Highly Nonlinear ◽  
Lagrange’S Method

The three-dimensional dynamic response of a double articulated offshore loading structure to noncollinear waves and a steady current is studied for various waves and varying current directions. The governing equations of motion are derived by the Lagrange’s method where the wave and current forces are computed by a modified form of the Morison’s equation which takes account for the relative motion of the water particles with respect to the oscillating structure. The resulting highly nonlinear equations are solved by using a block integration method. The computed results predict complex whirling oscillations of the structure to noncollinear waves and current.

Less=Moor: A Time-Efficient Computational Tool to Assess the Behavior of Moored Ships in Waves

2017 ◽  
Author(s):  
Yijun Wang ◽  
Alex van Deyzen ◽  
Benno Beimers
Keyword(s):  
Dynamic Response ◽  
Research Effort ◽  
Equations Of Motion ◽  
Line Tension ◽  
Mooring Line ◽  
Induced Response ◽  
Wave Forces ◽  
Computational Tool ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion

In the field of port design there is a need for a reliable but time-efficient method to assess the behavior of moored ships in order to determine if further detailed analysis of the behavior is required. The response of moored ships induced by gusting wind and/or waves is dynamic. Excessive motion response may cause interruption of the (un)loading operation. High line tension may cause lines to snap, introducing dangerous situations. A (detailed) Dynamic Mooring Analysis (DMA), however, is often a time-consuming and expensive exercise, especially when responses in many different environmental conditions need to be assessed. Royal HaskoningDHV has developed a time-efficient computational tool in-house to assess the wave (sea or swell) induced dynamic response of ships moored to exposed berths. The mooring line characteristics are linearized and the equations of motion are solved in the frequency domain with both the 1st and 2nd wave forces taken into account. This tool has been termed Less=Moor. The accuracy and reliability of the computational tool has been illustrated by comparing motions and mooring line forces to results obtained with software that solves the nonlinear equations of motion in the time domain (aNySIM). The calculated response of a Floating Storage and Regasification Unit (FSRU) moored to dolphins located offshore has been presented. The results show a good comparison. The computational tool can therefore be used to indicate whether the wave induced response of ships moored at exposed berths proves to be critical. The next step is to make this tool suitable to assess the dynamic response of moored ships with large wind areas, e.g. container ships, cruise vessels, RoRo or car carriers, to gusting wind. In addition, assessment of ship responses in a complicated wave field (e.g. with reflected infra-gravity waves) also requires more research effort.

Simulation of Engine Vibration on Nonlinear Hydraulic Engine Mounts

2005 ◽  
Author(s):  
A. R. Ohadi ◽  
G. Maghsoodi
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Governing Equations ◽  
Engine Mounts ◽  
Engine Vibration ◽  
Engine Mount ◽  
Rotational Motions ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion ◽  
Four Cylinders

In this paper, vibration behavior of engine on nonlinear hydraulic engine mount including inertia track and decoupler is studied. In this regard, after introducing the nonlinear factors of this mount (i.e. inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between rubber and hydraulic engine mounts, a 6 degree of freedom four cylinders V-shaped engine under inertia and balancing masses forces and torques is considered. By solving the time domain nonlinear equations of motion of engine on three inclined mounts, translational and rotational motions of engines body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of hydraulic one in low frequency region.

Dynamics Simulation and Analysis of Transition Stage of Tilt-Rotor Aircraft

2016 ◽  
Vol 842 ◽  
pp. 251-258 ◽  
Author(s):  
Muhammad Rafi Hadytama ◽  
Rianto A. Sasongko
Keyword(s):  
Dynamic Response ◽  
Equations Of Motion ◽  
Flight Dynamics ◽  
Dynamics Simulation ◽  
Tilt Rotor ◽  
Vertical Takeoff And Landing ◽  
Improved Stability ◽  
Simulation Results ◽  
Vtol Aircraft ◽  
Vertical Takeoff

This paper presents the flight dynamics simulation and analysis of a tilt-rotor vertical takeoff and landing (VTOL) aircraft on transition phase, that is conversion from vertical or hover to horizontal or level flight and vice versa. The model of the aircraft is derived from simplified equations of motion comprising the forces and moments working on the aircraft in the airplane's longitudinal plane of motion. This study focuses on the problem of the airplane's dynamic response during conversion phase, which gives an understanding about the flight characteristics of the vehicle. The understanding about the flight dynamics characteristics is important for the control system design phase. Some simulation results are given to provide better visualization about the behaviour of the tilt-rotor. The simulation results show that both transition phases are quite stable, although an improved stability can give better manoeuver and attitude handling. Improvement on the simulation model is also required to provide more accurate and realistic dynamic response of the vehicle.

Dynamic Behavior of a Hydraulically Actuated Mechanism. Part 2: Nonlinear Character

1986 ◽  
Vol 108 (2) ◽  
pp. 250-254
Author(s):  
V. Venkatraman ◽  
R. W. Mayne
Keyword(s):  
Dynamic Response ◽  
Transient Response ◽  
Adequate Description ◽  
Linear Behavior ◽  
Transmission Angle ◽  
Dimensionless Groups ◽  
Hydraulically Actuated ◽  
Nonlinear Character ◽  
The Common ◽  
Nonlinear Nature

The first of these papers considering a hydraulically actuated mechanism presents the common oscillating cylinder arrangement and sets of equations which describe the dynamic system. It then defines dimensionless groups that characterize the actuator-mechanism and explores the quasi-linear behavior of the system. This present paper focuses on the nonlinear nature of the system. Effects of transmission angle, mechanism geometry and loading are considered as well as the range of operation in which the small perturbation behavior provides an adequate description of the dynamic response. The paper closes by identifying a new parameter which plays an important role in characterizing the dependence of the system transient response on mechanism geometry.

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