Mode shape — where it appears
Named by 4 essays across one field — each of them below, with the objects they name alongside it.
The period nobody chose
Every structure has a natural period, it decides the answer to every question in this field, and no drawing anywhere records it. It is a consequence of a mass picked for one reason and a stiffness picked for another — and it has already been computed, by the serviceability check.
A structure has more than one period
One mass on one spring has one period. A building with eight floors has eight, each with a shape of its own, and the second one bends the building into a curve nobody drew. They are not harmonics, they do not interfere, and each behaves as though the others were not there.
Most of the mass moves together
A sixteen-storey frame has sixteen modes, and the first one carries eighty-four per cent of the mass. That is why a hand calculation on one mode gets the base shear right to within a tenth — and why the same calculation gets the acceleration at roof level wrong by a factor of two.
The mass that helps by being late
Hang three per cent of a building's mass from a spring in its roof, tune the spring so the mass arrives a quarter-cycle behind the motion, and the peak response falls by a factor of seven. Nothing was strengthened and nothing was stiffened.
Named alongside it
The objects these essays reach for when they reach for this one.
Modal analysisModal massNatural periodBase shearCharacteristic equationDampingDeflectionDegrees of freedomDetuningEigenvalueFixed pointsFloor acceleration