00036___c5acd3236334652171987c0fd330d852

00036___c5acd3236334652171987c0fd330d852 - playing a...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Sec. 1.5 VIBRATIONS 15 Deflection (a) Ideal plasticity ..il. Deflection (b) Linear elastic - ideal plastic material Fig. 1.4:l. Structural steel behaves pretty much like an ideal plastic material, ex- cept that when the load (measured in terms of the maximum shear stress) is smaller than the critical load (called the yield shear stress), the load- deflection curve is an inclined straight line (Hooke’s Law). Upon unloading, there is a small rebound. There are some details at the yield point that were ignored in the statement above. Other metals, such as copper, aluminum, lead, stainless steel, etc., behave in a somewhat similar, but more complex manner. Metals at a sufficiently high temperature may behave more like a fluid. Theories that deal with these features of materials are called the theories of plasticity, which are presented in Chapter 6. 1.5. VIBRATIONS We know vibrations by experience while driving a car, flying an airplane,
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: playing a musical instrument. The trees sway in the wind. A building shakes in an earthquake. Sometimes we want to know if a structure is safe in vibration. Sometimes we want to design a cushion that isolates an instrument from vibrations. A prototype of this kind of problem is shown in Fig. 1.5:1(a). A body with mass M is attached to an initially vertical massless spring, which has a spring constant k, and a damping constant c, and is “built-in” to a “ground” which moves horizontally with a displacement history s(t). Let x ( t ) denote the horizontal displacement of the mass and a dot over x or s denote a differentiation with respect to time. Then 2 is the acceleration of the body, k ( x - s) is the spring force acting on the body, and c(k - S) is the viscous damping force acting on the body. Newton’s second law requires that (1) MX + ~ ( 2 - S) + k ( ~ - S) = 0. If we let (2) y = x - s ,...
View Full Document

This note was uploaded on 01/04/2012 for the course ENG 501 taught by Professor Thomson during the Fall '05 term at MIT.

Ask a homework question - tutors are online