Spring mass dashpot system pdf

The simplest springdamper system can be modeled as follows. Using the same steps used to arrive at the solution for the springmass system, the solution for the springmassdamper system can be written as. The massspringdamper model consists of discrete mass nodes distributed throughout an. Mass enters the system dynamics through the fundamental. Locate the various springs and masses for the massspringdashpot experimental system. The example in this section is about ideal case of single spring and single mass system and it is assumed that there is no friction, no damping i. The basic vibration model of a simple oscillatory system consists of a mass, a massless spring, and a damper. Returning to the horizontal springmass system and adding a damper to it, as shown in fig. In this paper, we consider an initialboundary value problem for a homogeneous string or wave equation. Suppose that the mass is set in motion with x0 2m and x0 7ms. A dashpot is a common component in a door closer to prevent it from slamming shut. Massspringdamper systems the theory the unforced massspring system the diagram shows a mass, m, suspended from a spring of natural length l and modulus of elasticity if the elastic limit of the spring is not exceeded and the mass hangs in equilibrium, the spring will extend by an amount, e, such that by hookes law the tension in the. A beammass system a massspringdamper system model can be used to model a exible cantilevered beam with an a xed mass on the end, as shown below.

Impulse an impulse is a large force applied over a very short period of time. This video describes the free body diagram approach to developing the equations of motion of a springmassdamper system. The mass moment of inertia of the rod about a is i a 1 3 ml2. Suppose that the position of the bottom of the dashpot is given by yt and the position of the mass is given by xt, arranged so that x 0 when the spring is relaxed. In reality, you cannot have this kind of idea system. Peter avitabile, jeffrey hodgkins mechanical engineering department university of massachusetts lowell american society for engineering education salt lake city, utah june 2004 mass spring accelerometer lvdt fixed support. Design tools eindhoven university of technology a very simple model of the front side of a truck is a lumped springdashpotmass system. Next the equations are written in a graphical format suitable for input. Simulink tutorial introduction starting the program. Consider a simple system with a mass that is separated from a wall by a spring and a dashpot. Model model this system as a multidegreeoffreedom springmassdamper one with a rigid frictionless base. No external force is applied and the object is pulled 2 in. For example, this means that once the unit impulse response wt is calculated for the system, one only has to put in the di. An example of a system that is modeled using the basedexcited massspringdamper is a class of motion sensors sometimes called seismic sensors.

The spring has spring constant k and the dashpot characterized by damping constant b. Vibrations of a lumped parameter massspringdashpot system wherein the spring is described by a noninvertible elongationforce constitutive function. Springmass systems now consider a horizontal system in the form of masses on springs again solve via decoupling and matrix methods obtain the energy within the system. Driving through the dashpot now suppose instead that we. The simulink model uses signal connections, which define how data flows from one block to another. If a force is applied to a translational mechanical system, then it is opposed by opposing forces due to mass, elasticity and friction of the system. Suppose the massspring system is on a horizontal track and that the mass is kept o the track by a cushion of air so friction is almost zero and can be ignored.

Of primary interest for such a system is its natural frequency of vibration. On the weakly damped vibrations of a string attached to a. Pdf on the weakly damped vibrations of a string attached. Students pick up half pages of scrap paper when they come into the classroom, jot down on them what they found to be the most confusing point in the days lecture or the question they would have liked to ask. The unsprung mass wheel axle and sprung mass chassis are m2 and m3, respectively. For example, in many applications the acceleration of an object is known by some physical laws like newtons second law of motion f ma. Introduction all systems possessing mass and elasticity are capable of free vibration, or vibration that takes place in the absence of external excitation.

All these blocks may be considered to have a force as an input and displacement as an output. Pdf vibrations of a lumped parameter massspringdashpot. The data acquisition system and transducers are intentionally selected such that the majority of possible errors exist in the data drift, bias, offset, quantization, etc. Students acquire digital data using an lvdt, accelerometer and other transducers to obtain this displacement and acceleration data. In the previous lab you were given some physical parameters and asked to see how well the. The cylinder is completely filled with water and has an outlet valve to regulate the outflow.

The uniform rod of mass m is supported by a pin at a and a spring at b. Now lets add one more spring mass to make it 4 masses and 5 springs connected as shown below. On the weakly damped vibrations of a string attached to a spring mass dashpot system article pdf available in journal of vibration and control 911 november 2003 with 116 reads. These systems mainly consist of three basic elements. The right hand side encodes the input signal, an external force. Equations of motion of a springmassdamper system youtube. Spring dashpot model university of north carolina at. The mass could represent a car, with the spring and dashpot representing the cars bumper. Thus the motions of the mass 1 and mass 2 are out of phase. The mass m is a constant at velocities well below the speed of light and not to be confused with its weight w mg. The driving massspring workstation includes an ecp model 210a rectilinear control system that is connected to a pc containing the required ecp software. This document discusses the response of a secondorder system, like the massspringdashpot system shown in fig.

The mechanism of consolidation was explained by terzaghi with the help of a springdashpot model using soilspring analogy. As before, although we model a very simple system, the behavior we predict turns out to be representative of a wide range of real engineering systems. The left hand side represents the system, the springmassdashpot system. Determine the amplitude of the mass and the phase angle.

The spring mass dashpot system shown is released with velocity from position at time. Also the mass is acted on by an external force ft20cost. An example of a system that is modeled using the basedexcited mass spring damper is a class of motion sensors sometimes called seismic sensors. A cantilevered beam can be modeled as a simple translational spring with indicated sti ness. Massspring damper systems the theory the unforced mass spring system the diagram shows a mass, m, suspended from a spring of natural length l and modulus of elasticity if the elastic limit of the spring is not exceeded and the mass hangs in equilibrium, the spring will extend by an amount, e, such that by hookes law the tension in the. Investigate the possibility of practical resonance of this. Once again, we follow the standard approach to solving problems like. Translational mechanical systems move along a straight line. The rectilinear control system consists of three mass carriages, three encoders, two dashpot dampers, a control box, and a mechanical actuator.

Equivalent mass inertia elements the mass of a body is a fundamental material property and thought as the amount of matter within a body. Dashpotdriven system again we will consider x as the system response, and the position of the back end of the dashpot, y, as the input signal. One end of the string is assumed to be fixed and the other end of the string is attached to a springmassdashpot system, where the damping generated by. On the determination of the damping coefficient of non. Mathematical models of translating mechanical systems. This section provides the lecture notes for every lecture session. The diagram shows a mass, m, suspended from a spring of natural. Consider a mass suspended on a spring with the dashpot between the mass and the. It is desired that the mass drops on to the plank resulting in the system settling at a new equilibrium 0. This form of damping is simulated in the twodegreeoffreedom discrete massspringdashpot system shown in figure 1. Massspring system an overview sciencedirect topics. A mass of 30 kg is supported on a spring of stiffness 60 000 nm.

Dashpot forces opposing motion mass inertial or resistance to acceleration a mechanical system does not have to be really made up of springs, dashpots, and masses to have the properties of stiffness, damping, and inertia. Homework statement suppose that the mass in a massspringdashpot system with m 25, c 10, and k 226 is set in motion with x0 2 and x0 4. We would like to look at the response of the system using the scope. The system is subject to constraints not shown that confine its motion to the vertical direction only. It is shown that the properties of the ball model can be related to the coef. A mass spring dashpot subsystem in a falling container of mass m 1 is shown. Springmass systems with damping the equations for the springmass model, developed in the previous module free response. With relatively small tip motion, the beammass approximates a massspring system reasonably well. In practice, an example of an impulse would be a hammer striking a surface. A spring applies force to close the door, which the dashpot offsets by forcing fluid to flow through an orifice, often adjustable, between reservoirs, which slows the motion of the door. The horizontal vibrations of a singlestory building can be conveniently modeled as a single degree of freedom system. If b is given a small sideward displacement and released, determine the natural period of vibration. Autoscale the plot so that you can see the response the autoscale button looks like a pair of binoculars. Objective and constraints simulate this mechanical system ms with equivalent electrical components i.

Numerical evaluation of displacement and acceleration for a mass, spring, dashpot system dr. Now lets summarize the governing equation for each of the mass and create the differential equation for each of the mass spring and combine them into a system matrix. Design spring mass damping system in simulink part 1 duration. Me451 s07 transfer function massspringdamper system. Disconnect the damper by unhooking the damper rod from the mass. A mass, spring, and damper system is depicted in fig.

Some lecture sessions also have supplementary files called muddy card responses. Another common misconception is that the model shown in figure 1. The spring and damper elements are in mechanical parallel and support the seismic mass within the case. Some other investigators in the view of contact mechanics, introduced a few more accurate and sophisticated contact relations 6, 7. The mass m 2, linear spring of undeformed length l 0 and spring constant k, and the linear dashpot of dashpot constant c of the internal subsystem are also shown.